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  <siteinfo>
    <sitename>LiteratePrograms</sitename>
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  <page>
    <title>Main Page</title>
    <id>3045</id>
    <revision>
      <id>9326</id>
      <timestamp>2007-03-02T22:33:49Z</timestamp>
      <contributor>
        <username>Lar</username>
        <id>100</id>
      </contributor>
      <comment>rdr</comment>
      <text xml:space="preserve">#redirect [[LiteratePrograms:Welcome]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer</title>
    <id>2896</id>
    <revision>
      <id>8505</id>
      <timestamp>2007-01-08T15:00:58Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>#REDIRECT [[:Category:99 Bottles of Beer]]</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:99 Bottles of Beer]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Alice ML)</title>
    <id>2929</id>
    <revision>
      <id>8664</id>
      <timestamp>2007-01-24T06:18:51Z</timestamp>
      <contributor>
        <ip>76.185.186.143</ip>
      </contributor>
      <comment>add alice ml version (stripped down)</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
  
  99 bottles of beer on the wall, 99 bottles of beer.
  Take one down and pass it around, 99 bottles of beer on the wall.

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

  2 bottles of beer on the wall, 2 bottles of beer.
  Take one down and pass it around, 1 bottle of beer on the wall.

  1 bottle of beer on the wall, 1 bottle of beer.
  Take one down and pass it around, no more bottles of beer on the wall.

  No more bottles of beer on the wall, no more bottles of beer.
  Go to the store and buy some more, 99 bottles of beer on the wall.

Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.  The very last verse is also different from all the others.

== The Implementation ==

By using functions we can narrow down the 100 verses and contend with the differences.  To begin, we'll declare a kind of exception that can be thrown when an invalid parameter is supplied.  The bottles function will expect a value to be between 0 and 99.  Anything out of that range will raise an exception which has a string attached that should describe the nature of the problem.
&lt;codeblock language=aliceml&gt;
&lt;&lt;bottles.aml&gt;&gt;=
exception Bottles of string
&lt;/codeblock&gt;

Before we begin with the singing, we can use a helper function to sort out the singular or plural form of how to say &quot;n bottles of beer&quot;.
&lt;codeblock language=aliceml&gt;
&lt;&lt;bottles.aml&gt;&gt;=
fun bottle_count 0 = &quot;no more bottles of beer&quot;
  | bottle_count 1 = &quot;1 bottle of beer&quot;
  | bottle_count n = (Int.toString n ^ &quot; bottles of beer&quot;)
&lt;/codeblock&gt;

With that out of the way, we can construct the main function.  The function will be split into two special cases.  The first is the verse when the tune is seeded with the value 0.  This is the base case in that it is the very last verse that is sung.  The second part of the function will be used to sing every verse except the last one.  And just in case the function is called outside of the expected domain of 0 to 99, we raise an exception to indicate an invalid input.
&lt;codeblock language=aliceml&gt;
&lt;&lt;bottles.aml&gt;&gt;=
fun bottles 0 =
      let
         val finish = bottle_count 99
      in
         print (&quot;No more bottles of beer on the wall, no more bottles of beer.\n&quot;);
         print (&quot;Go to the store and buy some more, &quot; ^ finish ^ &quot; on the wall.\n\n&quot;)
      end
  | bottles n if (n &gt;= 1 andalso n &lt;= 99) =
      let
         val start = bottle_count n
         val finish = bottle_count (n-1)
      in
         print (start ^ &quot; on the wall, &quot; ^ start ^ &quot;.\n&quot;);
         print (&quot;Take one down and pass it around, &quot; ^ finish ^ &quot; on the wall.\n\n&quot;);
         bottles (n-1)
      end
  | bottles _ = raise Bottles &quot;You're too drunk to count!\n&quot;
&lt;/codeblock&gt;

Now that we have a function built, we can invoke that function whenever we want to sing '99 Bottles.  The function is used to create a side-effect (printing of verses) and returns nothing useful to the caller (though technically the function returns a value of type unit).  Because we only use the function for side-effects and are not interested in the return value, we can assign the results to the wildcard ''val _ ='', which effectively ignores any values returned from the function call.
&lt;codeblock language=aliceml&gt;
&lt;&lt;bottles.aml&gt;&gt;=
val _ = bottles 99
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Alice ML]]
[[Category:Programming language:Alice ML]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Erlang)</title>
    <id>3572</id>
    <revision>
      <id>14723</id>
      <timestamp>2008-09-24T14:34:01Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;maim&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14724</id>
      <timestamp>2008-09-24T14:38:56Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <comment>/* The Implementation */</comment>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;NinetyNineBottles.sh&gt;&gt;=
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;maim&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14725</id>
      <timestamp>2008-09-24T14:39:52Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;NinetyNineBottles.sh&gt;&gt;=
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14726</id>
      <timestamp>2008-09-24T14:47:39Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

We are using [http://www.erlang.org/doc/man/escript.html ''escript''] to run this program.  ''escript'' calls a 
function name ''main()'' with a list of command line arguments as the entry point.  This in turn calls the 
recursive function bottles with the number of bottles (99) that we start with on the wall. 

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

This snippet of code tells the shell script how to run this program.  For most ''Linux'' computers this line will
get the shell script to run the correct program. 

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

To run this dowload the code and make NinetyNineBottles.sh executable and run it.

&lt;codeblock language=erlang&gt;
&lt;&lt;NinetyNineBottles.sh&gt;&gt;=
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14727</id>
      <timestamp>2008-09-24T15:01:51Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <minor/>
      <comment>[[99 Bottles of Beer (erlang)]] moved to [[99 Bottles of Beer (Erlang)]]: format</comment>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

We are using [http://www.erlang.org/doc/man/escript.html ''escript''] to run this program.  ''escript'' calls a 
function name ''main()'' with a list of command line arguments as the entry point.  This in turn calls the 
recursive function bottles with the number of bottles (99) that we start with on the wall. 

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

This snippet of code tells the shell script how to run this program.  For most ''Linux'' computers this line will
get the shell script to run the correct program. 

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

To run this dowload the code and make NinetyNineBottles.sh executable and run it.

&lt;codeblock language=erlang&gt;
&lt;&lt;NinetyNineBottles.sh&gt;&gt;=
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14729</id>
      <timestamp>2008-09-24T15:03:29Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">== The Implementation ==

As normal with erlang we use recursion to solve this problem.

&lt;codeblock language=erlang&gt;
&lt;&lt;program&gt;&gt;=
bottles(2) -&gt;
    io:fwrite(&quot;Two bottles of beer on the wall,~nTwo bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~nOne bottle of beer on the wall!~n~n&quot;, []),
    bottles(1).
bottles(1) -&gt;
    io:fwrite(&quot;One bottle of beer on the wall,~nOne bottle of beer!~n&quot; ++
              &quot;Take it down,~nPass it around,~nNo more bottles of beer on the wall!~n&quot;, []),
    true;
bottles(N) when N &gt; 1 -&gt;
    io:fwrite(&quot;~p bottles of beer on the wall,~n~p bottles of beer!~n&quot; ++
              &quot;Take one down,~nPass it around,~n~p bottles of beer on the wall!~n~n&quot;, [N, N, N-1]),
    bottles(N - 1).
&lt;/codeblock&gt;

We are using [http://www.erlang.org/doc/man/escript.html ''escript''] to run this program.  ''escript'' calls a 
function name ''main()'' with a list of command line arguments as the entry point.  This in turn calls the 
recursive function bottles with the number of bottles (99) that we start with on the wall. 

&lt;codeblock language=erlang&gt;
&lt;&lt;main&gt;&gt;=
main(_) -&gt;
        bottles(99).
&lt;/codeblock&gt;

This snippet of code tells the shell script how to run this program.  For most ''Linux'' computers this line will
get the shell script to run the correct program. 

&lt;codeblock language=erlang&gt;
&lt;&lt;header&gt;&gt;=
#!/usr/bin/env escript

&lt;/codeblock&gt;

To run this dowload the code and make NinetyNineBottles.sh executable and run it.

&lt;codeblock language=erlang&gt;
&lt;&lt;NinetyNineBottles.sh&gt;&gt;=
&lt;&lt;header&gt;&gt;
&lt;&lt;program&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Erlang]]
[[Category:Programming language:Erlang]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Haskell)</title>
    <id>3619</id>
    <revision>
      <id>15000</id>
      <timestamp>2008-10-13T23:49:57Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>translated from ocaml</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a List monad to iterate over the range of numbers and collect the lines to print in a list.  Because this is Haskell, we like to modularize and separate the logic of the program from the actual I/O operations; and someone else can decide what they want to do with the resulting list lazily.

In &lt;code&gt;countdown&lt;/code&gt; function, we make use of two other auxiliary functions, &lt;code&gt;bottleCount&lt;/code&gt; and &lt;code&gt;nextAction&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.

&lt;codeblock language=haskell&gt;
&lt;&lt;countdown&gt;&gt;=
countdown :: Integer -&gt; [String]
countdown n = do i &lt;- [n,n-1..0]
                 let b    = bottleCount i
                     b1   = bottleCount (i-1)
                     next = nextAction i
                 [(b ++ &quot; on the wall, &quot; ++ b ++ &quot;.&quot;),
                  (next ++ &quot;, &quot; ++ b1 ++ &quot; on the wall.&quot;),
                  &quot;&quot;]
&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottleCount&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which is all we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottleCount&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottleCount&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use Haskell's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=haskell&gt;
&lt;&lt;bottleCount&gt;&gt;=
bottleCount 0 = &quot;No more bottles of beer&quot;
bottleCount 1 = &quot;1 bottle of beer&quot;
bottleCount n | n &gt; 0 = show n ++ &quot; bottles of beer&quot;
bottleCount _ = show n ++ &quot; bottles of beer&quot;
&lt;/codeblock&gt;

Next, we have &lt;code&gt;nextAction&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=haskell&gt;
&lt;&lt;nextAction&gt;&gt;=
nextAction 0 = &quot;Go to the store, buy some more&quot;
nextAction _ = &quot;Take one down, pass it around&quot;
&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottleCount&lt;/code&gt;, &lt;code&gt;nextAction&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottleCount&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
bottles :: Integer -&gt; [String]
bottles n | n &gt; 0     = countdown n
          | otherwise = error &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
  where &lt;&lt;countdown&gt;&gt;
        &lt;&lt;bottleCount&gt;&gt;
        &lt;&lt;nextAction&gt;&gt;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers. We run putStrLn on each line, which will print each string in the list returned by bottles as a line.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
main :: IO ()
main = mapM_ putStrLn (bottles 99)
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16920</id>
      <timestamp>2010-09-24T08:00:08Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">WOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOP</text>
    </revision>
    <revision>
      <id>16921</id>
      <timestamp>2010-09-24T08:00:53Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <minor/>
      <comment>[[99 Bottles of Beer (Haskell)]] moved to [[Phat]]</comment>
      <text xml:space="preserve">WOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOP</text>
    </revision>
    <revision>
      <id>16944</id>
      <timestamp>2010-09-24T20:18:17Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a List monad to iterate over the range of numbers and collect the lines to print in a list.  Because this is Haskell, we like to modularize and separate the logic of the program from the actual I/O operations; and someone else can decide what they want to do with the resulting list lazily.

In &lt;code&gt;countdown&lt;/code&gt; function, we make use of two other auxiliary functions, &lt;code&gt;bottleCount&lt;/code&gt; and &lt;code&gt;nextAction&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.

&lt;codeblock language=haskell&gt;
&lt;&lt;countdown&gt;&gt;=
countdown :: Integer -&gt; [String]
countdown n = do i &lt;- [n,n-1..0]
                 let b    = bottleCount i
                     b1   = bottleCount (i-1)
                     next = nextAction i
                 [(b ++ &quot; on the wall, &quot; ++ b ++ &quot;.&quot;),
                  (next ++ &quot;, &quot; ++ b1 ++ &quot; on the wall.&quot;),
                  &quot;&quot;]
&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottleCount&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which is all we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottleCount&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottleCount&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use Haskell's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=haskell&gt;
&lt;&lt;bottleCount&gt;&gt;=
bottleCount 0 = &quot;No more bottles of beer&quot;
bottleCount 1 = &quot;1 bottle of beer&quot;
bottleCount n | n &gt; 0 = show n ++ &quot; bottles of beer&quot;
bottleCount _ = show n ++ &quot; bottles of beer&quot;
&lt;/codeblock&gt;

Next, we have &lt;code&gt;nextAction&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=haskell&gt;
&lt;&lt;nextAction&gt;&gt;=
nextAction 0 = &quot;Go to the store, buy some more&quot;
nextAction _ = &quot;Take one down, pass it around&quot;
&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottleCount&lt;/code&gt;, &lt;code&gt;nextAction&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottleCount&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
bottles :: Integer -&gt; [String]
bottles n | n &gt; 0     = countdown n
          | otherwise = error &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
  where &lt;&lt;countdown&gt;&gt;
        &lt;&lt;bottleCount&gt;&gt;
        &lt;&lt;nextAction&gt;&gt;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers. We run putStrLn on each line, which will print each string in the list returned by bottles as a line.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
main :: IO ()
main = mapM_ putStrLn (bottles 99)
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16945</id>
      <timestamp>2010-09-24T20:19:11Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>[[Phat]] moved to [[99 Bottles of Beer (Haskell)]]: revert vandalism</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a List monad to iterate over the range of numbers and collect the lines to print in a list.  Because this is Haskell, we like to modularize and separate the logic of the program from the actual I/O operations; and someone else can decide what they want to do with the resulting list lazily.

In &lt;code&gt;countdown&lt;/code&gt; function, we make use of two other auxiliary functions, &lt;code&gt;bottleCount&lt;/code&gt; and &lt;code&gt;nextAction&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.

&lt;codeblock language=haskell&gt;
&lt;&lt;countdown&gt;&gt;=
countdown :: Integer -&gt; [String]
countdown n = do i &lt;- [n,n-1..0]
                 let b    = bottleCount i
                     b1   = bottleCount (i-1)
                     next = nextAction i
                 [(b ++ &quot; on the wall, &quot; ++ b ++ &quot;.&quot;),
                  (next ++ &quot;, &quot; ++ b1 ++ &quot; on the wall.&quot;),
                  &quot;&quot;]
&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottleCount&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which is all we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottleCount&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottleCount&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use Haskell's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=haskell&gt;
&lt;&lt;bottleCount&gt;&gt;=
bottleCount 0 = &quot;No more bottles of beer&quot;
bottleCount 1 = &quot;1 bottle of beer&quot;
bottleCount n | n &gt; 0 = show n ++ &quot; bottles of beer&quot;
bottleCount _ = show n ++ &quot; bottles of beer&quot;
&lt;/codeblock&gt;

Next, we have &lt;code&gt;nextAction&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=haskell&gt;
&lt;&lt;nextAction&gt;&gt;=
nextAction 0 = &quot;Go to the store, buy some more&quot;
nextAction _ = &quot;Take one down, pass it around&quot;
&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottleCount&lt;/code&gt;, &lt;code&gt;nextAction&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottleCount&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
bottles :: Integer -&gt; [String]
bottles n | n &gt; 0     = countdown n
          | otherwise = error &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
  where &lt;&lt;countdown&gt;&gt;
        &lt;&lt;bottleCount&gt;&gt;
        &lt;&lt;nextAction&gt;&gt;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers. We run putStrLn on each line, which will print each string in the list returned by bottles as a line.

&lt;codeblock language=haskell&gt;
&lt;&lt;beer99.hs&gt;&gt;=
main :: IO ()
main = mapM_ putStrLn (bottles 99)
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Inform 7)</title>
    <id>2974</id>
    <revision>
      <id>8806</id>
      <timestamp>2007-02-03T14:22:52Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{codedump}}
this currently shows off some features of Inform 7:
* tables
* automatic plurals
* phrase options
* new actions

but I can't seem to use the following:
* phrase precedence instead of if-then to select base case
* &quot;Rule for supplying a missing noun&quot; to default the bottle count to 99
&lt;codeblock language=&quot;inform7&quot;&gt;
&quot;99 bottles&quot; by Dave

Table 1.0 - Special Numbers
value	text
24	&quot;a two-four&quot;
12	&quot;a dozen bottles&quot;
0	&quot;no more bottles&quot;

To say inventory of (n - a number):
	if n is a value listed in the Table of Special Numbers,
		say &quot;[text entry] of beer&quot;;
	otherwise say &quot;[n] bottle[s] of beer&quot;.

To versify for (n - a number) bottles, in recursion or al capo:
	if in recursion, say &quot;[inventory of n].[line break]&quot;;
	say &quot;[inventory of n] on the wall, [inventory of n].&quot;;
	if n is zero begin;
		say &quot;go to the store to buy some more, &quot;;
	otherwise;
		say &quot;take one down and pass it around, &quot;;
		versify for n - 1 bottles, in recursion;
	end if;
	if al capo, say &quot;[inventory of n]&quot;.

caterwauling is an action applying to a number.
report caterwauling: versify for the number understood bottles, al capo.

understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing, versify for 99 bottles, al capo.

The stage is a room. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;
[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8807</id>
      <timestamp>2007-02-03T18:53:51Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>better imp</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&quot;99 bottles&quot; by Dave
&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8808</id>
      <timestamp>2007-02-03T18:55:33Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* understanding */</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify on ... with ...''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&quot;99 bottles&quot; by Dave
&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8809</id>
      <timestamp>2007-02-03T18:58:05Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* wrapping up */ fix codeblock</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify on ... with ...''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;99bottles.txt&gt;&gt;=
&quot;99 bottles&quot; by Dave
&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8810</id>
      <timestamp>2007-02-03T19:13:13Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* wrapping up */ fix codeblock</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify on ... with ...''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;99bottles.txt&gt;&gt;=
&quot;99 bottles&quot; by Dave
&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.

&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8811</id>
      <timestamp>2007-02-03T19:18:17Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* wrapping up */ fix codeblock</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify on ... with ...''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;99bottles.txt&gt;&gt;=
&quot;99 bottles&quot; by Dave

&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
    <revision>
      <id>8990</id>
      <timestamp>2007-02-10T23:56:20Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* wrapping up */ use &quot;inform7&quot; extension</comment>
      <text xml:space="preserve">By shifting phase, mid-verse to mid-verse, a typical repeat of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:

  Take one down and pass it around, 98 bottles of beer on the wall.
  
  98 bottles of beer on the wall, 98 bottles of beer.

==theory==

We implement &quot;99 bottles&quot; recursively, using the phrase precedence rules of Inform 7 (in case of ambiguity, the most specific match is chosen) to avoid any explicit alternation (if-thens) in the code.

==practice==

===all in all, you're just another bottle on the wall===

Inform 7 has a relatively sophisticated condition matching system, but it seems to only work for objects, not numeric values.  Therefore we create a '''wall''' class as a thin wrapper around the variable ('''inventory''') we use to keep track of the number of bottles.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;wall definition&gt;&gt;=
A wall is a kind of room.  A wall has a number called the inventory.
To stock (w - a wall) with (n - a number) bottles: change the inventory of w to n.
To drink from (w - a wall): decrease the inventory of w by 1.
&lt;&lt;typical verses&gt;&gt;
&lt;&lt;base case&gt;&gt;
&lt;/codeblock&gt;

===we don't need no alternation===

The typical verse translates straightforwardly.  A peculiarity of Inform is the use of the built-in '''[s]''' for simple automatic pluralization.

''Question: in which position is the recursive call for '''act on'''?''

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;typical verses&gt;&gt;=
To say beer count of (w - a wall): say &quot;[inventory of w] bottle[s] of beer&quot;.
To act on (w - a wall):
	say &quot;take one down and pass it around, &quot;;
	drink from w;
	say &quot;[beer count of w].[line break]&quot;;
	say &quot;[beer count of w] on the wall, [beer count of w].&quot;;
	act on w.
&lt;/codeblock&gt;

By defining ''empty wall'', we can add phrases to handle the base case separately.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;base case&gt;&gt;=
Definition: a wall is empty if its inventory is zero.
To say beer count of (w - an empty wall): say &quot;no more bottles of beer&quot;.
To act on (w - an empty wall): say &quot;go to the store to buy some more, &quot;.
&lt;/codeblock&gt;

''Question: how similar are Inform 7's definitions and conditions to COBOL 88-levels?

===(re)stocking===

The (slight) advantage of choosing the recursive over the iterative is that we need neither save nor pass on the initial bottle count for restocking.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;stocking&gt;&gt;=
To versify on (w - a wall) with (n - a number) bottles:
	stock w with n bottles;
	say &quot;You start to sing:[line break]&quot;;
	say &quot;'[beer count of w] on the wall, [beer count of w].&quot;;
	act on w;
	stock w with n bottles; say &quot;[beer count of w].'&quot;.
&lt;/codeblock&gt;

===understanding===

Of course, now that we've implemented this behavior, we need some way for the player to trigger it.  We define a new action, '''caterwauling''' to go along with the '''versify on ... with ...''' phrase, then retarget the built-in ''sing'' verb to trigger our behavior.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;hook up actions&gt;&gt;=
caterwauling is an action applying to a number.
understand &quot;sing [a number]&quot; as caterwauling.
understand &quot;[a number]&quot; as caterwauling.
instead of singing: change the number understood to 99; try caterwauling.
carry out caterwauling: 
	let n be the number understood;
	versify on the stage with n bottles.
&lt;/codeblock&gt;

''Exercise: this is suitable for our example, but not very good Inform 7.''
* ''text output should occur in the &quot;report&quot; phase instead of the &quot;carry out&quot; phase for an action.''
* ''normally, new code-level actions are paired with new verbs.''
''Write an alternative to this section by re-implementing the verb &quot;to sing&quot;, with &quot;check&quot;, &quot;carry out&quot; and &quot;report&quot; phases for the singing action behaving appropriately.''

==wrapping up==

Finally, we add the header boilerplate, an initial location with instructions, and a minimal test suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;99bottles.inform7&gt;&gt;=
&quot;99 bottles&quot; by Dave

&lt;&lt;wall definition&gt;&gt;
&lt;&lt;stocking&gt;&gt;
&lt;&lt;hook up actions&gt;&gt;
The stage is a wall. &quot;type 'sing' to sing '99 bottles of beer'&quot;.
test me with &quot;sing&quot;.
&lt;/codeblock&gt;

We can test this either with ''test me'' for the full 99 bottles, or ''sing 3'' (or even ''3'') for a shorter test.

&lt;pre&gt;
&gt;sing 3
You start to sing:
&quot;3 bottles of beer on the wall, 3 bottles of beer.
take one down and pass it around, 2 bottles of beer.

2 bottles of beer on the wall, 2 bottles of beer.
take one down and pass it around, 1 bottle of beer.

1 bottle of beer on the wall, 1 bottle of beer.
take one down and pass it around, no more bottles of beer.

no more bottles of beer on the wall, no more bottles of beer.
go to the store to buy some more, 3 bottles of beer.&quot;
&lt;/pre&gt;

[[Category:99 Bottles of Beer|Inform 7]]
[[Category:Programming language:Inform 7]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Java)</title>
    <id>3783</id>
    <revision>
      <id>6524</id>
      <timestamp>2006-06-29T18:57:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>First draft of ninety-nine bottles of beer in Java. Won't compile yet!</comment>
      <text xml:space="preserve">{{develop}}
&lt;codeblock language=&quot;java&quot; /&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
/**
 * 99 bottles of beer implemented in Java
 */
public class NinetyNineBottles {

   &lt;&lt;print 99 bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.go();
   }
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6525</id>
      <timestamp>2006-06-29T19:26:26Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix broken codeblock tag</comment>
      <text xml:space="preserve">{{develop}}
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
/**
 * 99 bottles of beer implemented in Java
 */
public class NinetyNineBottles {

   &lt;&lt;print 99 bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.go();
   }
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6526</id>
      <timestamp>2006-06-29T20:22:36Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Second draft. Ready for testing.</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int bottles = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles down to zero.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;
int nBottles = BOTTLES;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles = 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6527</id>
      <timestamp>2006-06-29T20:25:08Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Changed name of compile-time constant</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles = 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6528</id>
      <timestamp>2006-06-29T20:29:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added chunks to class. Not quite ready yet!</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles = 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6529</id>
      <timestamp>2006-06-29T21:58:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>correcting noweb</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles = 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6530</id>
      <timestamp>2006-06-29T22:03:21Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>should generate code now!</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles = 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6531</id>
      <timestamp>2006-06-29T22:05:56Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Corrected syntax error in chunk: generate verse</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here I'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
I don't propose to be clever and write code to convert integers to strings, so my version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   return nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; +
        (nBottles - 1) + &quot; bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

The final verse (one bottle of beer on the wall is special so we deal with that in a 
special way. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles == 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6533</id>
      <timestamp>2006-06-29T22:18:29Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Should now be correct!</comment>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
We don't propose to be clever and write code to convert integers to strings, so our version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;how may bottles are left?&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;one bottle&lt;/code&gt; we handle that with a conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how may bottles are left?&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!/n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n&quot;;
&lt;/codeblock&gt;
The final verse (one bottle of beer on the wall) is also special. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles == 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6534</id>
      <timestamp>2006-06-29T22:20:28Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
We don't propose to be clever and write code to convert integers to strings, so our version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;how may bottles are left?&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;one bottle&lt;/code&gt; we handle that with a conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how may bottles are left?&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;
The final verse (one bottle of beer on the wall) is also special. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles == 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6535</id>
      <timestamp>2006-06-29T22:20:55Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Ready for review</comment>
      <text xml:space="preserve">First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

A typical verse is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implenting this in Java, the loop index is used to provide the number in each verse.
We don't propose to be clever and write code to convert integers to strings, so our version will be:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;how may bottles are left?&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;one bottle&lt;/code&gt; we handle that with a conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how may bottles are left?&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;
The final verse (one bottle of beer on the wall) is also special. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles == 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6536</id>
      <timestamp>2006-06-29T22:33:32Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Started refactoring the explanation</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implementing this in Java (or indeed any other language) will will use iteration
to count down from 99 to 0 while using the count to provide the number in each verse.
We could be clever and convert the count from a number into a string, but in this version
we take the easier option of writing the verse with numbers like this:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

== Compile-Time Constants ==
First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

The key to this program is a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;



This is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;how may bottles are left?&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;one bottle&lt;/code&gt; we handle that with a conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how may bottles are left?&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;
The final verse (one bottle of beer on the wall) is also special. We want the verse to be:
  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
so we simply write another function for this case.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later I'll trap it and return an empty string if it occurs. My verse generation function will then be:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
/**
 * Get the next verse of the bottle song.
 * param nBottles the current number of bottles.
 */
private String getVerse(int nBottles)
{
    if (nBottles &lt;= 0) return &quot;&quot;;
    else if (nBottles == 1) return finalVerse();
    else return verseForNBottles(nBottles);
}
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by &lt;code&gt;getVerse&lt;/code&gt; and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
System.out.println(getVerse(nBottles));
&lt;/codeblock&gt;

To print the whole song, we simply call the main loop from the &lt;code&gt;printSong()&lt;/code&gt; function, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;generate verse&gt;&gt;

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer]]</text>
    </revision>
    <revision>
      <id>6537</id>
      <timestamp>2006-06-30T10:00:46Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Refactored documentation to make it more like a complete article. Code was also refactored so still needs testing.</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

When implementing this in Java (or indeed any other language) will will use iteration
to count down from 99 to 0 while using the count to provide the number in each verse.
We could be clever and convert the count from a number into a string, but in this version
we take the easier option of writing the verse with numbers like this:
 99 bottles of beer on the wall,
 99 bottles of beer!
    Take one down,
    Pass it around,
 98 bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses. 

== The Implementation ==

The implementation of the solution in any [[http://en.wikipedia.org/wiki/Imperative_programming imperative programming]] language will require the use of at each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

  
=== Dealing with the Special Cases: Branching ===

==== The Final Verse =====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse =====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;


==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6538</id>
      <timestamp>2006-06-30T10:02:10Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Program Requirements */</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [[http://en.wikipedia.org/wiki/Imperative_programming imperative programming]] language will require the use of at each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

  
=== Dealing with the Special Cases: Branching ===

==== The Final Verse =====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse =====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;


==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6539</id>
      <timestamp>2006-06-30T10:12:30Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Strill refactoring to documentation</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

  
=== Dealing with the Special Cases: Branching ===

==== The Final Verse =====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse =====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;


==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6540</id>
      <timestamp>2006-06-30T10:13:31Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Final Verse = */</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

  
=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse =====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;


==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6541</id>
      <timestamp>2006-06-30T10:13:48Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Penultimate Verse = */</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

  
=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6542</id>
      <timestamp>2006-06-30T10:17:29Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added validation to verseForNBottles(int nBottles)</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This shouldn't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later (defensive programming), I'll ensure that a verse is generate only if &lt;code&gt;nBottles &gt; 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate verse&gt;&gt;=
if (nBottles &gt; 0) 
{
    &lt;&lt;choose verse&gt;&gt;
}
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6543</id>
      <timestamp>2006-06-30T10:20:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Defined validation</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;generate verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6544</id>
      <timestamp>2006-06-30T10:23:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Correction to code</comment>
      <text xml:space="preserve">{{develop}}
== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Functions ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing the a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6545</id>
      <timestamp>2006-06-30T10:26:39Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Literate program released</comment>
      <text xml:space="preserve">== The Program Requirements ==

A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6546</id>
      <timestamp>2006-06-30T10:28:33Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Removed top heading so that requirements opens the article</comment>
      <text xml:space="preserve">A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6547</id>
      <timestamp>2006-06-30T10:37:55Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added a concluding paragraph mentioning extensions and a similar song</comment>
      <text xml:space="preserve">A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above is to replace the integer numbers by a string. This
will require a quite sophisticated algorithm to convert integers to text and is probably
worthy of another literate programming article in its own right.

A similar song popular in Kindergarten is ''10 green bottles''[http://www.kididdles.com/mouseum/t050.html] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6548</id>
      <timestamp>2006-06-30T10:40:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Suggested Extensions and Similar Problems */</comment>
      <text xml:space="preserve">A typical verse of the ''99 bottles of beer'' song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above is to replace the integer numbers by a string. This
requires quite a sophisticated algorithm and is probably
worthy of another literate programming article in its own right.

A similar song popular in Kindergarten is ''10 green bottles''[http://www.kididdles.com/mouseum/t050.html] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6549</id>
      <timestamp>2006-06-30T10:57:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added links to wikipedia and created a blank for &quot;integer to string&quot;</comment>
      <text xml:space="preserve">A typical verse of the [[Wikipedia|99 bottles of beer]] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [[Wikipedia|99 bottles of beer]] article gives several variations of the song. A similar song popular in the UK is [[Wikipedia|10 green bottles]] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6550</id>
      <timestamp>2006-06-30T10:57:53Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>punctuation</comment>
      <text xml:space="preserve">A typical verse of the [[Wikipedia|99 bottles of beer]] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [[Wikipedia|99 bottles of beer]] article gives several variations of the song. A similar song popular in the UK is [[Wikipedia|10 green bottles]] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6586</id>
      <timestamp>2006-07-01T10:27:44Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Interwiki links to Wikipedia don't seem to work here!</comment>
      <text xml:space="preserve">A typical verse of the [[Wikipedia|99 bottles of beer]] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [[http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer]] article gives several variations of the song. A similar song popular in the UK is [[http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles]] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6587</id>
      <timestamp>2006-07-01T10:28:08Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Suggested Extensions and Similar Problems */</comment>
      <text xml:space="preserve">A typical verse of the [[Wikipedia|99 bottles of beer]] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6588</id>
      <timestamp>2006-07-01T10:29:53Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Corected another interwiki link</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this effects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7181</id>
      <timestamp>2006-08-09T06:51:02Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* The Penultimate Verse */ effect &lt;&gt; affect</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accidently fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7182</id>
      <timestamp>2006-08-09T06:52:32Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Suggested Extensions and Similar Problems */</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will    use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultiate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is special because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7183</id>
      <timestamp>2006-08-09T14:52:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultimate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is a special case because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7408</id>
      <timestamp>2006-08-18T11:19:56Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added link to 99-bottles of beer web site which I heard about on a Swampcast Podcast</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take it down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultimate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is a special case because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. The [http://www.99-bottles-of-beer.net/ 99 Bottles of Beer] website gives ''995'' other programs for producing the same output as this program including this [http://www.99-bottles-of-beer.net/language-java-1162.html Java implementation].

A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7792</id>
      <timestamp>2006-10-10T20:11:31Z</timestamp>
      <contributor>
        <username>Chobbit</username>
        <id>96</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take one down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take it down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultimate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is a special case because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. The [http://www.99-bottles-of-beer.net/ 99 Bottles of Beer] website gives ''995'' other programs for producing the same output as this program including this [http://www.99-bottles-of-beer.net/language-java-1162.html Java implementation].

A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7793</id>
      <timestamp>2006-10-10T22:28:06Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Minor edit &quot;take it down&quot; to &quot;take one down&quot; in explanation of final verse</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take one down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take one down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take one down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultimate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is a special case because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. The [http://www.99-bottles-of-beer.net/ 99 Bottles of Beer] website gives ''995'' other programs for producing the same output as this program including this [http://www.99-bottles-of-beer.net/language-java-1162.html Java implementation].

A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8383</id>
      <timestamp>2007-01-01T14:57:42Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>/* Suggested Extensions and Similar Problems */ link update</comment>
      <text xml:space="preserve">A typical verse of the [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 bottles of beer] song is:
 Ninety-nine bottles of beer on the wall,
 Ninety-nine bottles of beer!
    Take one down,
    Pass it around,
 Ninety-eight bottles of beer on the wall!

The last two verses (two and one bottle of beer on the wall) are special cases:
  Two bottles of beer on the wall,
  Two bottles of beer!
      Take one down,
      Pass it around,
  One bottle of beer on the wall!

  One bottle of beer on the wall,
  One bottle of beer!
      Take it down,
      Pass it around,
  No more bottles of beer on the wall!
Note that when we get to ''one bottle of beer'' the verse changes from the plural ''bottles'' to the singular ''bottle'', and the final line ''No more bottles of beer on the wall!'' of the song is different from all the preceding verses.

== The Implementation ==

The implementation of the solution in any [http://en.wikipedia.org/wiki/Imperative_programming imperative programming] language will require the use of each of the fundamental structures from the list: 
* Sequence
* Iteration
* Branching 
Although not strictly necessary, the solution also provides an opportunity to use a fourth fundamental which is the ''subroutine'' (or ''function'').

=== Sketch of the Solution ===

* When implementing a program to print the song in Java (or indeed any other language) we will use ''iteration'' to count down from 99 to 0 while using the count to provide the number in each verse. We could be clever and convert the count from a number into a string, but in this version we take the easier option of writing the verse with numbers like this:
    99 bottles of beer on the wall,
    99 bottles of beer!
      Take one down,
      Pass it around,
    98 bottles of beer on the wall!
* We will define ''functions'' to generate the next verse based on the current ''bottles count''.
* We will use ''branching'' to cope with the special cases described above

=== Compile-Time Constants ===

First we define how many bottles we want to have. For convenience, we make this a compile-time constant so that we can later use the same program to print the ''10 bottles of beer song'', or even the ''999 bottles of beer song'' simply by changing one statement.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;how many bottles?&gt;&gt;=
private static int NUMBER_BOTTLES_OF_BEER_ON_THE_WALL = 99;
&lt;/codeblock&gt;  

=== The Algorithm: Iteration ===

The key to the program is iteration implemented in Java as a simple loop. We could use a ''for'' loop, or the new Java 5 ''foreach'' loop, but here we'll use the standard ''while'' loop. In this loop we start a count from the number of bottles of beer on the wall down to zero, printing a verse of the song each time we iterate.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;the main loop&gt;&gt;=
int nBottles = NUMBER_BOTTLES_OF_BEER_ON_THE_WALL;
while (nBottles &gt; 0) {
  &lt;&lt;print verse&gt;&gt;
  nBottles--;
}
&lt;/codeblock&gt;

=== Printing a Single Verse: Function ===

As (most of the time) the verse follows a standard pattern, it is best implemented as a function which takes the current number of bottles as an argument and returns the verse as a string.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return a verse for n bottles&gt;&gt;=
/**
 * Return verse for N bottles of beer (where N is &gt; 1)
 * @param nBottles the current number of bottles of beer on the wall.
 * @return verse appropriate for the number of bottles of beer on the wall.
 */
private String verseForNBottles(int nBottles)
{
   &lt;&lt;validate argument&gt;&gt;
   String verse = nBottles + &quot; bottles of beer on the wall,\n&quot; +
        nBottles + &quot; bottles of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot;;
   &lt;&lt;add the bottles that are left&gt;&gt;
   return verse;
}
&lt;/codeblock&gt;

=== Dealing with the Special Cases: Branching ===

==== The Final Verse ====

The final verse (one bottle of beer on the wall) breaks the pattern of the song. If we simply called &lt;code&gt;verseForNBottles(1)&lt;/code&gt; the verse returned would be:
  1 bottles of beer on the wall,
  1 bottles of beer!
      Take one down,
      Pass it around,
  0 bottles of beer on the wall!
rather than the verse required:
  1 bottle of beer on the wall,
  1 bottle of beer!
      Take one down,
      Pass it around,
  No more bottles of beer on the wall!
To avoid this we have two choices. We can add conditional code to the &lt;code&gt;verseForNBottles&lt;/code&gt; to emit a different verse when &lt;code&gt;nBottles == 1&lt;/code&gt; or we can write a special function to write the final verse. Both solutions have merit, but to help the reader and avoid adding additional potentially confusing code to the &lt;code&gt;verseForNBottles&lt;/code&gt; function, we choose the latter.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return the final verse&gt;&gt;=
/**
 * Print final verse for one bottle of beer.
 * @return the final verse (one bottle of beer on the wall).
 */
private String finalVerse()
{
   return &quot;1 bottle of beer on the wall,\n&quot; +
        &quot;1 bottle of beer!\n&quot; + 
        &quot;   Take one down,\n&quot; +
        &quot;   Pass it around,\n&quot; + 
        &quot;No more bottles of beer on the wall!\n\n&quot;;
}
&lt;/codeblock&gt;

==== The Penultimate Verse ====

If you naively code the &lt;code&gt;verseForNBottles&lt;/code&gt; function (as I did the first time I wrote it!) the song prints fine until you reach the penultimate verse:
   2 bottles of beer on the wall,
   2 bottles of beer!
     Take one down,
     Pass it around,
   1 bottles of beer on the wall!
The penultimate verse is a special case because it goes from &lt;code&gt;2 bottles&lt;/code&gt; to
&lt;code&gt;1 bottle&lt;/code&gt;. As this affects only one line of the song, we handle it with a conditional inside &lt;code&gt;verseForNBottles&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add the bottles that are left&gt;&gt;=
int bottlesLeft = nBottles - 1;
if (bottlesLeft &gt; 1)
    verse += bottlesLeft + &quot; bottles of beer on the wall!\n\n&quot;;
else
    verse += &quot;1 bottle of beer on the wall!\n\n&quot;;
&lt;/codeblock&gt;

==== Handling &quot;Corner Cases&quot; ====

Another special case is when the verse printer is called with an argument representing 0 or a negative number of bottles. This won't happen in the ''main loop'' as defined here, but to be sure that it won't become a bug later when the function &lt;code&gt;verseForNBottles(nBottles)&lt;/code&gt; is reused in an unanticipated context (defensive programming), I'll ensure that an empty string is returned if &lt;code&gt;nBottles &lt;= 0&lt;/code&gt;: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate argument&gt;&gt;=
if (nBottles &lt;= 0) return &quot;&quot;;
&lt;/codeblock&gt;

=== Printing a Verse of the Song ===

With the verse generation code abstracted into functions our verse generation algorithm becomes a simple conditional:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;choose verse&gt;&gt;=
if (nBottles &gt; 1) verse += verseForNBottles(nBottles);
else verse += finalVerse();
&lt;/codeblock&gt;

To print a verse of the song, we simply take the string returned by the conditional and print it to the console (System.out):
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print verse&gt;&gt;=
String verse = &quot;&quot;;
&lt;&lt;choose verse&gt;&gt;
System.out.println(verse);
&lt;/codeblock&gt;

=== Print the Whole Song ===

To print the whole song, we simply call the main loop inside a &lt;code&gt;printSong()&lt;/code&gt; method, like so:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print bottles song&gt;&gt;=
/**
 * Print the 99 bottles of beer song to the console.
 */
public void printSong()
{
  &lt;&lt;the main loop&gt;&gt;
}
&lt;/codeblock&gt;

== The Program ==

The program consists of the compile-time constants and functions defined in the solution and a ''main'' method that instantiates an object and calls the &lt;code&gt;printSong&lt;/code&gt; method. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;NinetyNineBottles.java&gt;&gt;=
public class NinetyNineBottles {
   
   &lt;&lt;how many bottles?&gt;&gt;

   &lt;&lt;print bottles song&gt;&gt;

   public static void main(String[] args) {
       NinetyNineBottles nnb = new NinetyNineBottles();
       nnb.printSong();
   }

   //private methods

   &lt;&lt;return a verse for n bottles&gt;&gt;
 
   &lt;&lt;return the final verse&gt;&gt;
}
&lt;/codeblock&gt;

== Suggested Extensions and Similar Problems ==

An obvious extension, hinted at above, is to [[Convert Integer to String (Java)|convert integer numbers into a string]]. 

The [http://en.wikipedia.org/wiki/99_Bottles_of_Beer 99 Bottles of Beer] article gives several variations of the song. The [http://www.99-bottles-of-beer.net/ 99 Bottles of Beer] website gives ''995'' other programs for producing the same output as this program including this [http://www.99-bottles-of-beer.net/language-java-1162.html Java implementation].

A similar song popular in the UK is [http://en.wikipedia.org/wiki/10_green_bottles 10 Green Bottles] which goes:
  Ten green bottles 
  Hanging on the wall
  Ten green bottles
  Hanging on the wall
    And if one green bottle
    Should accident'lly fall
  There'll be nine green bottles
  hanging on the wall.

The implementation of this in Java is left as an exercise for the reader.

[[Category:99 Bottles of Beer|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (OCaml)</title>
    <id>2938</id>
    <revision>
      <id>8700</id>
      <timestamp>2007-01-26T18:53:22Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <comment>Initial article entry</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a recursive function &lt;code&gt;countdown&lt;/code&gt;.

In &lt;code&gt;countdown&lt;/code&gt;, we make use of two other auxiliary functions, &lt;code&gt;bottle_count&lt;/code&gt; and &lt;code&gt;next_action&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.  If the number of beers we have on hand is zero or more, we compute these phrases, and assemble and print them via a printf statement before recursing with one less bottle.  If, however, our beer count is negative, then we have reached our base case of the recursion and silently return.

&lt;codeblock language=ocaml&gt;
&lt;&lt;countdown&gt;&gt;=
let rec countdown n = 
  if n &gt;= 0 then 
    let b = bottle_count n and b1 = bottle_count (n-1) and next = next_action n in
    Printf.printf &quot;%s on the wall, %s.\n%s, %s on the wall.\n\n&quot; b b next b1;
    countdown (n-1)
&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottle_count&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which isall we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottle_count&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottle_count&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use OCaml's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=ocaml&gt;
&lt;&lt;bottle_count&gt;&gt;=
let bottle_count = function
| 0 -&gt; &quot;No more bottles of beer&quot;
| 1 -&gt; &quot;1 bottle of beer&quot;
| n when n &gt; 0 -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;
| _ -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;
&lt;/codeblock&gt;

Next, we have &lt;code&gt;next_action&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=ocaml&gt;
&lt;&lt;next_action&gt;&gt;=
let next_action = function
| 0 -&gt; &quot;Go to the store, buy some more&quot;
| _ -&gt; &quot;Take one down, pass it around&quot;
&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottle_count&lt;/code&gt;, &lt;code&gt;next_action&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottle_count&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let bottles n = 
  &lt;&lt;bottle_count&gt;&gt;
  in
  &lt;&lt;next_action&gt;&gt;
  in
  &lt;&lt;countdown&gt;&gt;
  in
  if n &gt; 0 then countdown n
  else failwith &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
;;

&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let _ = bottles 99;;
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8701</id>
      <timestamp>2007-01-26T18:54:31Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <minor/>
      <comment>Code formatting tweak</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a recursive function &lt;code&gt;countdown&lt;/code&gt;.

In &lt;code&gt;countdown&lt;/code&gt;, we make use of two other auxiliary functions, &lt;code&gt;bottle_count&lt;/code&gt; and &lt;code&gt;next_action&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.  If the number of beers we have on hand is zero or more, we compute these phrases, and assemble and print them via a printf statement before recursing with one less bottle.  If, however, our beer count is negative, then we have reached our base case of the recursion and silently return.

&lt;codeblock language=ocaml&gt;
&lt;&lt;countdown&gt;&gt;=
let rec countdown n = 
  if n &gt;= 0 then 
    let b = bottle_count n and b1 = bottle_count (n-1) and next = next_action n in
    Printf.printf &quot;%s on the wall, %s.\n%s, %s on the wall.\n\n&quot; b b next b1;
    countdown (n-1)&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottle_count&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which isall we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottle_count&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottle_count&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use OCaml's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=ocaml&gt;
&lt;&lt;bottle_count&gt;&gt;=
let bottle_count = function
| 0 -&gt; &quot;No more bottles of beer&quot;
| 1 -&gt; &quot;1 bottle of beer&quot;
| n when n &gt; 0 -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;
| _ -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;&lt;/codeblock&gt;

Next, we have &lt;code&gt;next_action&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=ocaml&gt;
&lt;&lt;next_action&gt;&gt;=
let next_action = function
| 0 -&gt; &quot;Go to the store, buy some more&quot;
| _ -&gt; &quot;Take one down, pass it around&quot;&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottle_count&lt;/code&gt;, &lt;code&gt;next_action&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottle_count&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let bottles n = 
  &lt;&lt;bottle_count&gt;&gt;
  in
  &lt;&lt;next_action&gt;&gt;
  in
  &lt;&lt;countdown&gt;&gt;
  in
  if n &gt; 0 then countdown n
  else failwith &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
;;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let _ = bottles 99;;&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11959</id>
      <timestamp>2008-01-05T20:41:24Z</timestamp>
      <contributor>
        <ip>86.145.49.239</ip>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a recursive function &lt;code&gt;countdown&lt;/code&gt;.

In &lt;code&gt;countdown&lt;/code&gt;, we make use of two other auxiliary functions, &lt;code&gt;bottle_count&lt;/code&gt; and &lt;code&gt;next_action&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.  If the number of beers we have on hand is zero or more, we compute these phrases, and assemble and print them via a printf statement before recursing with one less bottle.  If, however, our beer count is negative, then we have reached our base case of the recursion and silently return.

&lt;codeblock language=ocaml&gt;
&lt;&lt;countdown&gt;&gt;=
let rec countdown n = 
  if n &gt;= 0 then 
    let b = bottle_count n and b1 = bottle_count (n-1) and next = next_action n in
    Printf.printf &quot;%s on the wall, %s.\n%s, %s on the wall.\n\n&quot; b b next b1;
    countdown (n-1)&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottle_count&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which is all we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottle_count&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottle_count&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use OCaml's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=ocaml&gt;
&lt;&lt;bottle_count&gt;&gt;=
let bottle_count = function
| 0 -&gt; &quot;No more bottles of beer&quot;
| 1 -&gt; &quot;1 bottle of beer&quot;
| n when n &gt; 0 -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;
| _ -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;&lt;/codeblock&gt;

Next, we have &lt;code&gt;next_action&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=ocaml&gt;
&lt;&lt;next_action&gt;&gt;=
let next_action = function
| 0 -&gt; &quot;Go to the store, buy some more&quot;
| _ -&gt; &quot;Take one down, pass it around&quot;&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottle_count&lt;/code&gt;, &lt;code&gt;next_action&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottle_count&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let bottles n = 
  &lt;&lt;bottle_count&gt;&gt;
  in
  &lt;&lt;next_action&gt;&gt;
  in
  &lt;&lt;countdown&gt;&gt;
  in
  if n &gt; 0 then countdown n
  else failwith &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
;;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let _ = bottles 99;;&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14999</id>
      <timestamp>2008-10-13T23:24:05Z</timestamp>
      <contributor>
        <ip>128.97.245.129</ip>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Here, we use a recursive function &lt;code&gt;countdown&lt;/code&gt;.

In &lt;code&gt;countdown&lt;/code&gt;, we make use of two other auxiliary functions, &lt;code&gt;bottle_count&lt;/code&gt; and &lt;code&gt;next_action&lt;/code&gt;, which will compute for us the correct phrase to sing and the correct next action to take, given the number of bottles of beer we have on hand.  If the number of beers we have on hand is zero or more, we compute these phrases, and assemble and print them via a printf statement before recursing with one less bottle.  If, however, our beer count is negative, then we have reached our base case of the recursion and silently return.

&lt;codeblock language=ocaml&gt;
&lt;&lt;countdown&gt;&gt;=
let rec countdown n = 
  if n &gt;= 0 then 
    let b = bottle_count n and b1 = bottle_count (n-1) and next = next_action n in
    Printf.printf &quot;%s on the wall, %s.\n%s, %s on the wall.\n\n&quot; b b next b1;
    countdown (n-1)&lt;/codeblock&gt;

So let us look at these helper functions.  The first function, &lt;code&gt;bottle_count&lt;/code&gt;, is fairly straight-forward, given the number of bottles of beer on hand, and returns the properly pluralized phase for the song.  The only tricky points here are the last pattern match condition.  In the first three conditions, we've covered all of the non-negative numbers of beer, which is all we would expect to encounter.  However, adding a case to handle negative numbers allows us to easily process the final verse of the song.

Note that in each verse, the end of the second line tells us how many bottles we will have after taking one down.  This works fine, so long as we have at least one bottle to take down, the first three cases of &lt;code&gt;bottle_count&lt;/code&gt; handle that properly.  But in the last verse, we no longer take down a bottle, as we have none, so instead, we head to the store to restock, back up to our original number of beers.  If we add a case that handles negative beers, then we can compute the last half of the second line of each verse in the same way, by calling &lt;code&gt;bottle_count&lt;/code&gt; with one less beer than we currently have.  And so when we are out of beers, we will call it with an argument of -1, triggering this case.  Now then, notice how this case works.  As we have thrown out the value of the argument in this case, we do not use it in the construction of the phrase.  Instead, we will use OCaml's closure properties to return a phrase using a value of n which comes from outside this function.  As you will see, this value is the original number of beers we started with.

&lt;codeblock language=ocaml&gt;
&lt;&lt;bottle_count&gt;&gt;=
let bottle_count = function
| 0 -&gt; &quot;No more bottles of beer&quot;
| 1 -&gt; &quot;1 bottle of beer&quot;
| n -&gt; (string_of_int n) ^ &quot; bottles of beer&quot;&lt;/codeblock&gt;

Next, we have &lt;code&gt;next_action&lt;/code&gt;.  This function is about as simple as it gets. If the number of beers we have on hand is zero, then we go to the store for more.  Otherwise, if we still have some left, we take it down and pass it around.

&lt;codeblock language=ocaml&gt;
&lt;&lt;next_action&gt;&gt;=
let next_action = function
| 0 -&gt; &quot;Go to the store, buy some more&quot;
| _ -&gt; &quot;Take one down, pass it around&quot;&lt;/codeblock&gt;

Finally we put it all together with the wrapper function &lt;code&gt;bottles&lt;/code&gt;.  we pass in to &lt;code&gt;bottles&lt;/code&gt; the number of bottles of beer we have to start with (sure, most folk start with 99, but we can start with 2 or 17, or 999999 if we so choose -- flexibility is a good thing).  We then locally define our helper functions &lt;code&gt;bottle_count&lt;/code&gt;, &lt;code&gt;next_action&lt;/code&gt;, and &lt;code&gt;countdown&lt;/code&gt; (note that this is where the final case of &lt;code&gt;bottle_count&lt;/code&gt; gets its value for n), and then we do a quick sanity check on the number of beers we would like to start with.  If that number is zero or less, then we raise an exception, and inform the caller that we are worried about the health of his liver.  Otherwise, if we have some beer to tork with, we begin the countdown.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let bottles n = 
  &lt;&lt;bottle_count&gt;&gt;
  in
  &lt;&lt;next_action&gt;&gt;
  in
  &lt;&lt;countdown&gt;&gt;
  in
  if n &gt; 0 then countdown n
  else failwith &quot;Not even a single bottle of beer?  You must have a drinking problem...&quot;
;;
&lt;/codeblock&gt;

Finally, we offer a sample invocation that will test our function with the traditional 99 beers.

&lt;codeblock language=ocaml&gt;
&lt;&lt;beer99.ml&gt;&gt;=
let () = bottles 99;;&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Perl)</title>
    <id>3379</id>
    <revision>
      <id>13236</id>
      <timestamp>2008-04-27T10:00:37Z</timestamp>
      <contributor>
        <ip>82.41.202.174</ip>
      </contributor>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15699</id>
      <timestamp>2008-12-28T07:47:20Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <comment>Adding an alternate version that does not duplicate print statements as much and deals with the counting much more like humans in that the flow is one single loop.</comment>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

A much more compact way would look like:

&lt;codeblock language=perl&gt;
#!/usr/bin/perl                                                                                                                                                       
use strict;
use warnings;

# how many bottles to start with
my $max = 99; 
# deal with bottle(s)
sub container { (shift == 1) ? 'bottle' : 'bottles' }

# what should we say the round is (deal with 0 =&gt; 'no')
sub count { ($_[0]) ? $_[0] : 'no' }

# print out our verses
sub verse { 
   my $round = shift; #what round are we on?

   # first verse, use sprintf's placement matching to deal with repetition
   # also were ucfirst-ing the first call to n so that 'no' picked up as it should be capitalized.
   printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, ucfirst(count($round)), count($round), container($round);

   # work out what the next part should be (the zero case)
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, count($round-1), container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, $max ;
   }
}

# the range op only runs one way so we need to reverse it to get what we want
# but other then lets start singing
for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15700</id>
      <timestamp>2008-12-28T07:54:46Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

A much more compact way would look like:

&lt;codeblock language=perl&gt;
#!/usr/bin/perl                                                                                                                                                       
use strict;
use warnings;

# how many bottles to start with
my $max = 99; 

# deal with bottle(s)
sub container { (shift == 1) ? 'bottle' : 'bottles' }

# what should we say the round is (deal with 0 =&gt; 'no')
sub count { ($_[0]) ? $_[0] : 'no' }

# print out our verses
sub verse { 
   my $round = shift; #what round are we on?

   # first verse, use sprintf's placement matching to deal with repetition
   # also were ucfirst-ing the first call to n so that 'no' picked up as it should be capitalized.
   printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, ucfirst(count($round)), count($round), container($round);

   # work out what the next part should be (the zero case)
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, count($round-1), container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, $max ;
   }
}

# the range op only runs one way so we need to reverse it to get what we want
# but other then lets start singing
for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15703</id>
      <timestamp>2008-12-28T09:17:32Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <comment>Changing my formating to be more LP in practice (use &lt;&lt;&gt;&gt;= tags) and not just in intent.</comment>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

First we set how many bottles to start with.
  &lt;codeblock language=perl&gt;
  &lt;&lt;how many bottles of beer&gt;&gt;=
  my $max = 99; 
  &lt;/codeblock&gt;

Next Lets create a function that will correctly pluralize the word bottles
based on what round we are on.
  &lt;codeblock language=perl&gt;
  &lt;&lt;function to pluralize bottles&gt;&gt;=
  sub container { (shift == 1) ? 'bottle' : 'bottles' }
  &lt;/codeblock&gt;

Along the same lines it would be handy to have a function that will allow 
us to return 'no' for the 0 round.
  &lt;codeblock language=perl&gt;
  &lt;&lt;function to return no for zero&gt;&gt;=
  sub count { ($_[0]) ? $_[0] : 'no' }
  &lt;/codeblock&gt;

With these steps out of the way we can now assemble the first part of our 
repeating verse. This is accomplished by leveraging sprintf's placement
operator to better manage duplication, while also allowing us to insert
the correct values in to the verse. We are also using ucfirst so that
when we get to the 0/no verse that the first letter is capatilized.
  &lt;codeblock language=perl&gt;
  &lt;&lt;first half of verse&gt;&gt;=
  printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, 
    ucfirst(count($round)), 
    count($round), 
    container($round);
  &lt;/codeblock&gt;

For the second half of the verse there are a few things going on, we need
to check to see if this is the 0/no verse as it is completely diffrent. The
rest of the verses just need to decrement the round by one and print. The 
round does not need to be stored as the next time thru the verse loop, the
round will already have been decremented if it needs to be.
  &lt;codeblock language=perl&gt;
  &lt;&lt;second half of verse&gt;&gt;=
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, 
        count($round-1), 
        container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, 
        $max ;
   }
  &lt;/codeblock&gt;

To tie the two verse parts together we will wrap them up in to one function. 
  &lt;codeblock language=perl&gt;
  &lt;&lt;function to print out verse&gt;&gt;=
  sub verse { 
     my $round = shift; #what round are we on?
     &lt;&lt;first half of verse&gt;&gt;
     &lt;&lt;second half of verse&gt;&gt;
  }
  &lt;/codeblock&gt;

Finally to wrap it all together we create a for loop that will itterate
along a range. Though note, in perl the range opperator only runs positively,
thus for what we need we reverse the list. Then for every instance in that 
list we pass that to the verse function as the round. And now we have our song.
  &lt;codeblock language=perl&gt;
  &lt;&lt;loop over all the rounds&gt;&gt;=
  for (reverse(0..$max)) { verse($_)} 
  &lt;/codeblock&gt;



Final code would look like:
  &lt;codeblock language=perl&gt;
  &lt;&lt;99.pl&gt;&gt;=
  #!/usr/bin/perl 
  use strict;
  use warnings;

  &lt;&lt;how many bottles of beer&gt;&gt;

  &lt;&lt;function to pluralize bottles&gt;&gt;

  &lt;&lt;function to return no for zero&gt;&gt;

  &lt;&lt;function to print out verse&gt;&gt;

  &lt;&lt;loop over all the rounds&gt;&gt;
  &lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15704</id>
      <timestamp>2008-12-28T16:13:25Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

First we set how many bottles to start with.
&lt;codeblock language=perl&gt;
&lt;&lt;how many bottles of beer&gt;&gt;=
  my $max = 99; 
&lt;/codeblock&gt;

Next Lets create a function that will correctly pluralize the word bottles
based on what round we are on.
&lt;codeblock language=perl&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;=
  sub container { (shift == 1) ? 'bottle' : 'bottles' }
&lt;/codeblock&gt;

Along the same lines it would be handy to have a function that will allow 
us to return 'no' for the 0 round.
&lt;codeblock language=perl&gt;
&lt;&lt;function to return no for zero&gt;&gt;=
  sub count { ($_[0]) ? $_[0] : 'no' }
&lt;/codeblock&gt;

With these steps out of the way we can now assemble the first part of our 
repeating verse. This is accomplished by leveraging sprintf's placement
operator to better manage duplication, while also allowing us to insert
the correct values in to the verse. We are also using ucfirst so that
when we get to the 0/no verse that the first letter is capatilized.
&lt;codeblock language=perl&gt;
&lt;&lt;first half of verse&gt;&gt;=
  printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, 
    ucfirst(count($round)), 
    count($round), 
    container($round);
&lt;/codeblock&gt;

For the second half of the verse there are a few things going on, we need
to check to see if this is the 0/no verse as it is completely diffrent. The
rest of the verses just need to decrement the round by one and print. The 
round does not need to be stored as the next time thru the verse loop, the
round will already have been decremented if it needs to be.
&lt;codeblock language=perl&gt;
&lt;&lt;second half of verse&gt;&gt;=
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, 
        count($round-1), 
        container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, 
        $max ;
   }
&lt;/codeblock&gt;

To tie the two verse parts together we will wrap them up in to one function. 
&lt;codeblock language=perl&gt;
&lt;&lt;function to print out verse&gt;&gt;=
  sub verse { 
     my $round = shift; #what round are we on?
     &lt;&lt;first half of verse&gt;&gt;
     &lt;&lt;second half of verse&gt;&gt;
  }
&lt;/codeblock&gt;

Finally to wrap it all together we create a for loop that will itterate
along a range. Though note, in perl the range opperator only runs positively,
thus for what we need we reverse the list. Then for every instance in that 
list we pass that to the verse function as the round. And now we have our song.
&lt;codeblock language=perl&gt;
&lt;&lt;loop over all the rounds&gt;&gt;=
  for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;



Final code would look like:
&lt;codeblock language=perl&gt;
&lt;&lt;99.pl&gt;&gt;=
  #!/usr/bin/perl 
  use strict;
  use warnings;

&lt;&lt;how many bottles of beer&gt;&gt;

&lt;&lt;function to pluralize bottles&gt;&gt;

&lt;&lt;function to return no for zero&gt;&gt;

&lt;&lt;function to print out verse&gt;&gt;

&lt;&lt;loop over all the rounds&gt;&gt;
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15705</id>
      <timestamp>2008-12-28T16:17:51Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

First we set how many bottles to start with.
&lt;codeblock language=perl&gt;
&lt;&lt;how many bottles of beer&gt;&gt;=
  my $max = 99; 
&lt;/codeblock&gt;

Next Lets create a function that will correctly pluralize the word bottles
based on what round we are on.
&lt;codeblock language=perl&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;=
  sub container { (shift == 1) ? 'bottle' : 'bottles' }
&lt;/codeblock&gt;

Along the same lines it would be handy to have a function that will allow 
us to return 'no' for the 0 round.
&lt;codeblock language=perl&gt;
&lt;&lt;function to return no for zero&gt;&gt;=
  sub count { ($_[0]) ? $_[0] : 'no' }
&lt;/codeblock&gt;

With these steps out of the way we can now assemble the first part of our 
repeating verse. This is accomplished by leveraging sprintf's placement
operator to better manage duplication, while also allowing us to insert
the correct values in to the verse. We are also using ucfirst so that
when we get to the 0/no verse that the first letter is capatilized.
&lt;codeblock language=perl&gt;
&lt;&lt;first half of verse&gt;&gt;=
  printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, 
    ucfirst(count($round)), 
    count($round), 
    container($round);
&lt;/codeblock&gt;

For the second half of the verse there are a few things going on, we need
to check to see if this is the 0/no verse as it is completely diffrent. The
rest of the verses just need to decrement the round by one and print. The 
round does not need to be stored as the next time thru the verse loop, the
round will already have been decremented if it needs to be.
&lt;codeblock language=perl&gt;
&lt;&lt;second half of verse&gt;&gt;=
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, 
        count($round-1), 
        container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, 
        $max ;
   }
&lt;/codeblock&gt;

To tie the two verse parts together we will wrap them up in to one function. 
&lt;codeblock language=perl&gt;
&lt;&lt;function to print out verse&gt;&gt;=
  sub verse { 
     my $round = shift; #what round are we on?
     &lt;&lt;first half of verse&gt;&gt;
     &lt;&lt;second half of verse&gt;&gt;
  }
&lt;/codeblock&gt;

Finally to wrap it all together we create a for loop that will itterate
along a range. Though note, in perl the range opperator only runs positively,
thus for what we need we reverse the list. Then for every instance in that 
list we pass that to the verse function as the round. And now we have our song.
&lt;codeblock language=perl&gt;
&lt;&lt;loop over all the rounds&gt;&gt;=
  for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;


Final code would look like:
&lt;codeblock language=perl&gt;
&lt;&lt;99.pl&gt;&gt;=
  #!/usr/bin/perl 
  use strict;
  use warnings;

&lt;&lt;how many bottles of beer&gt;&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;
&lt;&lt;function to return no for zero&gt;&gt;
&lt;&lt;function to print out verse&gt;&gt;
&lt;&lt;loop over all the rounds&gt;&gt;
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15706</id>
      <timestamp>2008-12-28T16:18:24Z</timestamp>
      <contributor>
        <username>Notbenh</username>
        <id>1757</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

First we set how many bottles to start with.
&lt;codeblock language=perl&gt;
&lt;&lt;how many bottles of beer&gt;&gt;=
  my $max = 99; 
&lt;/codeblock&gt;

Next Lets create a function that will correctly pluralize the word bottles
based on what round we are on.
&lt;codeblock language=perl&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;=
  sub container { (shift == 1) ? 'bottle' : 'bottles' }
&lt;/codeblock&gt;

Along the same lines it would be handy to have a function that will allow 
us to return 'no' for the 0 round.
&lt;codeblock language=perl&gt;
&lt;&lt;function to return no for zero&gt;&gt;=
  sub count { ($_[0]) ? $_[0] : 'no' }
&lt;/codeblock&gt;

With these steps out of the way we can now assemble the first part of our 
repeating verse. This is accomplished by leveraging sprintf's placement
operator to better manage duplication, while also allowing us to insert
the correct values in to the verse. We are also using ucfirst so that
when we get to the 0/no verse that the first letter is capatilized.
&lt;codeblock language=perl&gt;
&lt;&lt;first half of verse&gt;&gt;=
  printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, 
    ucfirst(count($round)), 
    count($round), 
    container($round);
&lt;/codeblock&gt;

For the second half of the verse there are a few things going on, we need
to check to see if this is the 0/no verse as it is completely diffrent. The
rest of the verses just need to decrement the round by one and print. The 
round does not need to be stored as the next time thru the verse loop, the
round will already have been decremented if it needs to be.
&lt;codeblock language=perl&gt;
&lt;&lt;second half of verse&gt;&gt;=
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, 
        count($round-1), 
        container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, 
        $max ;
   }
&lt;/codeblock&gt;

To tie the two verse parts together we will wrap them up in to one function. 
&lt;codeblock language=perl&gt;
&lt;&lt;function to print out verse&gt;&gt;=
  sub verse { 
     my $round = shift; #what round are we on?
     &lt;&lt;first half of verse&gt;&gt;
     &lt;&lt;second half of verse&gt;&gt;
  }
&lt;/codeblock&gt;

Finally to wrap it all together we create a for loop that will itterate
along a range. Though note, in perl the range opperator only runs positively,
thus for what we need we reverse the list. Then for every instance in that 
list we pass that to the verse function as the round. And now we have our song.
&lt;codeblock language=perl&gt;
&lt;&lt;loop over all the rounds&gt;&gt;=
  for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;


Final code would look like:
&lt;codeblock language=perl&gt;
&lt;&lt;bottles99.pl&gt;&gt;=
  #!/usr/bin/perl 
  use strict;
  use warnings;

&lt;&lt;how many bottles of beer&gt;&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;
&lt;&lt;function to return no for zero&gt;&gt;
&lt;&lt;function to print out verse&gt;&gt;
&lt;&lt;loop over all the rounds&gt;&gt;
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Introductory Examples]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16969</id>
      <timestamp>2010-12-01T05:40:16Z</timestamp>
      <contributor>
        <username>Irritate</username>
        <id>2165</id>
      </contributor>
      <minor/>
      <comment>Cleaning up the categories. 99 Bottles of Beer is a subcategory of Introductory examples.</comment>
      <text xml:space="preserve">The following is a perl program to write the lyrics to the song &quot;99 bottles of beer&quot;

The song's first verse goes:
    99 bottles of beer on the wall, 99 bottles of beer.
    Take one down, pass it around, 98 bottles of beer on the wall.

Each verse the decrements the number of bottles by one and repeats all the way to the end, or until the singing children are informed that they will be walking home if they do not stop.

From this we can see that a variable will be required to store the number of bottles left.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles of beer&gt;&gt;=
my $bottles_of_beer = 99;
&lt;/codeblock&gt;

The verse is then constructed by inserting the $bottles_of_beer variable into the correct points in the verse and printing the result.  The $bottles_of_beer variable has to be decremented after the first line to display the correct value in the second line.
&lt;codeblock language=perl&gt;
&lt;&lt;verse&gt;&gt;=
print $bottles_of_beer, &quot; bottles of beer on the wall, &quot;, $bottles_of_beer, &quot;.\n&quot;;
$bottles_of_beer = $bottles_of_beer - 1;
print &quot;Take one down, pass it around, &quot;, $bottles_of_beer, &quot; bottles of beer on the wall.\n&quot;
&lt;/codeblock&gt;

This is then wrapped up in a loop to print almost all of the required verses.
&lt;codeblock language=perl&gt;
&lt;&lt;verse loop&gt;&gt;=
while ($bottles_of_beer &gt; 2) {
  &lt;&lt;verse&gt;&gt;
}
&lt;/codeblock&gt;

The last three verses of the song are not handled in the loop because they are special cases.  Once a single bottle of beer is referred to, we have to use the singular &quot;bottle&quot; instead of &quot;bottles&quot;.
&lt;codeblock language=perl&gt;
&lt;&lt;two bottles left&gt;&gt;=
if ($bottles_of_beer == 2) {
  print &quot;2 bottles of beer on the wall, 2 bottles of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, 1 bottle of beer on the wall\n&quot;;
}
&lt;/codeblock&gt;

In this example the if statement is not strictly required because by the time the thread of execution reaches this part of the code $bottles_of_beer will be two.  It is included for completeness in case the original value of $bottles_of_beer is set to one or less.

&lt;codeblock language=perl&gt;
&lt;&lt;one bottle left&gt;&gt;=
if ($bottles_of_beer == 1) {
  print &quot;1 bottle of beer on the wall, 1 bottle of beer\n&quot;;
  $bottles_of_beer = $bottles_of_beer - 1;
  print &quot;take one down, pass it around, no bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

The final verse is quite different to the rest.
&lt;codeblock language=perl&gt;
&lt;&lt;no bottles left&gt;&gt;=
if ($bottles_of_beer == 0) {
  print &quot;No bottles of beer on the wall, no bottles of beer.\n&quot;;
  print &quot;Go to the store, buy some more, 99 bottles of beer on the wall.\n&quot;;
}
&lt;/codeblock&gt;

Restting the $bottles_of_beer variable and introducing the extra code that results in an infinte loop is left to the reader.  To conclude this article we simply need to dust some standard perl around our existing definitions to produce a working program.
&lt;codeblock language=perl&gt;
&lt;&lt;bottles.pl&gt;&gt;=
#!/usr/bin/perl -w

use strict;

&lt;&lt;bottles of beer&gt;&gt;

&lt;&lt;verse loop&gt;&gt;

&lt;&lt;two bottles left&gt;&gt;

&lt;&lt;one bottle left&gt;&gt;

&lt;&lt;no bottles left&gt;&gt;
&lt;/codeblock&gt;


=== ALTERNATE VERSION ===

First we set how many bottles to start with.
&lt;codeblock language=perl&gt;
&lt;&lt;how many bottles of beer&gt;&gt;=
  my $max = 99; 
&lt;/codeblock&gt;

Next Lets create a function that will correctly pluralize the word bottles
based on what round we are on.
&lt;codeblock language=perl&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;=
  sub container { (shift == 1) ? 'bottle' : 'bottles' }
&lt;/codeblock&gt;

Along the same lines it would be handy to have a function that will allow 
us to return 'no' for the 0 round.
&lt;codeblock language=perl&gt;
&lt;&lt;function to return no for zero&gt;&gt;=
  sub count { ($_[0]) ? $_[0] : 'no' }
&lt;/codeblock&gt;

With these steps out of the way we can now assemble the first part of our 
repeating verse. This is accomplished by leveraging sprintf's placement
operator to better manage duplication, while also allowing us to insert
the correct values in to the verse. We are also using ucfirst so that
when we get to the 0/no verse that the first letter is capatilized.
&lt;codeblock language=perl&gt;
&lt;&lt;first half of verse&gt;&gt;=
  printf qq{%1\$s %3\$s of beer on the wall, %2\$s %3\$s of beer.\n}, 
    ucfirst(count($round)), 
    count($round), 
    container($round);
&lt;/codeblock&gt;

For the second half of the verse there are a few things going on, we need
to check to see if this is the 0/no verse as it is completely diffrent. The
rest of the verses just need to decrement the round by one and print. The 
round does not need to be stored as the next time thru the verse loop, the
round will already have been decremented if it needs to be.
&lt;codeblock language=perl&gt;
&lt;&lt;second half of verse&gt;&gt;=
   if ( $round &gt; 0 ) {
      printf qq{  Take one down, pass it around, %s %s of beer on the wall.\n}, 
        count($round-1), 
        container($round-1) ;
   }
   else {
      printf qq{  Go to the store, buy some more, %d bottles of beer on the wall.\n}, 
        $max ;
   }
&lt;/codeblock&gt;

To tie the two verse parts together we will wrap them up in to one function. 
&lt;codeblock language=perl&gt;
&lt;&lt;function to print out verse&gt;&gt;=
  sub verse { 
     my $round = shift; #what round are we on?
     &lt;&lt;first half of verse&gt;&gt;
     &lt;&lt;second half of verse&gt;&gt;
  }
&lt;/codeblock&gt;

Finally to wrap it all together we create a for loop that will itterate
along a range. Though note, in perl the range opperator only runs positively,
thus for what we need we reverse the list. Then for every instance in that 
list we pass that to the verse function as the round. And now we have our song.
&lt;codeblock language=perl&gt;
&lt;&lt;loop over all the rounds&gt;&gt;=
  for (reverse(0..$max)) { verse($_)} 
&lt;/codeblock&gt;


Final code would look like:
&lt;codeblock language=perl&gt;
&lt;&lt;bottles99.pl&gt;&gt;=
  #!/usr/bin/perl 
  use strict;
  use warnings;

&lt;&lt;how many bottles of beer&gt;&gt;
&lt;&lt;function to pluralize bottles&gt;&gt;
&lt;&lt;function to return no for zero&gt;&gt;
&lt;&lt;function to print out verse&gt;&gt;
&lt;&lt;loop over all the rounds&gt;&gt;
&lt;/codeblock&gt;


[[Category:99 Bottles of Beer|Perl]]
[[Category:Programming language:Perl]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Python)</title>
    <id>3328</id>
    <revision>
      <id>12660</id>
      <timestamp>2008-03-01T22:19:48Z</timestamp>
      <contributor>
        <username>Aledubr</username>
        <id>135</id>
      </contributor>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

botle_number=99                             #The starting point
countdown=99                                #And the counter

while botle_number&gt;2:                       #Beginning of the loop
                   
    print botle_number, &quot;bottles of beer on the wall,&quot;, botle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, botle_number-1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown=countdown-1
    botle_number=countdown


if botle_number==2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!


[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12661</id>
      <timestamp>2008-03-01T22:28:44Z</timestamp>
      <contributor>
        <username>Aledubr</username>
        <id>135</id>
      </contributor>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

botle_number = 99                             #The starting point
countdown = 99                                #And the counter

while botle_number &gt; 2:                       #Beginning of the loop
                   
    print botle_number, &quot;bottles of beer on the wall,&quot;, botle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, botle_number-1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown=countdown-1
    botle_number=countdown


if botle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!


[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12662</id>
      <timestamp>2008-03-01T22:30:55Z</timestamp>
      <contributor>
        <username>Aledubr</username>
        <id>135</id>
      </contributor>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

botle_number = 99                             #The starting point
countdown = 99                                #And the counter

while botle_number &gt; 2:                       #Beginning of the loop
                   
    print botle_number, &quot;bottles of beer on the wall,&quot;, botle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, botle_number - 1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown = countdown - 1
    botle_number = countdown


if botle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!


[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14099</id>
      <timestamp>2008-07-24T14:32:11Z</timestamp>
      <contributor>
        <ip>82.123.57.125</ip>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

bottle_number = 99                            #The starting point
countdown = 99                                #And the counter

while bottle_number &gt; 2:                      #Beginning of the loop
                   
    print bottle_number, &quot;bottles of beer on the wall,&quot;, bottle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, bottle_number - 1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown = countdown - 1
    bottle_number = countdown


if bottle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!


[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15218</id>
      <timestamp>2008-10-21T19:03:57Z</timestamp>
      <contributor>
        <username>JimD</username>
        <id>1734</id>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

bottle_number = 99                            #The starting point
countdown = 99                                #And the counter

while bottle_number &gt; 2:                      #Beginning of the loop
                   
    print bottle_number, &quot;bottles of beer on the wall,&quot;, bottle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, bottle_number - 1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown = countdown - 1
    bottle_number = countdown


if bottle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!

A far more elegant approach:

&lt;codeblock language=python&gt;

verse=&quot;&quot;&quot;
%d bottles of beer on the wall. %d bottles of beer.
Take one down and pass it around,&quot;, %s bottles of beer on the wall.
&quot;&quot;&quot;

for eachBottle in range(99,1,-1):
   if eachBottle == 1:
      remainingBottles = &quot;No more&quot;
   else:
      remainingBottles = eachBottle - 1
   print verse % (eachBottle, eachBottle, remainingBottles)

lastverse = &quot;&quot;&quot;
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;

print lastverse
&lt;/codeblock&gt;

This example simply uses a template string and Python's string interpolation operator (the &quot;%&quot; operator as overloaded for strings) along with the built-in ''range()'' function.  In Python 2.5 or later the handling for the last bottle could be done using the ternary expression support that was added in that version: 

&lt;codeblock language=python&gt;
        remainingBottles = (eachBottle - 1) if eachBottle &gt; 1 else &quot;No more&quot; 
&lt;/codeblock&gt;

... or the expression could be place directly in the argument tuple of the ''print'' statement, of course.

[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15219</id>
      <timestamp>2008-10-21T19:11:02Z</timestamp>
      <contributor>
        <username>JimD</username>
        <id>1734</id>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

bottle_number = 99                            #The starting point
countdown = 99                                #And the counter

while bottle_number &gt; 2:                      #Beginning of the loop
                   
    print bottle_number, &quot;bottles of beer on the wall,&quot;, bottle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, bottle_number - 1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown = countdown - 1
    bottle_number = countdown


if bottle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!

A far more elegant approach:

&lt;codeblock language=python&gt;

verse = &quot;&quot;&quot;
%d bottles of beer on the wall. %d bottles of beer.
Take one down and pass it around,&quot;, %s bottles of beer on the wall.
&quot;&quot;&quot;

for eachBottle in range(99,1,-1):
   if eachBottle == 1:
      remainingBottles = &quot;No more&quot;
   else:
      remainingBottles = eachBottle - 1
   print verse % (eachBottle, eachBottle, remainingBottles)

lastverse = &quot;&quot;&quot;
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;

print lastverse
&lt;/codeblock&gt;

This example simply uses a template string and Python's string interpolation operator (the &quot;%&quot; operator as overloaded for strings) along with the built-in ''range()'' function.  In Python 2.5 or later the handling for the last bottle could be done using the ternary expression support that was added in that version: 

&lt;codeblock language=python&gt;
        remainingBottles = (eachBottle - 1) if eachBottle &gt; 1 else &quot;No more&quot; 
&lt;/codeblock&gt;

... or the expression could be place directly in the argument tuple of the ''print'' statement, of course.

As a matter of style one might prefer to explicitly convert the numeric expressions to strings for the &quot;%s&quot; interpolation.  As a practical matter, Python automatically does so by calling the ''.__str__()'' method of any object which is being interpolated into a &quot;%s&quot; placeholder during string interpolation.  Use of  &quot;%d&quot; and &quot;%s&quot; are almost interchangeable until one wants to use additional formatting options (such as decimal precision, zero padding, string width padding, etc). 

[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15220</id>
      <timestamp>2008-10-21T19:37:20Z</timestamp>
      <contributor>
        <username>JimD</username>
        <id>1734</id>
      </contributor>
      <comment>/* The implementation */</comment>
      <text xml:space="preserve">A typical verse of the 99 bottles of beer song is:

'' 99 bottles of beer on the wall, 99 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 98 bottles of beer on the wall.''&lt;br /&gt;

The verse is then repeated starting with the new count for the number of bottles left on the wall:

'' 98 bottles of beer on the wall, 98 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 97 bottles of beer on the wall.''&lt;br /&gt;

The last three verses (two, one and zero bottles of beer on the wall) are special cases:

'' 2 bottles of beer on the wall, 2 bottles of beer.''&lt;br /&gt;
'' Take one down and pass it around, 1 bottle of beer on the wall.''

'' 1 bottle of beer on the wall, 1 bottle of beer.''&lt;br /&gt;
'' Take one down and pass it around, no more bottles of beer on the wall.''

'' No more bottles of beer on the wall, no more bottles of beer.''&lt;br /&gt;
'' Go to the store and buy some more, 99 bottles of beer on the wall.''&lt;br /&gt;

Note that when we get to one bottle of beer the verse changes from the plural bottles to the singular bottle, and the final line No more bottles of beer on the wall! of the song is different from all the preceding verses. The very last verse is also different from all the others.  

==The implementation==

Because the song is so structured, with only the number of bottles changing in most verses, and pluralization and the next action to take changing in a few other verses, the song can easily be structured as a loop.  Perharps the easiest way of the program is the &lt;code&gt;while&lt;/code&gt; loop.

&lt;codeblock language=python&gt;

bottle_number = 99                            #The starting point
countdown = 99                                #And the counter

while bottle_number &gt; 2:                      #Beginning of the loop
                   
    print bottle_number, &quot;bottles of beer on the wall,&quot;, bottle_number, &quot;bottles of beer.&quot;
    print &quot;Take one down and pass it around,&quot;, bottle_number - 1, &quot;bottles of beer on the wall.&quot;
    print &quot; &quot;
    countdown = countdown - 1
    bottle_number = countdown


if bottle_number == 2:                        #From here on it's easier to do the rest &quot;manually&quot;

    print &quot;&quot;&quot;2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;
&lt;/codeblock&gt;

This is quite a primitive way but it works!

A far more elegant approach:

&lt;codeblock language=python&gt;

verse = &quot;&quot;&quot;
%s of beer on the wall. %s of beer.
Take one down and pass it around. %s of beer on the wall.
&quot;&quot;&quot;

def pluralize(n):
   if n &gt; 1:
      return &quot;%d bottles&quot; % n
   elif n &lt; 1:
      return &quot;No more bottles&quot;
   else:
      return &quot;1 bottle&quot;

for eachBottle in range(99, 0, -1):
   current = pluralize(eachBottle)
   print verse % (current, current, pluralize(eachBottle - 1))

lastverse = &quot;&quot;&quot;
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
&quot;&quot;&quot;

print lastverse
&lt;/codeblock&gt;

This example simply uses a template string and Python's string interpolation operator (the &quot;%&quot; operator as overloaded for strings) along with the built-in ''range()'' function.  Proper pluralization of the word &quot;bottles&quot; and the &quot;No more&quot; case is handled in it's own function.


[[Category:99 Bottles of Beer|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (Ruby)</title>
    <id>3748</id>
    <revision>
      <id>15713</id>
      <timestamp>2008-12-30T04:29:07Z</timestamp>
      <contributor>
        <username>Penguin673</username>
        <id>1759</id>
      </contributor>
      <text xml:space="preserve">99 Bottles of Beer is a very long song that goes like:

  99 bottles of beer on the wall, 99 bottles of beer.
  Take one down and pass it around, 98 bottles of beer on the wall.

  98 bottles of beer on the wall, 98 bottles of beer.
  Take one down and pass it around, 97 bottles of beer on the wall.

  97 bottles of beer on the wall, 97 bottles of beer.
  Take one down and pass it around, 96 bottles of beer on the wall.

The lyrics are repeated until the final 3 verses:

  2 bottles of beer on the wall, 2 bottles of beer.
  Take one down and pass it around, 1 bottle of beer on the wall.

  1 bottle of beer on the wall, 1 bottle of beer.
  Take one down and pass it around, no more bottles of beer on the wall.

  No more bottles of beer on the wall, no more bottles of beer.
  Go to the store and buy some more, 99 bottles of beer on the wall.

This song conforms with grammar and shifts to singular &quot;bottle&quot; instead of &quot;bottles&quot;.  This implementation thus has to reflect that.

==Final Verses==

First, let's implement the final 3 verses, because they're special, and to get a feel for ruby's print methods

===Using puts===

We could just use puts, which is the equivalent of System.out.println; it prints out a string and prints a newline.

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;end lyrics puts&gt;&gt;=
puts &quot;2 bottles of beer on the wall, 2 bottles of beer.&quot;
puts &quot;Take one down and pass it around, 1 bottles of beer on the wall.&quot;
puts &quot;&quot;
puts &quot;1 bottle of beer on the wall, 1 bottle of beer.&quot;
puts &quot;Take one down and pass it around, no more bottles of beer on the wall.&quot;
puts &quot;&quot;
puts &quot;No more bottles of beer on the wall, no more bottles of beer.&quot;
puts &quot;Go to the store and buy some more, 99 bottles of beer on the wall.&quot;
&lt;/codeblock&gt; 

===Using here documents===

Or, better yet, we could print the lyrics in a here document:

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;end lyrics here document&gt;&gt;=
puts &lt;&lt;END_LYRICS
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
END_LYRICS
&lt;/codeblock&gt;

The advantage of this is that the lyrics are unmodified; code is only around the lines.

==Lyrics Implementation==

These are the implementations of the other lyrics, that loop down from 99 to 3 bottles on the wall.

===Using downto===

Ruby is fully OOP, meaning that even numbers have methods.  And one of those methods happens to match this program's needs: downto.  It counts down from the number object that is called to the number object given (inclusive):

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;downto function call&gt;&gt;=
99.downto(3) do |number|
&lt;&lt;downto block&gt;&gt;
end
&lt;/codeblock&gt;  

Here the downto method will call the block with variable &quot;number&quot; as integers from 99 to 3, inclusive. The block will then print out the lyrics:

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;downto block&gt;&gt;=
puts &lt;&lt;LYRICS 
#{number} bottles of beer on the wall, #{number} bottles of beer.
Take one down and pass it around, #{number - 1} bottles of beer on the wall.

LYRICS
&lt;/codeblock&gt;  

Again, a here document is used.  In Ruby's here documents, #{} can evaluate an expression.

==The full program==

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;99beers.rb&gt;&gt;=
&lt;&lt;downto function call&gt;&gt;

&lt;&lt;end lyrics here document&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>15714</id>
      <timestamp>2008-12-30T04:33:49Z</timestamp>
      <contributor>
        <username>Penguin673</username>
        <id>1759</id>
      </contributor>
      <text xml:space="preserve">99 Bottles of Beer is a very long song that goes like:

  99 bottles of beer on the wall, 99 bottles of beer.
  Take one down and pass it around, 98 bottles of beer on the wall.

  98 bottles of beer on the wall, 98 bottles of beer.
  Take one down and pass it around, 97 bottles of beer on the wall.

  97 bottles of beer on the wall, 97 bottles of beer.
  Take one down and pass it around, 96 bottles of beer on the wall.

The lyrics are repeated until the final 3 verses:

  2 bottles of beer on the wall, 2 bottles of beer.
  Take one down and pass it around, 1 bottle of beer on the wall.

  1 bottle of beer on the wall, 1 bottle of beer.
  Take one down and pass it around, no more bottles of beer on the wall.

  No more bottles of beer on the wall, no more bottles of beer.
  Go to the store and buy some more, 99 bottles of beer on the wall.

This song conforms with grammar and shifts to singular &quot;bottle&quot; instead of &quot;bottles&quot;.  This implementation thus has to reflect that.

==Final Verses==

First, let's implement the final 3 verses, because they're special, and to get a feel for ruby's print methods

===Using puts===

We could just use puts, which is the equivalent of System.out.println; it prints out a string and prints a newline.

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;end lyrics puts&gt;&gt;=
puts &quot;2 bottles of beer on the wall, 2 bottles of beer.&quot;
puts &quot;Take one down and pass it around, 1 bottles of beer on the wall.&quot;
puts &quot;&quot;
puts &quot;1 bottle of beer on the wall, 1 bottle of beer.&quot;
puts &quot;Take one down and pass it around, no more bottles of beer on the wall.&quot;
puts &quot;&quot;
puts &quot;No more bottles of beer on the wall, no more bottles of beer.&quot;
puts &quot;Go to the store and buy some more, 99 bottles of beer on the wall.&quot;
&lt;/codeblock&gt; 

===Using here documents===

Or, better yet, we could print the lyrics in a here document:

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;end lyrics here document&gt;&gt;=
puts &lt;&lt;END_LYRICS
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.

1 bottle of beer on the wall, 1 bottle of beer.
Take one down and pass it around, no more bottles of beer on the wall.

No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
END_LYRICS
&lt;/codeblock&gt;

The advantage of this is that the lyrics are unmodified; code is only around the lines.

==Lyrics Implementation==

These are the implementations of the other lyrics, that loop down from 99 to 3 bottles on the wall.

===Using downto===

Ruby is fully OOP, meaning that even numbers have methods.  And one of those methods happens to match this program's needs: downto.  It counts down from the number object that is called to the number object given (inclusive):

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;downto function call&gt;&gt;=
99.downto(3) do |number|
&lt;&lt;downto block&gt;&gt;
end
&lt;/codeblock&gt;  

Here the downto method will call the block with variable &quot;number&quot; as integers from 99 to 3, inclusive. The block will then print out the lyrics:

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;downto block&gt;&gt;=
puts &lt;&lt;LYRICS 
#{number} bottles of beer on the wall, #{number} bottles of beer.
Take one down and pass it around, #{number - 1} bottles of beer on the wall.

LYRICS
&lt;/codeblock&gt;  

Again, a here document is used.  In Ruby's here documents, #{} can evaluate an expression.

==The full program==

&lt;codeblock language=&quot;ruby&quot;&gt;
&lt;&lt;99beers.rb&gt;&gt;=
&lt;&lt;downto function call&gt;&gt;

&lt;&lt;end lyrics here document&gt;&gt;
&lt;/codeblock&gt;

[[Category:99 Bottles of Beer|Ruby]]
[[Category:Programming language:Ruby]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>99 Bottles of Beer (erlang)</title>
    <id>3573</id>
    <revision>
      <id>14728</id>
      <timestamp>2008-09-24T15:01:51Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <comment>[[99 Bottles of Beer (erlang)]] moved to [[99 Bottles of Beer (Erlang)]]: format</comment>
      <text xml:space="preserve">#REDIRECT [[99 Bottles of Beer (Erlang)]]</text>
    </revision>
  </page>
  <page>
    <title>A* search (JavaScript)</title>
    <id>3184</id>
    <revision>
      <id>10701</id>
      <timestamp>2007-07-18T18:01:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created codedump</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

The priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

var grid=new Array();
var opened=new Array();

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;

	best=opencell(start, 0, start);
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();

		openadjacent(best);

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;



[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10702</id>
      <timestamp>2007-07-18T18:26:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>splitting it up, some text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;
=== Callbacks and more ===
&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;

	best=opencell(start, 0, start);
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();

		openadjacent(best);

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;



[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10703</id>
      <timestamp>2007-07-18T18:34:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>More text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;

	best=opencell(start, 0, start);
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();

		openadjacent(best);

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10704</id>
      <timestamp>2007-07-18T18:35:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>typo</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;

	best=opencell(start, 0, start);
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();

		openadjacent(best);

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10705</id>
      <timestamp>2007-07-18T18:43:31Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rearrange</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;

	best=opencell(start, 0, start);
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();

		openadjacent(best);

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10706</id>
      <timestamp>2007-07-18T19:00:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* The algorithm */ more text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

I this code, the word ''cell'' is used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utilityfunction that opens all nodes directly reachable from the ''best''.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often called to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10707</id>
      <timestamp>2007-07-18T19:02:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rm {{codedump}}, + {{develop}} - not finished, but not really a codedump anymore</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (opened) using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

I this code, the word ''cell'' is used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utilityfunction that opens all nodes directly reachable from the ''best''.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often called to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10718</id>
      <timestamp>2007-07-20T11:51:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Introduction */</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

I this code, the word ''cell'' is used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utilityfunction that opens all nodes directly reachable from the ''best''.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often called to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10719</id>
      <timestamp>2007-07-20T11:54:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* The algorithm */ typo</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

I this code, the word ''cell'' is used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often called to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;

	/* Extra cost for changing direction */
	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}

	/* Calculate total cost including estimated */
	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;

	/* Insert into &quot;opened&quot; */
	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;

	/* Update &quot;grid&quot; */
	grid[p.y][p.x]=p;

	/* Colorize */
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10720</id>
      <timestamp>2007-07-20T12:15:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* The algorithm */ describe opencell</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

I this code, the word ''cell'' is used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often called to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;
&lt;/codeblock&gt;

We optionally mark the opened positions with a color code. &lt;!-- TODO:Move this to User interface --&gt;

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10723</id>
      <timestamp>2007-07-21T15:09:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* The algorithm */</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;


== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10724</id>
      <timestamp>2007-07-21T15:10:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* The user interface */ mark node</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark node&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10725</id>
      <timestamp>2007-07-21T15:11:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>renamed chunk</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, this algorithm is used to find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10750</id>
      <timestamp>2007-07-25T11:19:25Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Introduction */ rephrase</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Implementation ==

=== Data structure ===

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

=== The algorithm ===

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

=== The user interface ===

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;


&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10751</id>
      <timestamp>2007-07-25T11:28:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rearranging some code</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be travrsed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10752</id>
      <timestamp>2007-07-25T11:29:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* The user interface */ typo</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be traversed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10754</id>
      <timestamp>2007-07-25T12:11:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Test instruction, link</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;
	this.tt=&quot;&quot;;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be traversed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;

To run this code, just save ''astar.js'' and ''astar.html'' to the same directory and open ''astar.html'' in your browser. A (possibly outdated) copy is located [http://hystad.com/astar.html here]. 


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10755</id>
      <timestamp>2007-07-25T12:15:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rm unused variable</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=new Array();
&lt;&lt;opened&gt;&gt;=
var opened=new Array();
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be traversed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=new Array();
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=new Array();

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;

To run this code, just save ''astar.js'' and ''astar.html'' to the same directory and open ''astar.html'' in your browser. A (possibly outdated) copy is located [http://hystad.com/astar.html here]. 


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>10852</id>
      <timestamp>2007-08-04T12:17:49Z</timestamp>
      <contributor>
        <username>Reinis</username>
        <id>999</id>
      </contributor>
      <comment>new Array(); is a seriously deprecated way of making arrays</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=[];
&lt;&lt;opened&gt;&gt;=
var opened=[];
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be traversed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=[];
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=[];

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;

To run this code, just save ''astar.js'' and ''astar.html'' to the same directory and open ''astar.html'' in your browser. A (possibly outdated) copy is located [http://hystad.com/astar.html here]. 


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
    <revision>
      <id>11799</id>
      <timestamp>2007-12-08T16:20:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>rm {{develop}}</comment>
      <text xml:space="preserve">
== Introduction ==

This article describes an implementation of the [http://en.wikipedia.org/wiki/A%2A_search_algorithm A* search algorithm] in JavaScript.

Given a graph with a start- and a target-node, the algorithm will, if possible, find a best path between those. This is the short version of how it works:
# The start node (S) has a cost (g()) of 0
# Look up each node connected to the start node and:
#* Store a reference to the start node 
#* Increase the cost (g()) based on the weight of the edge followed.
#* Calculate an estimated cost (h()) to reach the target node
#* Store the node in a priority queue (''opened'') using f()=g()+h() as the priority value.
# Repeat from 2, using the node with lowest f() as start node, until the target node is reached

When the target node is reached, the back-references can be followed to create a route.

This algorithm is normally used on graphs organized as a grid, where the nodes are implicitly connected to all neighbour cells.

== Data structure ==

Each node is represented by a ''pos'' object which is created like this:

&lt;codeblock language=js&gt;
&lt;&lt;pos&gt;&gt;=
function pos(x, y) {
	this.x=x; this.y=y;
	this.cost=0;
	this.totalcost=0;
	this.blocked=false;
	this.closed=false;
	this.prev=null;

	this.str=function() {
		return this.x+&quot;,&quot;+this.y;
	}
	this.equal=function(p) {return this.x==p.x &amp;&amp; this.y==p.y;}
}
&lt;/codeblock&gt;

The grid itself is stored in an ''Array'' of ''Array''s containing nodes (''pos''-objects).

The ''opened'' priority queue used is a sorted Array. While this is probably not an optimal solution when the number of nodes gets big, it is good enough in this case and very easy to implement. A [http://en.wikipedia.org/wiki/Binary_heap binary heap] might be a better choice in many situations.

&lt;codeblock language=js&gt;
&lt;&lt;grid&gt;&gt;=
var grid=[];
&lt;&lt;opened&gt;&gt;=
var opened=[];
&lt;/codeblock&gt;

== The algorithm ==

In this code, the word ''cell'' is sometimes used for nodes.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

function astar()
{
	var best;
	var n=0;

	var chb=document.getElementById(&quot;chb_paintopen&quot;);
	paint_open=chb.checked;
&lt;/codeblock&gt;

We start by &quot;opening&quot; the start node (called ''cell'' here).

The ''opencell()'' function takes three arguments:
* The first node's ''pos'' object
* The cost to reach the position
* The previous node's position (In ''start''s case, it is just ''start'')

The ''best'' variable represents the node we are currently examining.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	best=opencell(start, 0, start);
&lt;/codeblock&gt;

When ''best'' equals ''target'', we are done.
&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=
	while(best &amp;&amp; !best.equal(target)) {
		best.closed=true;
		opened.shift();
&lt;/codeblock&gt;

''openadjacent()'' is a utility function that opens all nodes directly reachable from the ''best''. In this implementation, there are no diagonal edges, so only nodes positioned on the same row or column are considered reachable.

&lt;codeblock lnaguage=js&gt;
&lt;&lt;astar&gt;&gt;=
		openadjacent(best);
&lt;&lt;openadjacent&gt;&gt;=

function openadjacent(p)
{
	var cost=grid[p.y][p.x].cost+10;
	if(p.x&gt;0) opencell(grid[p.y][p.x-1], cost, p);
	if(p.y&gt;0) opencell(grid[p.y-1][p.x], cost, p);
	if(p.y&lt;(sizey-1)) opencell(grid[p.y-(-1)][p.x], cost, p);
	if(p.x&lt;(sizex-1)) opencell(grid[p.y][p.x-(-1)], cost, p);
}
&lt;/codeblock&gt;

Unless the ''opened'' queue is empty, the node with the smallest total cost is assigned to ''best''.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

		if(opened.length&gt;0) best=opened[0];
		else best=null;

		if(++n&gt;10000) {best=null; break;}	/* Catch non-stop loops (should never happen) */
	}
	if(!best) {
		warn=&quot;No route found&quot;;
		return;
	}
&lt;/codeblock&gt;

When ''target'' is reached, we backtrack using the ''prev'' value stored in the each node.

&lt;codeblock language=js&gt;
&lt;&lt;astar&gt;&gt;=

	/* Find way back */
	while(!best.equal(start)) {
		setcolor(best, route_color);
		best=best.prev;
		if(!best) {
			alert(&quot;Something strange happend&quot;);	/* Should never happen */
			break;
		}
	}
}
&lt;/codeblock&gt;

In ''opencell()'' the ''cost'' variable refers to the cost from ''start'' (often refrred to as g()). ''totalcost'' is the sum of ''cost'' and the estimated cost to ''target''.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

function opencell(p, cost, prev)
{
	if(p.blocked) return null;
&lt;/codeblock&gt;

An extra cost (4) is applied if the direction is changed. This is intented to reflect the extra time spent accelerating a physical object.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	if(prev &amp;&amp; prev.prev &amp;&amp; !prev.equal(start)) {
		if(p.x-prev.x != prev.x-prev.prev.x ||
			p.y-prev.y != prev.y-prev.prev.y) cost+=4;
	}
&lt;/codeblock&gt;

The ''totalcost'' variable is the sum of ''cost'' and an extimated cost to reach ''target''. Here we just add the differences in x and y directions, and multiply with 14. This constant should probably be fine-tuned to get the best results.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var totalcost=parseFloat(cost)+14*(Math.abs(p.x-target.x)+Math.abs(p.y-target.y));
&lt;/codeblock&gt;

The A* algorithm normally also includes a ''closed'' queue, representing the nodes that have been considered. In this implementation, the ''close'' queue is implicitly defined as those who have a calculated ''totalcost'' and are not in the ''opened'' queue.

If we reach a node that is opened or closed, it should normally be left, but we might reach that node in a &quot;cheaper&quot; way than when it was first considered, so we see if the new ''totalcost'' is better than the stored one. If that is true, the node can be reopened.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	/* If position is already considered: check for better cost */
	if(p.totalcost!=0) {
		if(totalcost&lt;p.totalcost) {
			var nn;
&lt;/codeblock&gt;

When reopening a node, we must remove it from the ''opened'' queue. It will be reinserted into the correct position.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=
			for(nn=0; nn&lt;opened.length; ++nn) {
				if(p.equal(opened[nn])) {
					opened.splice(nn, 1);
					break;
				}
			}
		} else return null;
	}

	p.cost=cost;
	p.prev=prev;
	p.totalcost=totalcost;
&lt;/codeblock&gt;

As we use just a simple sorted ''Array'' for the ''opened'' queue, we iterate the queue to find the right position and use the ''splice()'' function to insert it.  This obviously has performance issues when the number of nodes grows.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	var n=0;
	for(n=0; n&lt;opened.length; ++n) {
		if(p.totalcost&lt;opened[n].totalcost) {
			opened.splice(n, 0, p);
			break;
		}
	}
	if(n&gt;=opened.length) opened[n]=p;
&lt;/codeblock&gt;

The ''pos'' object representing the node is also stored in the ''grid'' array, so that it easy to look up.

&lt;codeblock language=js&gt;
&lt;&lt;opencell&gt;&gt;=

	grid[p.y][p.x]=p;

&lt;&lt;mark opened&gt;&gt;
&lt;/codeblock&gt;


== The user interface ==

We use an html table to display the grid. The start and target positions can be changed by a user, who can also add and remove blockings (nodes that cannot be traversed).

&lt;codeblock language=html&gt;
&lt;&lt;astar.html&gt;&gt;=
&lt;html&gt;
&lt;head&gt;
 &lt;title&gt;A*&lt;/title&gt;
 &lt;script type=&quot;text/javascript&quot; src=&quot;astar.js&quot;&gt;&lt;/script&gt;
&lt;/head&gt;
&lt;body onload=&quot;doastar();&quot;&gt;
 &lt;h1&gt;A* Demo&lt;/h1&gt;
 &lt;h2&gt;Instructions&lt;/h2&gt;
 'S' is the start position, 'T' is the target position and black positions are blocked.&lt;br/&gt;
 Start and target positions are moved by clicking on them and then clicking on a new position. Any other position will be blocked or unblocked if clicked on.&lt;br/&gt;
 The script is successfully tested on Mozilla Firefox.&lt;br/&gt;
 &lt;input type=&quot;checkbox&quot; id=&quot;chb_paintopen&quot; checked=&quot;1&quot; onclick=&quot;chb_click();&quot;&gt;Mark open positions&lt;/input&gt;
 &lt;table id=&quot;grid&quot; border=&quot;1&quot;&gt;&lt;/table&gt;
 &lt;p id=&quot;expl&quot;&gt;&lt;/p&gt;
&lt;/body&gt;
&lt;/codeblock&gt;

The table created in the html code is initially empty. We use the ''mkgrid()'' function to generate a table of the wanted size.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function mkgrid()
{
	var table=document.getElementById(&quot;grid&quot;);
	table.onmouseout=astar_mouseout;

	var tbody=document.createElement(&quot;tbody&quot;);
	table.appendChild(tbody);

	var tr=document.createElement(&quot;tr&quot;);
	tr.appendChild(document.createElement(&quot;th&quot;));
	tbody.appendChild(tr);

	var x, y;
	for(x=0; x&lt;sizex; ++x) {
		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(x));
		tr.appendChild(th);
	}

	for(y=0; y&lt;sizey; ++y) {
		grid[y]=[];
		var tr=document.createElement(&quot;tr&quot;);
		tbody.appendChild(tr);

		var th=document.createElement(&quot;th&quot;);
		th.appendChild(document.createTextNode(y));
		tr.appendChild(th);

		for(x=0; x&lt;sizex; ++x) {
			grid[y][x]=new pos(x, y);
			var td=document.createElement(&quot;td&quot;);
			td.appendChild(document.createTextNode(&quot;&quot;));
&lt;/codeblock&gt;

All nodes are identified by their ''x'' and ''y'' positions in the ''id'' attribute.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=
			td.id=x+&quot;,&quot;+y;
			td.width=20;
			td.onclick=astar_click;
			td.onmouseover=astar_mouseover;
			td.setAttribute(&quot;x&quot;, x);
			td.setAttribute(&quot;y&quot;, y);
			tr.appendChild(td);
		}
	}
}
&lt;/codeblock&gt;

The ''wipe()'' function is used to clean up the table and the associated data structures before rerunning the algorithm.

&lt;codeblock language=js&gt;
&lt;&lt;DOM&gt;&gt;=

function wipe()
{
	var y, x;

	warn=&quot;&quot;;
	opened=[];

	for(y=0; y&lt;sizey; ++y) {
		for(x=0; x&lt;sizex; ++x) {
			grid[y][x].cost=0;
			grid[y][x].totalcost=0;
			grid[y][x].prev=null;
			grid[y][x].closed=false;

			if(grid[y][x].blocked) setcolor(grid[y][x], blocked_color);
			else setcolor(grid[y][x], nothing_color);
		}
	}
	setcolor(start, start_color);
	setcolor(target, target_color);
}

function settext(p, text)
{
	var td=document.getElementById(p.str());
	td.firstChild.data=text;
}

function setcolor(p, color)
{
	var td=document.getElementById(p.str());
	td.setAttribute(&quot;bgColor&quot;, color);
}

function setstart(p)
{
	if(start) {
		settext(start, &quot;&quot;);
		setcolor(start, nothing_color);
	}
	start=p;
	settext(start, &quot;S&quot;);
	setcolor(start, start_color);
}

function settarget(p)
{
	if(target) {
		settext(target, &quot;&quot;);
		setcolor(target, nothing_color);
	}
	target=p;
	settext(target, &quot;T&quot;);
	setcolor(target, target_color);
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;setblock&gt;&gt;=

function setblock(p1, p2, block)
{
	for(var y=p1.y; y&lt;=p2.y; ++y) {
		for(var x=p1.x; x&lt;=p2.x; ++x) {
			if(block) {
				setcolor(grid[y][x], blocked_color);
				grid[y][x].blocked=true;
			} else {
				setcolor(grid[y][x], nothing_color);
				grid[y][x].blocked=false;
			}
		}
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;callbacks&gt;&gt;=

function astar_click(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	var p=grid[y][x];

	if(start_moving &amp;&amp; !p.equal(target)) {
		setstart(p); 
		start_moving=false;
		setblock(p, p, null);
	} else if(target_moving &amp;&amp; !p.equal(start)) {
		settarget(p);
		target_moving=false;
		setblock(p, p, null);
	} else if(p.equal(start)) start_moving=true;
	else if(p.equal(target)) target_moving=true;
	else {
		if(grid[y][x].blocked) setblock(p, p, null);
		else setblock(p, p, 1);
	}

	if(!start_moving &amp;&amp; !target_moving) {
		wipe();
		astar();
	}

	astar_explain(x, y);
}

function chb_click()
{
	wipe();
	astar();
}

function astar_explain(x, y)
{
	var expl=document.getElementById(&quot;expl&quot;);
	var p=grid[y][x];
	var heuristic=p.totalcost-p.cost;

	if(start_moving) expl.innerHTML=&quot;Click to set new start position at &quot;+p.str();
	else if(target_moving) expl.innerHTML=&quot;Click to set new target position at &quot;+p.str();
	else if(p.blocked) expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Currently blocked. Click to unblock&quot;;
	else if(p.equal(start)) expl.innerHTML=&quot;Start position - Click to move&quot;;
	else if(p.equal(target)) expl.innerHTML=&quot;Target position - Click to move&quot;;
	else if(p.cost==0) expl.innerHTML=p.str()+&quot;&lt;br&gt;Click to block this position&quot;;
	else expl.innerHTML=p.str()+
		&quot;&lt;br&gt;Cost from start: &quot;+p.cost+
		&quot;&lt;br&gt;Heuristic estimate to target: &quot;+heuristic+
		&quot;&lt;br&gt;Total cost: &quot;+p.totalcost+
		&quot;&lt;br&gt;Click to block this position&quot;;

	if(warn.length&gt;0) expl.innerHTML+=&quot;&lt;br&gt;&lt;div style=\&quot;color:red\&quot;&gt;&quot;+warn+&quot;&lt;div&gt;&quot;;
}

function astar_mouseover(e)
{
	if(!e) var e=window.event;

	var x=this.getAttribute(&quot;x&quot;);
	var y=this.getAttribute(&quot;y&quot;);

	astar_explain(x, y);
}

function astar_mouseout()
{
	var expl=document.getElementById(&quot;expl&quot;);
	expl.innerHTML=&quot;&quot;;
}

&lt;/codeblock&gt;

Opened positions are optionally marked with a color code.

&lt;codeblock language=js&gt;
&lt;&lt;mark opened&gt;&gt;=
	if(paint_open &amp;&amp; !p.equal(start)) {
		var intensity=Math.floor(totalcost*4/5);
		
		if(intensity&gt;255) intensity=255;
		setcolor(p, &quot;#&quot;+intensity.toString(16)+&quot;ff&quot;+intensity.toString(16));
	}

	return p;
}
&lt;/codeblock&gt;

== Test code ==

&lt;codeblock language=&quot;js&quot;&gt;
&lt;&lt;astar.js&gt;&gt;=
var sizex=16;
var sizey=16;

var start=null;
var target=null;

&lt;&lt;grid&gt;&gt;
&lt;&lt;opened&gt;&gt;

var expl_text=null;

var paint_open=false;

var start_moving=false;
var target_moving=false;

var nothing_color=&quot;#ffffff&quot;;
var blocked_color=&quot;#000000&quot;;
var start_color=&quot;#00ff00&quot;;
var target_color=&quot;#0000ff&quot;;
var route_color=&quot;#00ffff&quot;;

var warn=&quot;&quot;;

&lt;&lt;pos&gt;&gt;
&lt;&lt;DOM&gt;&gt;
&lt;&lt;setblock&gt;&gt;
&lt;&lt;opencell&gt;&gt;
&lt;&lt;openadjacent&gt;&gt;
&lt;&lt;astar&gt;&gt;
&lt;&lt;callbacks&gt;&gt;
&lt;&lt;doastar&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=js&gt;
&lt;&lt;doastar&gt;&gt;=
function doastar()
{
	mkgrid();

	setstart(new pos(6, 2));
	settarget(new pos(9, 14));
	setblock(new pos(1, 3), new pos(10, 4), true);
	setblock(new pos(12, 4), new pos(15, 4), true);
	setblock(new pos(2, 6), new pos(14, 12), true);
	setblock(new pos(0, 6), new pos(0, 9), true);
	setblock(new pos(9, 6), new pos(10, 11), false);
	setblock(new pos(11, 11), new pos(14, 11), false);

	astar();
}
&lt;/codeblock&gt;

To run this code, just save ''astar.js'' and ''astar.html'' to the same directory and open ''astar.html'' in your browser. A (possibly outdated) copy is located [http://hystad.com/astar.html here]. 


[[Category:A* search]]
[[Category:Programming language:JavaScript]]</text>
    </revision>
  </page>
  <page>
    <title>Abstract factory (Java)</title>
    <id>1623</id>
    <revision>
      <id>2436</id>
      <timestamp>2006-03-06T01:42:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Abstract factory (Java) moved to Abstract factory pattern (Java): Less vague</comment>
      <text xml:space="preserve">#redirect [[Abstract factory pattern (Java)]]</text>
    </revision>
  </page>
  <page>
    <title>Abstract factory pattern (Java)</title>
    <id>1619</id>
    <revision>
      <id>2423</id>
      <timestamp>2006-03-06T01:28:44Z</timestamp>
      <contributor>
        <username>Kjetilos</username>
        <id>27</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteFactory.java&gt;&gt;=
public class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA()
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractProducts.java&gt;&gt;=
abstract class A {}
abstract class B {}
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteProducts.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;Client.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    AbstractA abstractA = factory.createProductA();
    AbstractB abstractB = factory.createProductB();
    // do something useful with abstract{A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.


[[Category:Programming language:Java]]
[[Category:Design patterns]]</text>
    </revision>
    <revision>
      <id>2424</id>
      <timestamp>2006-03-06T01:32:43Z</timestamp>
      <contributor>
        <username>Kjetilos</username>
        <id>27</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteFactory.java&gt;&gt;=
public class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractProducts.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteProducts.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;Client.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    AbstractA abstractA = factory.createProductA();
    AbstractB abstractB = factory.createProductB();
    // do something useful with abstract{A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.


[[Category:Programming language:Java]]
[[Category:Design patterns]]</text>
    </revision>
    <revision>
      <id>2426</id>
      <timestamp>2006-03-06T01:35:48Z</timestamp>
      <contributor>
        <username>Kjetilos</username>
        <id>27</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteFactory.java&gt;&gt;=
public class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractProducts.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;ConcreteProducts.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;Client.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.


[[Category:Programming language:Java]]
[[Category:Design patterns]]</text>
    </revision>
    <revision>
      <id>2431</id>
      <timestamp>2006-03-06T01:39:20Z</timestamp>
      <contributor>
        <username>Kjetilos</username>
        <id>27</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.


[[Category:Programming language:Java]]
[[Category:Design patterns]]</text>
    </revision>
    <revision>
      <id>2433</id>
      <timestamp>2006-03-06T01:41:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move to subcategory</comment>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.

[[Category:Programming language:Java]]
[[Category:Abstract factory pattern]]</text>
    </revision>
    <revision>
      <id>2435</id>
      <timestamp>2006-03-06T01:42:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Abstract factory (Java) moved to Abstract factory pattern (Java)</comment>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.

[[Category:Programming language:Java]]
[[Category:Abstract factory pattern]]</text>
    </revision>
    <revision>
      <id>2464</id>
      <timestamp>2006-03-06T03:45:10Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>sp</comment>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependent objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.

[[Category:Programming language:Java]]
[[Category:Abstract factory pattern]]</text>
    </revision>
    <revision>
      <id>6768</id>
      <timestamp>2006-07-11T12:44:58Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Abstract factory pattern (Java)]] moved to [[Abstract factory pattern (Java) on Wheels]]</comment>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependent objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.

[[Category:Programming language:Java]]
[[Category:Abstract factory pattern]]</text>
    </revision>
    <revision>
      <id>6940</id>
      <timestamp>2006-07-11T14:25:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Abstract factory pattern (Java) on Wheels]] moved to [[Abstract factory pattern (Java)]]: revert</comment>
      <text xml:space="preserve">{{develop}}

The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependent objects without specifying their concrete classes. 

In the abstract factory pattern there are five roles:
* Abstract factory
* Concrete factory
* Abstract product
* Concrete product
* Client

The abstract factory declares the methods that create products.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
public abstract class AbstractFactory {
  public abstract A createProductA();
  public abstract B createProductB();
}
&lt;/codeblock&gt;

The concrete factory extends the abstract factory and implements the creation methods declared in the abstract factory
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteFactory extends AbstractFactory {
  public A createProductA() {
    return new ConcreteA();
  }

  public B createProductB() {
    return new ConcreteB();
  }
}
&lt;/codeblock&gt;

We also have to declare the abstract products which we want the abstract factory to produce.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
abstract class A { }
abstract class B { }
&lt;/codeblock&gt;

The implementations of the abstract products are called concrete products, these are created by the concrete factories.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class ConcreteA extends A { }
class ConcreteB extends B { }
&lt;/codeblock&gt;

To use all the above code we need a client which is hopefully interrested in our abstract products. Note that this is where we instantiate the factory with the concrete factory of our choice. If we later want another implementation of the abstract factory we only need to change one line of code.
&lt;codeblock language=java&gt;
&lt;&lt;AbstractFactory.java&gt;&gt;=
class Client {
  public void init() {
    AbstractFactory factory = new ConcreteFactory();
    A abstractA = factory.createProductA();
    B abstractB = factory.createProductB();
    // do something useful with {A,B}
  }
}
&lt;/codeblock&gt;

TODO: Example with data access object creations where the client asks the abstract factory for a data access object implementation. There will be two different data access object classes, one using memory storage and one using the Java serialization to file abilities.

[[Category:Programming language:Java]]
[[Category:Abstract factory pattern]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Alice ML)</title>
    <id>2925</id>
    <revision>
      <id>8636</id>
      <timestamp>2007-01-23T18:15:34Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <comment>Start with a simple one in AliceML just to see how LP works.</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock langage=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, n) if (m &gt; 0 andalso n = 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock langage=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n = 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8637</id>
      <timestamp>2007-01-23T18:46:11Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>change pattern match to shorter form</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock langage=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock langage=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n = 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8638</id>
      <timestamp>2007-01-23T18:46:36Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>change pattern match to shorter form</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock langage=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock langage=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock langage=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8642</id>
      <timestamp>2007-01-23T20:04:47Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <comment>Add a fast implementation</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8651</id>
      <timestamp>2007-01-23T23:10:17Z</timestamp>
      <contributor>
        <ip>69.15.198.171</ip>
      </contributor>
      <comment>add support for infinite integers</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=

fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=

val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (i, n) if (n = inf_0) = inf_1
  | inf_pow (i, n) if (n &gt; inf_0) = i * inf_pow(i, n - inf_1)
  | inf_pow _ = raise Domain

fun big_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | big_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | big_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | big_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | big_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      big_ackermann (m - inf_1, inf_1)
  | big_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      big_ackermann (m - inf_1, big_ackermann (m, n - inf_1))
  | big_ackermann _ = raise Domain
&lt;/codeblock&gt;

The big_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- big_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
19730 digits
1602.....3885 (* total 19730 digits *)
- big_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
19729 digits
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8652</id>
      <timestamp>2007-01-23T23:14:26Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <comment>Change name for large int function</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (i, n) if (n = inf_0) = inf_1
  | inf_pow (i, n) if (n &gt; inf_0) = i * inf_pow(i, n - inf_1)
  | inf_pow _ = raise Domain

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann (m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann (m - inf_1, inf_ackermann (m, n - inf_1))
  | inf_ackermann _ = raise Domain
  | big_ackermann _ = raise Domain
&lt;/codeblock&gt;

The big_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
19730 digits
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
19729 digits
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8653</id>
      <timestamp>2007-01-23T23:14:56Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>missed one</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (i, n) if (n = inf_0) = inf_1
  | inf_pow (i, n) if (n &gt; inf_0) = i * inf_pow(i, n - inf_1)
  | inf_pow _ = raise Domain

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann (m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann (m - inf_1, inf_ackermann (m, n - inf_1))
  | inf_ackermann _ = raise Domain
  | big_ackermann _ = raise Domain
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
19730 digits
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
19729 digits
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8654</id>
      <timestamp>2007-01-23T23:17:04Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>minor cleanup on output</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (i, n) if (n = inf_0) = inf_1
  | inf_pow (i, n) if (n &gt; inf_0) = i * inf_pow(i, n - inf_1)
  | inf_pow _ = raise Domain

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann (m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann (m - inf_1, inf_ackermann (m, n - inf_1))
  | inf_ackermann _ = raise Domain
  | big_ackermann _ = raise Domain
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8655</id>
      <timestamp>2007-01-23T23:24:03Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>couple of minor corrections.  hard to get the details right.</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using guards in pattern matching, Alice ML will determine that not all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using power function that takes integers (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (i, 0) = 1
  | int_pow (i, n) if (n &gt; 0) = i * int_pow(i, n-1)
  | int_pow _ = raise Domain

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann (m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann (m-1, fast_ackermann (m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (i, n) if (n = inf_0) = inf_1
  | inf_pow (i, n) if (n &gt; inf_0) = i * inf_pow(i, n - inf_1)
  | inf_pow _ = raise Domain

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann (m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann (m - inf_1, inf_ackermann (m, n - inf_1))
  | inf_ackermann _ = raise Domain
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8657</id>
      <timestamp>2007-01-24T02:38:48Z</timestamp>
      <contributor>
        <ip>76.185.186.143</ip>
      </contributor>
      <comment>change power function to iterative</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann(m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann(m-1, ackermann(m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1
&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using guards in pattern matching, Alice ML will determine that not all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock langage=aliceml&gt;
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using a power function that takes integers for arguments (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (base, exponent) =
   let
      fun iter_pow (i, 0, sum) = sum
        | iter_pow (i, n, sum) if (n &gt; 0) = iter_pow(i, n-1, i*sum)
        | iter_pow _ = raise Domain
   in
      iter_pow(base, exponent, 1)
   end

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann(m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann(m-1, fast_ackermann(m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (base, exponent) =
   let
      fun iter_pow (i, n, sum) if (n = inf_0) = sum : IntInf.t
        | iter_pow (i, n, sum) if (n &gt; inf_0) = iter_pow(i, n - inf_1, i*sum)
        | iter_pow _ = raise Domain
   in
      iter_pow(base, exponent, inf_1)
   end

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann(m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann(m - inf_1, inf_ackermann(m, n - inf_1))
  | inf_ackermann _ = raise Domain
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8658</id>
      <timestamp>2007-01-24T02:40:46Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>fix language attribute</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in Alice ML.

==Source code==
We begin the code by defining a recursive function named &lt;code&gt;ackermann&lt;/code&gt;, using pattern matching on the function parameters to handle the three cases given in the definition of the Ackermann function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun ackermann (0, n) = n + 1
  | ackermann (m, 0) if (m &gt; 0) = ackermann(m-1, 1)
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann(m-1, ackermann(m, n-1))
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

The first case we handle is the base case of the recursion, when m = 0.
&lt;codeblock language=aliceml&gt;
fun ackermann (0, n) = n + 1
&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.
&lt;codeblock language=aliceml&gt;
  | ackermann (m, 0) if (m &gt; 0) = ackermann (m-1, 1)
&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).
&lt;codeblock language=aliceml&gt;
  | ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) = ackermann (m-1, ackermann (m, n-1))
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise a Domain exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using guards in pattern matching, Alice ML will determine that not all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | ackermann _ = raise Domain
&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=aliceml&gt;
- ackermann (0, 0);
val it : int = 1
- ackermann (1, 1);
val it : int = 3
- ackermann (2, 13);
val it : int = 29
- ackermann (3, 1);
val it : int = 13
- ackermann (3, 7);
val it : int = 1021
- ackermann (3, 9);
val it : int = 4093
- ackermann (~1, 9);
Uncaught exception
   Domain
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using a power function that takes integers for arguments (the standard Math.pow function is real*real-&gt;real):

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
fun int_pow (base, exponent) =
   let
      fun iter_pow (i, 0, sum) = sum
        | iter_pow (i, n, sum) if (n &gt; 0) = iter_pow(i, n-1, i*sum)
        | iter_pow _ = raise Domain
   in
      iter_pow(base, exponent, 1)
   end

fun fast_ackermann (0, n) = n + 1
  | fast_ackermann (1, n) if (n &gt; 0) = n + 2
  | fast_ackermann (2, n) if (n &gt; 0) = 2*n + 3
  | fast_ackermann (3, n) if (n &gt; 0) = int_pow(2, n+3) - 3
  | fast_ackermann (m, 0) if (m &gt; 0) = fast_ackermann(m-1, 1)
  | fast_ackermann (m, n) if (m &gt; 0 andalso n &gt; 0) =
      fast_ackermann(m-1, fast_ackermann(m, n-1))
  | fast_ackermann _ = raise Domain
&lt;/codeblock&gt;

The fast_ackermann function allows us to rapidly compute some larger results.
&lt;codeblock language=aliceml&gt;
- fast_ackermann (3, 26);
val it : int = 536870909
- fast_ackermann (4, 1);
val it : int = 65533
- fast_ackermann (3, 27);
Uncaught exception
   Overflow
- fast_ackermann (4, 2);
Uncaught exception
   Overflow
&lt;/codeblock&gt;

==Unlimited Integer Sizes==

The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt =1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0, 1, 2, and 3.

&lt;codeblock language=aliceml&gt;
&lt;&lt;ackermann.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
val inf_2 = IntInf.fromInt 2
val inf_3 = IntInf.fromInt 3

fun inf_pow (base, exponent) =
   let
      fun iter_pow (i, n, sum) if (n = inf_0) = sum : IntInf.t
        | iter_pow (i, n, sum) if (n &gt; inf_0) = iter_pow(i, n - inf_1, i*sum)
        | iter_pow _ = raise Domain
   in
      iter_pow(base, exponent, inf_1)
   end

fun inf_ackermann (m, n) if (m = inf_0) =
      n + inf_1
  | inf_ackermann (m, n) if (m = inf_1 andalso n &gt; inf_0) =
      n + inf_2
  | inf_ackermann (m, n) if (m = inf_2 andalso n &gt; inf_0) =
      (inf_2 * n) + inf_3
  | inf_ackermann (m, n) if (m = inf_3 andalso n &gt; inf_0) =
      inf_pow(inf_2, n + inf_3) - inf_3
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n = inf_0) =
      inf_ackermann(m - inf_1, inf_1)
  | inf_ackermann (m, n) if (m &gt; inf_0 andalso n &gt; inf_0) =
      inf_ackermann(m - inf_1, inf_ackermann(m, n - inf_1))
  | inf_ackermann _ = raise Domain
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:

&lt;codeblock language=aliceml&gt;
- inf_ackermann (IntInf.fromInt 3, IntInf.fromInt 65536);
val it : IntInf.int =
1602.....3885 (* total 19730 digits *)
- inf_ackermann (IntInf.fromInt 4, IntInf.fromInt 2);
val it : IntInf.int =
2003.....6733 (* total 19729 digits *)
&lt;/codeblock&gt;

[[Category:Ackermann function|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (C)</title>
    <id>2784</id>
    <revision>
      <id>8102</id>
      <timestamp>2006-11-17T22:26:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Three C implementations of Ackermann function on machine words with test driver</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = naive_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;
&lt;math&gt;A(3, n) = 2^(n+3) - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = naive_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
#include &lt;stdio.h&gt;

static int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    int m = atoi(argv[1]), n = atoi(argv[2]), result;

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %d (%d calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %d (%d calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %d (%d calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

{{TODO}}

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8103</id>
      <timestamp>2006-11-17T22:26:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Test main */ &lt;&lt;ackermann.c&gt;&gt;=</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = naive_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;
&lt;math&gt;A(3, n) = 2^(n+3) - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = naive_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;

static int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    int m = atoi(argv[1]), n = atoi(argv[2]), result;

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %d (%d calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %d (%d calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %d (%d calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

{{TODO}}

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8104</id>
      <timestamp>2006-11-17T22:33:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Sample output</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = naive_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;
&lt;math&gt;A(3, n) = 2^(n+3) - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = naive_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    int m = atoi(argv[1]), n = atoi(argv[2]), result;

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %d (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %d (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %d (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8105</id>
      <timestamp>2006-11-17T22:34:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Test main */ Signed/unsigned</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = naive_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;
&lt;math&gt;A(3, n) = 2^(n+3) - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = naive_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8106</id>
      <timestamp>2006-11-17T22:38:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Precomputed for small ''m'' */ Format</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = naive_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = naive_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8107</id>
      <timestamp>2006-11-18T00:07:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Oops, recursively invoke same function (copy/paste bug)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = iterative_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = formula_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8108</id>
      <timestamp>2006-11-18T00:08:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Update output, many less calls, yay</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = iterative_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = formula_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13449</id>
      <timestamp>2008-05-23T15:09:58Z</timestamp>
      <contributor>
        <ip>62.68.25.105</ip>
      </contributor>
      <comment>/* Partially interative */ typo</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = iterative_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = formula_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is zero due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14914</id>
      <timestamp>2008-10-09T14:46:58Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Precomputed for small ''m'' */ overflow for shift is undefined</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in C. Of course, since most values of the Ackermann function exceed the size of a machine word (even a 64-bit word), these implementations are more useful for illustration than practical computation of Ackermann function values.

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We use unsigned types to avoid the possibility of illegal negative inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int naive_ackermann(unsigned int m, unsigned int n) {
    calls++;
    if (m == 0)
        return n + 1;
    else if (n == 0)
        return naive_ackermann(m - 1, 1);
    else
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1));
}
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int iterative_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while (m != 0) {
        if (n == 0) {
            n = 1;
        } else {
            n = iterative_ackermann(m, n - 1);
        }
        m--;
    }
    return n + 1;
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
unsigned int formula_ackermann(unsigned int m, unsigned int n) {
    calls++;
    while(1) {
        switch(m) {
        case 0:  return n + 1;
        case 1:  return n + 2;
        case 2:  return (n &lt;&lt; 1) + 3;
        case 3:  return (1 &lt;&lt; (n+3)) - 3;
        default:
            if (n == 0) {
                n = 1;
            } else {
                n = formula_ackermann(m, n - 1);
            }
            m--;
            break;
        }
    }
}
&lt;/codeblock&gt;

This doesn't quite work correctly for &lt;math&gt;n+3&lt;/math&gt; equal to the word size, for which &lt;code&gt;1 &lt;&lt; (n+3)&lt;/code&gt; is undefined due to overflow, but we ignore this here.

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=c&gt;
&lt;&lt;ackermann.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt; /* atoi() */

static unsigned int calls;

&lt;&lt;ackermann implementations&gt;&gt;

int main(int argc, char* argv[]) {
    unsigned int m, n, result;
    m = (unsigned)atoi(argv[1]);
    n = (unsigned)atoi(argv[2]);

    calls = 0;
    result = naive_ackermann(m, n);
    printf(&quot;Naive:     %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = iterative_ackermann(m, n);
    printf(&quot;Iterative: %u (%u calls)\n&quot;, result, calls);

    calls = 0;
    result = formula_ackermann(m, n);
    printf(&quot;Formula:   %u (%u calls)\n&quot;, result, calls);

    return 0;
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

[[Category:Ackermann function|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Erlang)</title>
    <id>3580</id>
    <revision>
      <id>14774</id>
      <timestamp>2008-09-28T16:31:54Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackernamm function&gt;&gt;=
ackerman(0, N) -&gt;
    N + 1;
ackerman(M, 0) -&gt;
    ackermann(M-1, 1);
ackerman(M, N) -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

    &lt;&lt;ackernamm function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14775</id>
      <timestamp>2008-09-28T16:36:15Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackerman(0, N) -&gt;
    N + 1;
ackerman(M, 0) -&gt;
    ackermann(M-1, 1);
ackerman(M, N) -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

    &lt;&lt;ackernamm function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14776</id>
      <timestamp>2008-09-28T16:38:24Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackerman(0, N) -&gt;
    N + 1;
ackerman(M, 0) -&gt;
    ackermann(M-1, 1);
ackerman(M, N) -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

    &lt;&lt;ackermann function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14777</id>
      <timestamp>2008-09-28T16:39:00Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackerman(0, N) -&gt;
    N + 1;
ackerman(M, 0) -&gt;
    ackermann(M-1, 1);
ackerman(M, N) -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

&lt;&lt;ackermann function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14778</id>
      <timestamp>2008-09-28T16:42:52Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackermann(0, N) -&gt;
    N + 1;
ackermann(M, 0) -&gt;
    ackermann(M-1, 1);
ackermann(M, N) -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

&lt;&lt;ackermann function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16052</id>
      <timestamp>2009-01-27T12:24:39Z</timestamp>
      <contributor>
        <ip>195.39.106.218</ip>
      </contributor>
      <comment>Input value check added.</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackermann(0, N) -&gt;
    N + 1;
ackermann(M, 0) when M &gt; 0 -&gt;
    ackermann(M-1, 1);
ackermann(M, N) when M &gt; 0, N &gt; 0-&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

&lt;&lt;ackermann function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16053</id>
      <timestamp>2009-01-27T12:25:29Z</timestamp>
      <contributor>
        <ip>195.39.106.218</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

Using recursion and pattern matching this function is extreamly easy to
impliment in ''Erlang''.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann function&gt;&gt;=
ackermann(0, N) -&gt;
    N + 1;
ackermann(M, 0) when M &gt; 0 -&gt;
    ackermann(M-1, 1);
ackermann(M, N) when M &gt; 0, N &gt; 0 -&gt;
    ackermann(M-1, ackermann(M, N - 1)).
&lt;/codeblock&gt;

Then all that is needed is some glue code to allow the function to be
accessed as a script.

&lt;codeblock language=erlang&gt;
&lt;&lt;ackermann&gt;&gt;=
#!/usr/bin/env escript

main([A, P]) -&gt;
    io:fwrite(&quot;~p~n&quot;, [xackermann(string:to_integer(A), string:to_integer(P))]).

xackermann({A, _}, {B, _}) -&gt;
    ackermann(A, B).

&lt;&lt;ackermann function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Ackermann function|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Forth)</title>
    <id>3198</id>
    <revision>
      <id>10767</id>
      <timestamp>2007-07-27T00:14:46Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This is a simple recursive version of the Ackermann function. Cell sized integers are used, so stack and integer overflow is likely. The function is easiest to implement and most stack efficient if the parameter ''m'' is on top of the stack.

&lt;codeblock language=forth&gt;
&lt;&lt;ackermann.f&gt;&gt;=
: ack ( n m -- a )
  ?dup if &lt;&lt;ackermann (m&gt;0)&gt;&gt;
     else &lt;&lt;ackermann (m=0)&gt;&gt; then ;
&lt;/codeblock&gt;

The easy case: m=0.  The use of '''?dup''' earlier has already thrown the zero argument away. The return value is the second argument incremented.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m=0)&gt;&gt;= 1+ &lt;/codeblock&gt;

When m&gt;0, we will be invoking the Ackermann function recursively, with different behavior depending on whether n&gt;0.  '''swap ?dup''' brings ''n'' to the top to be examined. Afterward, '''swap 1- recurse''' calls Ackermann(m-1, ...).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0)&gt;&gt;= swap ?dup if &lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;
                  else &lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;
                  then swap 1- recurse &lt;/codeblock&gt;

If n=0, the second parameter is simply one.  '''?dup''' had already eaten the zero argument.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;= 1 &lt;/codeblock&gt;

If n&gt;0, the second parameter is a further recursive call to Ackermann(m, n-1).  We had previously '''swap'''ped ''m'' and ''n'' so the stack currently has ( m n ).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;= 1- over recurse &lt;/codeblock&gt;

[[Category:Programming language:Forth]]
[[Category:Ackermann function|Forth]]</text>
    </revision>
    <revision>
      <id>10768</id>
      <timestamp>2007-07-27T00:17:04Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>formatting</comment>
      <text xml:space="preserve">This is a simple recursive version of the Ackermann function. Cell sized integers are used, so stack and integer overflow is likely. The function is easiest to implement and most stack efficient if the parameter ''m'' is on top of the stack.

&lt;codeblock language=forth&gt;
&lt;&lt;ackermann.f&gt;&gt;=
: ack ( n m -- a )
  ?dup if &lt;&lt;ackermann (m&gt;0)&gt;&gt;
     else &lt;&lt;ackermann (m=0)&gt;&gt; then ;
&lt;/codeblock&gt;

The easy case: m=0.  The use of '''?dup''' earlier has already thrown the zero argument away. The return value is the second argument incremented.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m=0)&gt;&gt;=
1+ &lt;/codeblock&gt;

When m&gt;0, we will be invoking the Ackermann function recursively, with different behavior depending on whether n&gt;0.  '''swap ?dup''' brings ''n'' to the top to be examined. Afterward, '''swap 1- recurse''' calls Ackermann(m-1, ...).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0)&gt;&gt;=
swap ?dup if &lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;
                  else &lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;
                  then swap 1- recurse &lt;/codeblock&gt;

If n=0, the second parameter is simply one.  '''?dup''' had already eaten the zero argument.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;=
1 &lt;/codeblock&gt;

If n&gt;0, the second parameter is a further recursive call to Ackermann(m, n-1).  We had previously '''swap'''ped ''m'' and ''n'' so the stack currently has ( m n ).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;=
1- over recurse &lt;/codeblock&gt;

[[Category:Programming language:Forth]]
[[Category:Ackermann function|Forth]]</text>
    </revision>
    <revision>
      <id>10769</id>
      <timestamp>2007-07-27T00:19:32Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>example</comment>
      <text xml:space="preserve">This is a simple recursive version of the Ackermann function. Cell sized integers are used, so stack and integer overflow is likely. The function is easiest to implement and most stack efficient if the parameter ''m'' is on top of the stack.

&lt;codeblock language=forth&gt;
&lt;&lt;ackermann.f&gt;&gt;=
: ack ( n m -- a )
  ?dup if &lt;&lt;ackermann (m&gt;0)&gt;&gt;
     else &lt;&lt;ackermann (m=0)&gt;&gt; then ;

2 3 ack .   \ 29 
&lt;/codeblock&gt;

The easy case: m=0.  The use of '''?dup''' earlier has already thrown the zero argument away. The return value is the second argument incremented.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m=0)&gt;&gt;=
1+ &lt;/codeblock&gt;

When m&gt;0, we will be invoking the Ackermann function recursively, with different behavior depending on whether n&gt;0.  '''swap ?dup''' brings ''n'' to the top to be examined. Afterward, '''swap 1- recurse''' calls Ackermann(m-1, ...).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0)&gt;&gt;=
swap ?dup if &lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;
                  else &lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;
                  then swap 1- recurse &lt;/codeblock&gt;

If n=0, the second parameter is simply one.  '''?dup''' had already eaten the zero argument.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;=
1 &lt;/codeblock&gt;

If n&gt;0, the second parameter is a further recursive call to Ackermann(m, n-1).  We had previously '''swap'''ped ''m'' and ''n'' so the stack currently has ( m n ).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;=
1- over recurse &lt;/codeblock&gt;

[[Category:Programming language:Forth]]
[[Category:Ackermann function|Forth]]</text>
    </revision>
    <revision>
      <id>10836</id>
      <timestamp>2007-07-31T22:01:46Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

This is a simple recursive version of the Ackermann function. Cell sized integers are used, so stack and integer overflow is likely. The function is easiest to implement and most stack efficient if the parameter ''m'' is on top of the stack.

&lt;codeblock language=forth&gt;
&lt;&lt;ackermann.f&gt;&gt;=
: ack ( n m -- a )
  ?dup if &lt;&lt;ackermann (m&gt;0)&gt;&gt;
     else &lt;&lt;ackermann (m=0)&gt;&gt; then ;

2 3 ack .   \ 29 
&lt;/codeblock&gt;

The easy case: m=0.  The use of '''?dup''' earlier has already thrown the zero argument away. The return value is the second argument incremented.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m=0)&gt;&gt;=
1+ &lt;/codeblock&gt;

When m&gt;0, we will be invoking the Ackermann function recursively, with different behavior depending on whether n&gt;0.  '''swap ?dup''' brings ''n'' to the top to be examined. Afterward, '''swap 1- recurse''' calls Ackermann(m-1, ...).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0)&gt;&gt;=
swap ?dup if &lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;
                  else &lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;
                  then swap 1- recurse &lt;/codeblock&gt;

If n=0, the second parameter is simply one.  '''?dup''' had already eaten the zero argument.
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n=0)&gt;&gt;=
1 &lt;/codeblock&gt;

If n&gt;0, the second parameter is a further recursive call to Ackermann(m, n-1).  We had previously '''swap'''ped ''m'' and ''n'' so the stack currently has ( m n ).
&lt;codeblock language=forth&gt;
&lt;&lt;ackermann (m&gt;0 n&gt;0)&gt;&gt;=
1- over recurse &lt;/codeblock&gt;

[[Category:Programming language:Forth]]
[[Category:Ackermann function|Forth]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Haskell)</title>
    <id>3496</id>
    <revision>
      <id>13784</id>
      <timestamp>2008-06-25T10:11:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Create based on deleted Category:Ackermann_function(Haskell)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

The Ackermann function is ideal for representation in Haskell and an excellent
use of its '''pattern matching''' facility and specifically '''''n+k'' pattern matching'''.

The Ackermann function could also have been easily implemented in Haskell with ''conditional code'' or ''guards''.

With pattern matching you create multiple definitions of a function and specify patterns for the arguments.
Haskell will use its pattern matching facility to invoke the first definition that matches the pattern.

Haskell has extremely little Housekeeping code
&lt;codeblock language=haskell&gt;
module Ackermann
    where
&lt;/codeblock&gt;

The case that bottoms out the recursion uses simple pattern matching to match the first
argument to 0 and binds the second argument to the variable n
&lt;codeblock language=haskell&gt;
ackermann 0 n = n+1
&lt;/codeblock&gt;

The case that reduces the first argument with primitive recursion
uses what is called ''n+k pattern matching'', in an ''n+k pattern'' match '''n&gt;= k'''.
In this case the ''n+k pattern'' is m+1 therefore the first argument or ''m'' must be
greater than 1.

The case that uses multiple recursion also uses ''n+k pattern matching''.
Therefore both the first and second argument must be greater than 1

&lt;codeblock language=haskell&gt;
ackermann (m+1) 0 = ackermann m 1
ackermann (m+1) (n+1) = ackermann m (ackermann (m+1) n)
&lt;/codeblock&gt;

Finally a &quot;catch all&quot; definition that use the underscore, which are wildcards
that don't even bother to bind the values.
Note the pattern matching goes in order, so something like this should always
be last.  This is nice approach for eeking out every bit of efficiency because
catching invalid negative arguments doesn't affect performance of algorithm
with valid arguments.  I suppose I could have spit out an error message, but
I simply return 0.
&lt;codeblock language=haskell&gt;
ackermann _ _ = 0
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>13785</id>
      <timestamp>2008-06-25T10:12:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Category</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

The Ackermann function is ideal for representation in Haskell and an excellent
use of its '''pattern matching''' facility and specifically '''''n+k'' pattern matching'''.

The Ackermann function could also have been easily implemented in Haskell with ''conditional code'' or ''guards''.

With pattern matching you create multiple definitions of a function and specify patterns for the arguments.
Haskell will use its pattern matching facility to invoke the first definition that matches the pattern.

Haskell has extremely little Housekeeping code
&lt;codeblock language=haskell&gt;
module Ackermann
    where
&lt;/codeblock&gt;

The case that bottoms out the recursion uses simple pattern matching to match the first
argument to 0 and binds the second argument to the variable n
&lt;codeblock language=haskell&gt;
ackermann 0 n = n+1
&lt;/codeblock&gt;

The case that reduces the first argument with primitive recursion
uses what is called ''n+k pattern matching'', in an ''n+k pattern'' match '''n&gt;= k'''.
In this case the ''n+k pattern'' is m+1 therefore the first argument or ''m'' must be
greater than 1.

The case that uses multiple recursion also uses ''n+k pattern matching''.
Therefore both the first and second argument must be greater than 1

&lt;codeblock language=haskell&gt;
ackermann (m+1) 0 = ackermann m 1
ackermann (m+1) (n+1) = ackermann m (ackermann (m+1) n)
&lt;/codeblock&gt;

Finally a &quot;catch all&quot; definition that use the underscore, which are wildcards
that don't even bother to bind the values.
Note the pattern matching goes in order, so something like this should always
be last.  This is nice approach for eeking out every bit of efficiency because
catching invalid negative arguments doesn't affect performance of algorithm
with valid arguments.  I suppose I could have spit out an error message, but
I simply return 0.
&lt;codeblock language=haskell&gt;
ackermann _ _ = 0
&lt;/codeblock&gt;

[[Category:Ackermann function]]
[[Category:Programming language:Haskell]]</text>
    </revision>
    <revision>
      <id>13786</id>
      <timestamp>2008-06-25T10:13:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add LP syntax</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

The Ackermann function is ideal for representation in Haskell and an excellent
use of its '''pattern matching''' facility and specifically '''''n+k'' pattern matching'''.

The Ackermann function could also have been easily implemented in Haskell with ''conditional code'' or ''guards''.

With pattern matching you create multiple definitions of a function and specify patterns for the arguments.
Haskell will use its pattern matching facility to invoke the first definition that matches the pattern.

Haskell has extremely little Housekeeping code
&lt;codeblock language=haskell&gt;
&lt;&lt;ackermann.hs&gt;&gt;=
module Ackermann
    where
&lt;/codeblock&gt;

The case that bottoms out the recursion uses simple pattern matching to match the first
argument to 0 and binds the second argument to the variable n
&lt;codeblock language=haskell&gt;
&lt;&lt;ackermann.hs&gt;&gt;=
ackermann 0 n = n+1
&lt;/codeblock&gt;

The case that reduces the first argument with primitive recursion
uses what is called ''n+k pattern matching'', in an ''n+k pattern'' match '''n&gt;= k'''.
In this case the ''n+k pattern'' is m+1 therefore the first argument or ''m'' must be
greater than 1.

The case that uses multiple recursion also uses ''n+k pattern matching''.
Therefore both the first and second argument must be greater than 1

&lt;codeblock language=haskell&gt;
&lt;&lt;ackermann.hs&gt;&gt;=
ackermann (m+1) 0 = ackermann m 1
ackermann (m+1) (n+1) = ackermann m (ackermann (m+1) n)
&lt;/codeblock&gt;

Finally a &quot;catch all&quot; definition that use the underscore, which are wildcards
that don't even bother to bind the values.
Note the pattern matching goes in order, so something like this should always
be last.  This is nice approach for eeking out every bit of efficiency because
catching invalid negative arguments doesn't affect performance of algorithm
with valid arguments.  I suppose I could have spit out an error message, but
I simply return 0.
&lt;codeblock language=haskell&gt;
&lt;&lt;ackermann.hs&gt;&gt;=
ackermann _ _ = 0
&lt;/codeblock&gt;

[[Category:Ackermann function]]
[[Category:Programming language:Haskell]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Java)</title>
    <id>2785</id>
    <revision>
      <id>8109</id>
      <timestamp>2006-11-18T00:24:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Java version derived from C version using BigIntegers</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        case 3:  return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
public class Ackermann {

private BigInteger calls;

&lt;&lt;ackermann implementations&gt;&gt;

public static void main(string[] args) {
    BigInteger m, n, result;
    m = new BigInteger(args[0]);
    n = new BigInteger(args[1]);

    calls = BigInteger.ZERO;
    result = naiveAckermann(m, n);
    System.out.println(&quot;Naive:     &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);

    calls = BigInteger.ZERO;
    result = iterativeAckermann(m, n);
    System.out.println(&quot;Iterative: &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);

    calls = BigInteger.ZERO;
    result = formulaAckermann(m, n);
    System.out.println(&quot;Formula:   &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8110</id>
      <timestamp>2006-11-18T00:28:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix compiler errors</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;code language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math;
&lt;/code&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        case 3:  return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(string[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8111</id>
      <timestamp>2006-11-18T00:29:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Syntax</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        case 3:  return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(string[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8112</id>
      <timestamp>2006-11-18T00:30:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Compiler errors</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        case 3:  return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot;(&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8113</id>
      <timestamp>2006-11-18T00:32:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Javac too dumb to realise end not reached in end of formulaAckermann, spaces</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8114</id>
      <timestamp>2006-11-18T00:34:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Precomputed for small ''m'' */ Oops, not modifying calls</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ ./ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8115</id>
      <timestamp>2006-11-18T00:34:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Test main */ Invocation syntax</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (2862984006 calls)
Formula:   65533 (108 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8116</id>
      <timestamp>2006-11-18T00:36:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix output</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8117</id>
      <timestamp>2006-11-18T00:42:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Note about computing A(4,2)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ java Ackermann 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8118</id>
      <timestamp>2006-11-18T00:44:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Time warning</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output (note: on a 2.4 GhZ machine this takes many minutes to run):

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ java Ackermann 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15800</id>
      <timestamp>2009-01-06T10:17:26Z</timestamp>
      <contributor>
        <ip>91.200.233.195</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

http://www.message_sittrocroac.com/

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output (note: on a 2.4 GhZ machine this takes many minutes to run):

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ java Ackermann 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15803</id>
      <timestamp>2009-01-06T15:39:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/91.200.233.195|91.200.233.195]] ([[User_talk:91.200.233.195|91.200.233.195]]); changed back to last version by [[User:Deco|Deco]]</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = new BigInteger(&quot;2&quot;);
    BigInteger THREE = new BigInteger(&quot;3&quot;);
    BigInteger FOUR = new BigInteger(&quot;4&quot;);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output (note: on a 2.4 GhZ machine this takes many minutes to run):

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ java Ackermann 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16642</id>
      <timestamp>2010-01-24T21:20:00Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Java. We use Java's &lt;a href=&quot;&quot;&gt;&lt;code&gt;BigInteger&lt;/code&gt;&lt;/a&gt; class for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory). &lt;code&gt;BigInteger&lt;/code&gt; is found in java.math:

&lt;codeblock language=java&gt;
&lt;&lt;imports&gt;&gt;=
import java.math.BigInteger;
&lt;/codeblock&gt;

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger naiveAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    if (m.signum() == 0)
        return n.add(BigInteger.ONE);
    else if (n.signum() == 0)
        return naiveAckermann(m.subtract(BigInteger.ONE), BigInteger.ONE);
    else
        return naiveAckermann(m.subtract(BigInteger.ONE),
                              naiveAckermann(m, n.subtract(BigInteger.ONE)));
}
&lt;/codeblock&gt;

==Partially interative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger iterativeAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    while (m.signum() != 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = iterativeAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    return n.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=java&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
static BigInteger formulaAckermann(BigInteger m, BigInteger n) {
    calls = calls.add(BigInteger.ONE);
    BigInteger TWO = BigInteger.valueOf(2);
    BigInteger THREE = BigInteger.valueOf(3);
    BigInteger FOUR = BigInteger.valueOf(4);
    while(m.compareTo(FOUR) &gt;= 0) {
        if (n.signum() == 0) {
            n = BigInteger.ONE;
        } else {
            n = formulaAckermann(m, n.subtract(BigInteger.ONE));
        }
        m = m.subtract(BigInteger.ONE);
    }
    switch(m.intValue()) {
        case 0:  return n.add(BigInteger.ONE);
        case 1:  return n.add(TWO);
        case 2:  return n.shiftLeft(1).add(THREE);
        default: return BigInteger.ONE.shiftLeft(n.intValue() + 3).subtract(THREE);
    }
}
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=java&gt;
&lt;&lt;Ackermann.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

public class Ackermann {

    private static BigInteger calls;

    &lt;&lt;ackermann implementations&gt;&gt;

    public static void main(String[] args) {
        BigInteger m, n, result;
        m = new BigInteger(args[0]);
        n = new BigInteger(args[1]);
    
        calls = BigInteger.ZERO;
        result = naiveAckermann(m, n);
        System.out.println(&quot;Naive:     &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = iterativeAckermann(m, n);
        System.out.println(&quot;Iterative: &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    
        calls = BigInteger.ZERO;
        result = formulaAckermann(m, n);
        System.out.println(&quot;Formula:   &quot; + result + &quot; (&quot; + calls + &quot; calls)&quot;);
    }

}
&lt;/codeblock&gt;

Here's some sample input/output (note: on a 2.4 GhZ machine this takes many minutes to run):

&lt;pre&gt;
$ java Ackermann 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ java Ackermann 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (OCaml)</title>
    <id>2783</id>
    <revision>
      <id>8095</id>
      <timestamp>2006-11-17T19:19:55Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <comment>Intial entry for the Ackermann function in OCaml</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function
&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1
&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)
&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))
&lt;/codeblock&gt;

Finally, we add a final clause to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Ackermann's function is only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock langage=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

The exact values of the function is given in the following table.
{| border=&quot;1&quot; cellpadding=&quot;2&quot;
|+ Values of ''A''(''m'',&amp;nbsp;''n'')
|-
! ''m''\''n''
! 0
! 1
! 2
! 3
! 4
! n
|-
! 0
| 1 || 2 || 3 || 4 || 5 || &lt;math&gt;n + 1&lt;/math&gt;
|-
! 1
| 2 || 3 || 4 || 5 || 6 || &lt;math&gt;n + 2&lt;/math&gt;
|-
! 2
| 3 || 5 || 7 || 9 || 11 || &lt;math&gt;2n + 3&lt;/math&gt;
|-
! 3
| 5 || 13 || 29 || 61 || 125 || &lt;math&gt;2^{(n+3)} - 3&lt;/math&gt;
|-
! 4
| 13 || 65533
| 2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3
| ''A''(3,&amp;nbsp;2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3)
| ''A''(3,&amp;nbsp;''A''(4,&amp;nbsp;3))
| &lt;math&gt;\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3 twos}\end{matrix}&lt;/math&gt;
|-
! 5
| 65533 || ''A''(4,&amp;nbsp;65533) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;2)) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;3))
|-
! 6
| ''A''(5,&amp;nbsp;1) || ''A''(5,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;A(6,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;2)) || ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;3))
|}

Thanks to the author of the [[Ackerman function (Prolog)]] page for the lovingly stolen table.

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8096</id>
      <timestamp>2006-11-17T19:21:30Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <minor/>
      <comment>fixed some extra whitespace in the generated code</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Ackermann's function is only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock langage=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

The exact values of the function is given in the following table.
{| border=&quot;1&quot; cellpadding=&quot;2&quot;
|+ Values of ''A''(''m'',&amp;nbsp;''n'')
|-
! ''m''\''n''
! 0
! 1
! 2
! 3
! 4
! n
|-
! 0
| 1 || 2 || 3 || 4 || 5 || &lt;math&gt;n + 1&lt;/math&gt;
|-
! 1
| 2 || 3 || 4 || 5 || 6 || &lt;math&gt;n + 2&lt;/math&gt;
|-
! 2
| 3 || 5 || 7 || 9 || 11 || &lt;math&gt;2n + 3&lt;/math&gt;
|-
! 3
| 5 || 13 || 29 || 61 || 125 || &lt;math&gt;2^{(n+3)} - 3&lt;/math&gt;
|-
! 4
| 13 || 65533
| 2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3
| ''A''(3,&amp;nbsp;2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3)
| ''A''(3,&amp;nbsp;''A''(4,&amp;nbsp;3))
| &lt;math&gt;\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3 twos}\end{matrix}&lt;/math&gt;
|-
! 5
| 65533 || ''A''(4,&amp;nbsp;65533) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;2)) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;3))
|-
! 6
| ''A''(5,&amp;nbsp;1) || ''A''(5,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;A(6,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;2)) || ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;3))
|}

Thanks to the author of the [[Ackerman function (Prolog)]] page for the lovingly stolen table.

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8098</id>
      <timestamp>2006-11-17T21:54:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>sp</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Ackermann's function is only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock langage=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

The exact values of the function is given in the following table.
{| border=&quot;1&quot; cellpadding=&quot;2&quot;
|+ Values of ''A''(''m'',&amp;nbsp;''n'')
|-
! ''m''\''n''
! 0
! 1
! 2
! 3
! 4
! n
|-
! 0
| 1 || 2 || 3 || 4 || 5 || &lt;math&gt;n + 1&lt;/math&gt;
|-
! 1
| 2 || 3 || 4 || 5 || 6 || &lt;math&gt;n + 2&lt;/math&gt;
|-
! 2
| 3 || 5 || 7 || 9 || 11 || &lt;math&gt;2n + 3&lt;/math&gt;
|-
! 3
| 5 || 13 || 29 || 61 || 125 || &lt;math&gt;2^{(n+3)} - 3&lt;/math&gt;
|-
! 4
| 13 || 65533
| 2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3
| ''A''(3,&amp;nbsp;2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3)
| ''A''(3,&amp;nbsp;''A''(4,&amp;nbsp;3))
| &lt;math&gt;\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3 twos}\end{matrix}&lt;/math&gt;
|-
! 5
| 65533 || ''A''(4,&amp;nbsp;65533) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;2)) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;3))
|-
! 6
| ''A''(5,&amp;nbsp;1) || ''A''(5,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;A(6,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;2)) || ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;3))
|}

Thanks to the author of the [[Ackermann function (Prolog)]] page for the lovingly stolen table.

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8100</id>
      <timestamp>2006-11-17T21:56:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Delete table taken from Wikipedia article (not suitably licensed)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Ackermann's function is only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock langage=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock langage=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8678</id>
      <timestamp>2007-01-25T19:51:34Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>fix spelling of &quot;language&quot; to get syntax highlighting</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Ackermann's function is only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock language=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13691</id>
      <timestamp>2008-06-19T04:10:44Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m = 0 -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n = 0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n when m &gt; 0 &amp;&amp; n &gt; 0 -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Ackermann's function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| _ -&gt; invalid_arg &quot;Ackermann's function is only defined over the non-negative integers&quot;&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock language=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13692</id>
      <timestamp>2008-06-19T04:17:47Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

First, we add a case to catch the cases when either argument is negative, because the Ackermann function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m &lt; 0 || n &lt; 0 -&gt; invalid_arg &quot;Ackermann's function is only defined over the non-negative integers&quot;&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| 0,n -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock language=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16606</id>
      <timestamp>2010-01-03T20:15:58Z</timestamp>
      <contributor>
        <username>Blue Prawn</username>
        <id>1959</id>
      </contributor>
      <comment>/* Execution result */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This page explains how to implement the '''Ackermann function''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==Source code==
We begin the code by defining a recursive value named &lt;code&gt;ackermann&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
let rec ackermann = function&lt;/codeblock&gt;

First, we add a case to catch the cases when either argument is negative, because the Ackermann function is only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| m,n when m &lt; 0 || n &lt; 0 -&gt; invalid_arg &quot;Ackermann's function is only defined over the non-negative integers&quot;&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Ackermann function.  The first case we handle is the base case of the recursion, when m = 0.  Note that because of the way we are doing the pattern matching, our function takes a single tuple as input.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=
| 0,n -&gt; n+1&lt;/codeblock&gt;

For the second case, when m &gt; 0 and n = 0, we make a simple recursive call to the &lt;code&gt;ackermann&lt;/code&gt; function.

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,0 -&gt; ackermann (m-1,1)&lt;/codeblock&gt;

In the third case, when m, n &gt; 0, a pair of recursive calls are made.  The first call determines the new value of n, and the second call which uses this new value along with the new value of m (a simple decrement).

&lt;codeblock language=ocaml&gt;
&lt;&lt;ackermann.ml&gt;&gt;=  
| m,n -&gt; ackermann (m-1,ackermann (m,n-1))&lt;/codeblock&gt;

==Execution result==
In this section we show the output of a few applications of &lt;code&gt;ackermann&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
# ackermann (0,0);;
- : int = 1
# ackermann (1,1);;
- : int = 3
# ackermann (2,13);;
- : int = 29
# ackermann (3,1);;
- : int = 13
# ackermann (3,7);;
- : int = 1021
# ackermann (3,9);;
- : int = 4093
# ackermann (-1,9);;
Exception:
Invalid_argument
 &quot;Ackermann's function is only defined over the non-negative integers&quot;.
&lt;/codeblock&gt;
Note, however, that due to the tremendous growth rate of Ackermann's function, the number of recursive calls to &lt;code&gt;ackermann&lt;/code&gt; quickly becomes too much to handle, even for relatively small values of m and n.

&lt;codeblock language=ocaml&gt;
# ackermann (4,1);;
Stack overflow during evaluation (looping recursion?).
&lt;/codeblock&gt;

We can resolve this problem in the usual way in OCaml which is to rewrite the code in a tail-recursive way:

&lt;codeblock language=ocaml&gt;
let rec find_option h v =
  try Some(Hashtbl.find h v)
  with Not_found -&gt; None
 
let rec a bounds caller todo m n =
  match m, n with
  | 0, n -&gt;
      let r = (n+1) in
      ( match todo with
        | [] -&gt; r
        | (m,n)::todo -&gt;
            List.iter (fun k -&gt;
              if not(Hashtbl.mem bounds k)
              then Hashtbl.add bounds k r) caller;
            a bounds [] todo m n )
 
  | m, 0 -&gt;
      a bounds caller todo (m-1) 1
 
  | m, n -&gt;
      match find_option bounds (m, n-1) with
      | Some a_rec -&gt;
          let caller = (m,n)::caller in
          a bounds caller todo (m-1) a_rec
      | None -&gt;
          let todo = (m,n)::todo
          and caller = [(m, n-1)] in
          a bounds caller todo m (n-1)
 
let a = a (Hashtbl.create 42 (* arbitrary *) ) [] [] ;;
&lt;/codeblock&gt;

This one uses the arbitrary precision, the tail-recursion, and the optimisation explain on the Wikipedia page about (m,n) = (3,_).

&lt;codeblock language=ocaml&gt;
open Big_int
let one  = unit_big_int
let zero = zero_big_int
let succ = succ_big_int
let pred = pred_big_int
let add = add_big_int
let sub = sub_big_int
let eq = eq_big_int
let three = succ(succ one)
let power = power_int_positive_big_int
 
let eq2 (a1,a2) (b1,b2) =
  (eq a1 b1) &amp;&amp; (eq a2 b2)
 
module H = Hashtbl.Make
  (struct
     type t = Big_int.big_int * Big_int.big_int
     let equal = eq2
     let hash (x,y) = Hashtbl.hash
       (Big_int.string_of_big_int x ^ &quot;,&quot; ^
          Big_int.string_of_big_int y)
       (* probably not a very good hash function *)
   end)
 
let rec find_option h v =
  try Some (H.find h v)
  with Not_found -&gt; None
 
let rec a bounds caller todo m n =
  let may_tail r =
    let k = (m,n) in
    match todo with
    | [] -&gt; r
    | (m,n)::todo -&gt;
        List.iter (fun k -&gt;
                     if not (H.mem bounds k)
                     then H.add bounds k r) (k::caller);
        a bounds [] todo m n
  in
  match m, n with
  | m, n when eq m zero -&gt;
      let r = (succ n) in
      may_tail r
 
  | m, n when eq n zero -&gt;
      let caller = (m,n)::caller in
      a bounds caller todo (pred m) one
 
  | m, n when eq m three -&gt;
      let r = sub (power 2 (add n three)) three in
      may_tail r
 
  | m, n -&gt;
      match find_option bounds (m, pred n) with
      | Some a_rec -&gt;
          let caller = (m,n)::caller in
          a bounds caller todo (pred m) a_rec
      | None -&gt;
          let todo = (m,n)::todo in
          let caller = [(m, pred n)] in
          a bounds caller todo m (pred n)
 
let a = a (H.create 42 (* arbitrary *)) [] [] ;;
&lt;/codeblock&gt;

We can use this last version this way:

&lt;codeblock language=ocaml&gt;
let () =
  let m, n =
    try
      big_int_of_string Sys.argv.(1),
      big_int_of_string Sys.argv.(2)
    with _ -&gt;
      Printf.eprintf &quot;usage: %s &lt;int&gt; &lt;int&gt;\n&quot; Sys.argv.(0);
      exit 1
  in
  let r = a m n in
  Printf.printf &quot;(a %s %s) = %s\n&quot;
      (string_of_big_int m)
      (string_of_big_int n)
      (string_of_big_int r);
;;
&lt;/codeblock&gt;

compile with:
 ocamlopt -o acker nums.cmxa acker.ml

[[Category:Ackermann function|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Prolog)</title>
    <id>2402</id>
    <revision>
      <id>6611</id>
      <timestamp>2006-07-02T14:00:31Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.
2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporal variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .
==Execution result==

[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6612</id>
      <timestamp>2006-07-02T14:09:27Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Execution result */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.
2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporal variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .
==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-

The exact values of the function is given in the following table.
{| border=&quot;1&quot; cellpadding=&quot;2&quot;
|+ Values of ''A''(''m'',&amp;nbsp;''n'')
|-
! ''m''\''n''
! 0
! 1
! 2
! 3
! 4
! n
|-
! 0
| 1 || 2 || 3 || 4 || 5 || &lt;math&gt;n + 1&lt;/math&gt;
|-
! 1
| 2 || 3 || 4 || 5 || 6 || &lt;math&gt;n + 2&lt;/math&gt;
|-
! 2
| 3 || 5 || 7 || 9 || 11 || &lt;math&gt;2n + 3&lt;/math&gt;
|-
! 3
| 5 || 13 || 29 || 61 || 125 || &lt;math&gt;2^{(n+3)} - 3&lt;/math&gt;
|-
! 4
| 13 || 65533
| 2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3
| ''A''(3,&amp;nbsp;2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3)
| ''A''(3,&amp;nbsp;''A''(4,&amp;nbsp;3))
| &lt;math&gt;\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3 twos}\end{matrix}&lt;/math&gt;
|-
! 5
| 65533 || ''A''(4,&amp;nbsp;65533) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;2)) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;3))
|-
! 6
| ''A''(5,&amp;nbsp;1) || ''A''(5,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;A(6,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;2)) || ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;3))
|}

[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6613</id>
      <timestamp>2006-07-02T14:10:32Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Source code */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.

2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporal variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .

==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-

The exact values of the function is given in the following table.
{| border=&quot;1&quot; cellpadding=&quot;2&quot;
|+ Values of ''A''(''m'',&amp;nbsp;''n'')
|-
! ''m''\''n''
! 0
! 1
! 2
! 3
! 4
! n
|-
! 0
| 1 || 2 || 3 || 4 || 5 || &lt;math&gt;n + 1&lt;/math&gt;
|-
! 1
| 2 || 3 || 4 || 5 || 6 || &lt;math&gt;n + 2&lt;/math&gt;
|-
! 2
| 3 || 5 || 7 || 9 || 11 || &lt;math&gt;2n + 3&lt;/math&gt;
|-
! 3
| 5 || 13 || 29 || 61 || 125 || &lt;math&gt;2^{(n+3)} - 3&lt;/math&gt;
|-
! 4
| 13 || 65533
| 2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3
| ''A''(3,&amp;nbsp;2&lt;sup&gt;65536&lt;/sup&gt;&amp;nbsp;&amp;minus;&amp;nbsp;3)
| ''A''(3,&amp;nbsp;''A''(4,&amp;nbsp;3))
| &lt;math&gt;\begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3 twos}\end{matrix}&lt;/math&gt;
|-
! 5
| 65533 || ''A''(4,&amp;nbsp;65533) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;2)) || ''A''(4,&amp;nbsp;''A''(5,&amp;nbsp;3))
|-
! 6
| ''A''(5,&amp;nbsp;1) || ''A''(5,&amp;nbsp;''A''(5,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;A(6,&amp;nbsp;1))
| ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;2)) || ''A''(5,&amp;nbsp;''A''(6,&amp;nbsp;3))
|}

[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8099</id>
      <timestamp>2006-11-17T21:56:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Delete table taken from Wikipedia article (not suitably licensed unless you created it)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.

2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporal variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .

==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-


[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8688</id>
      <timestamp>2007-01-26T13:42:44Z</timestamp>
      <contributor>
        <ip>128.8.89.68</ip>
      </contributor>
      <comment>corrected typo</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.

2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporary variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .

==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-


[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13014</id>
      <timestamp>2008-04-09T20:48:45Z</timestamp>
      <contributor>
        <ip>87.230.86.102</ip>
      </contributor>
      <comment>/* Source code */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.

2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporary variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .

==Tricky version==
In this version we use the &lt;code&gt;!&lt;/code&gt; (the cut operator) to avoid unnecessary backtracking. Also
the try_asserta/1 predicate is an effort to save intermediate results thus using them when needed,
some useless comparisons checks are removed too.

&lt;codeblock&gt;
:- dynamic acr/3.

try_asserta(F) :- % if we already have the result do nothing
 F,
 !.

try_asserta(F) :- % if we do not have the result store it
 !,
 asserta(F).

ackermann(M, N, A) :- % use precomputed result if that exists
 acr(M, N, A),
 !.

ackermann(0, N, A) :- % special case
 !,
 A is N + 1,
 try_asserta(acr(0, N, A)).

ackermann(M, 0, A) :- % special case
 !,
 M1 is M - 1,
 ackermann(M1, 1, A),
 try_asserta(acr(M, 0, A)),
 try_asserta(acr(M1, 1, A)).

ackermann(M, N, A) :- % main recursions
 !,
 M1 is M - 1,
 N1 is N - 1,
 ackermann(M, N1, Temp),
 try_asserta(acr(M, N1, Temp)),
 ackermann(M1, Temp, A),
 try_asserta(acr(M, N, A)),
 try_asserta(acr(M1, Temp, A)).
&lt;/codeblock&gt;

==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-


[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13015</id>
      <timestamp>2008-04-09T21:03:55Z</timestamp>
      <contributor>
        <ip>87.230.86.102</ip>
      </contributor>
      <comment>/* Tricky version */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}
This page explains how to implement the '''Ackermann function''' in Prolog. In Prolog, functions are defined as relations while both the arguments and the result are given to the relation as parameters. In this article, &lt;code&gt;ackermann(M, N, A)&lt;/code&gt; denotes that '&lt;code&gt;A&lt;/code&gt; is the value of &lt;math&gt;A(m, n)\ &lt;/math&gt;.'

==Source code==
The source code is composed of three cases explained above.

1. if m = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(0, N, A) :- A is N + 1.
&lt;/codeblock&gt;
Note that the &lt;code&gt;is&lt;/code&gt; operator assigns the arithmetic operation to the variable.

2. if m &gt; 0 and n = 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, 0, A) :-
  M &gt; 0,
  M1 is M - 1,
  ackermann(M1, 1, A).
&lt;/codeblock&gt;
3. if m &gt; 0 and n &gt; 0
&lt;codeblock&gt;
&lt;&lt;ackermann.pl&gt;&gt;=
ackermann(M, N, A) :-
  M &gt; 0,
  N &gt; 0,
  M1 is M - 1,
  N1 is N - 1,
  ackermann(M, N1, Temp),
  ackermann(M1, Temp, A).
&lt;/codeblock&gt;
This case is a little tricky. As logic programming languages do not support functional composition, we have to employ a temporary variable &lt;code&gt;Temp&lt;/code&gt; for &lt;math&gt;A(m, n-1)\ &lt;/math&gt; .

==Tricky version==
In this version we use the &lt;code&gt;!&lt;/code&gt; (the cut operator) to avoid unnecessary backtracking. Also
the try_asserta/1 predicate is an effort to save intermediate results thus using them when needed,
some useless comparisons checks are removed too.

&lt;codeblock language = prolog&gt;
&lt;&lt;tricky_ackermann.pl&gt;&gt;

:- dynamic acr/3.

try_asserta(F) :- % if we already have the result do nothing
 F,
 !.

try_asserta(F) :- % if we do not have the result store it
 !,
 asserta(F).

ackermann(M, N, A) :- % use precomputed result if that exists
 acr(M, N, A),
 !.

ackermann(0, N, A) :- % special case
 !,
 A is N + 1,
 try_asserta(acr(0, N, A)).

ackermann(M, 0, A) :- % special case
 !,
 M1 is M - 1,
 ackermann(M1, 1, A),
 try_asserta(acr(M, 0, A)),
 try_asserta(acr(M1, 1, A)).

ackermann(M, N, A) :- % main recursions
 !,
 M1 is M - 1,
 N1 is N - 1,
 ackermann(M, N1, Temp),
 try_asserta(acr(M, N1, Temp)),
 ackermann(M1, Temp, A),
 try_asserta(acr(M, N, A)),
 try_asserta(acr(M1, Temp, A)).
&lt;/codeblock&gt;

==Execution result==
This section contains a number of execution results of the Ackermann function implementation in Prolog.
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['ackermann.pl'].
 % ackermann.pl compiled 0.00 sec, 1,112 bytes
 
 Yes
 ?- ackermann(0, 0, A).
 
 A = 1
 
 Yes
 
 ?- ackermann(1, 6, A).
 
 A = 8
 
 Yes
 
 ?- ackermann(2, 3, A).
 
 A = 9
 
 Yes
 
 ?- ackermann(3, 3, A).
 
 A = 61
 
 Yes
 
 ?- ackermann(4, 3, A).
 ERROR: Out of local stack
 ?-


[[Category:Ackermann function|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ackermann function (Python)</title>
    <id>3486</id>
    <revision>
      <id>13689</id>
      <timestamp>2008-06-19T03:53:53Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>translated from java</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Python. We use Python's &lt;code&gt;long&lt;/code&gt; type for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def naive_ackermann(m, n):
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def iterative_ackermann(m, n):
    calls += 1
    while m != 0:
        if n == 0:
            n = 1
        else:
            n = iterative_ackermann(m, n - 1)
        m -= 1
    return n + 1
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def formula_ackermann(m, n):
    calls += 1
    while m &gt;= 4:
        if n == 0:
            n = 1
        else:
            n = formula_ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return 1 &lt;&lt; (n + 3) - 3
    elif m == 2:
        return n &lt;&lt; 1 + 3
    elif m == 1:
        return n + 2
    else: # m == 0
        return n + 1
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann.py&gt;&gt;=
import sys # for argv

calls = 0

&lt;&lt;ackermann implementations&gt;&gt;

if __name__ == &quot;__main__&quot;:
    m = long(sys.argv[1])
    n = long(sys.argv[2])

    calls = 0
    result = naive_ackermann(m, n)
    print &quot;Naive:     %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = iterative_ackermann(m, n)
    print &quot;Iterative: %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = formula_ackermann(m, n)
    print &quot;Formula:   %d (%d calls)&quot; % (result, calls)
&lt;/codeblock&gt;

Here's some sample input/output (note: on a 2.4 GhZ machine this takes many minutes to run):

&lt;pre&gt;
$ python ackermann.py 4 1
Naive:     65533 (2862984010 calls)
Iterative: 65533 (1431459240 calls)
Formula:   65533 (2 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ python ackermann.py 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13690</id>
      <timestamp>2008-06-19T04:07:30Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Python. We use Python's &lt;code&gt;long&lt;/code&gt; type for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def naive_ackermann(m, n):
    global calls
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def iterative_ackermann(m, n):
    global calls
    calls += 1
    while m != 0:
        if n == 0:
            n = 1
        else:
            n = iterative_ackermann(m, n - 1)
        m -= 1
    return n + 1
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def formula_ackermann(m, n):
    global calls
    calls += 1
    while m &gt;= 4:
        if n == 0:
            n = 1
        else:
            n = formula_ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return (1 &lt;&lt; n + 3) - 3
    elif m == 2:
        return (n &lt;&lt; 1) + 3
    elif m == 1:
        return n + 2
    else: # m == 0
        return n + 1
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann.py&gt;&gt;=
import sys # for argv

calls = 0

&lt;&lt;ackermann implementations&gt;&gt;

if __name__ == &quot;__main__&quot;:
    m = long(sys.argv[1])
    n = long(sys.argv[2])

    calls = 0
    result = naive_ackermann(m, n)
    print &quot;Naive:     %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = iterative_ackermann(m, n)
    print &quot;Iterative: %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = formula_ackermann(m, n)
    print &quot;Formula:   %d (%d calls)&quot; % (result, calls)
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ python ackermann.py 3 6
Naive:     509 (172233 calls)
Iterative: 509 (85866 calls)
Formula:   509 (1 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ python ackermann.py 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16289</id>
      <timestamp>2009-03-24T17:20:13Z</timestamp>
      <contributor>
        <username>Commodore Guff</username>
        <id>1761</id>
      </contributor>
      <comment>/* Partially iterative */</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Python. We use Python's &lt;code&gt;long&lt;/code&gt; type for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def naive_ackermann(m, n):
    global calls
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def iterative_ackermann(m, n, calls = 0):
	calls += 1
	while m != 0:
		if n == 0:
			n = 1
		else:
			n = iterative_ackermann(m, n - 1, calls)
		m -= 1
	return n + 1
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def formula_ackermann(m, n):
    global calls
    calls += 1
    while m &gt;= 4:
        if n == 0:
            n = 1
        else:
            n = formula_ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return (1 &lt;&lt; n + 3) - 3
    elif m == 2:
        return (n &lt;&lt; 1) + 3
    elif m == 1:
        return n + 2
    else: # m == 0
        return n + 1
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann.py&gt;&gt;=
import sys # for argv

calls = 0

&lt;&lt;ackermann implementations&gt;&gt;

if __name__ == &quot;__main__&quot;:
    m = long(sys.argv[1])
    n = long(sys.argv[2])

    calls = 0
    result = naive_ackermann(m, n)
    print &quot;Naive:     %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = iterative_ackermann(m, n)
    print &quot;Iterative: %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = formula_ackermann(m, n)
    print &quot;Formula:   %d (%d calls)&quot; % (result, calls)
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ python ackermann.py 3 6
Naive:     509 (172233 calls)
Iterative: 509 (85866 calls)
Formula:   509 (1 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ python ackermann.py 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16290</id>
      <timestamp>2009-03-24T17:22:47Z</timestamp>
      <contributor>
        <username>Commodore Guff</username>
        <id>1761</id>
      </contributor>
      <minor/>
      <comment>nevermind, I'm stupid</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Python. We use Python's &lt;code&gt;long&lt;/code&gt; type for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative, and we test for zero efficiently using the &lt;code&gt;signum()&lt;/code&gt; method, which returns zero if and only if the number is zero.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def naive_ackermann(m, n):
    global calls
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def iterative_ackermann(m, n):
    global calls
    calls += 1
    while m != 0:
        if n == 0:
            n = 1
        else:
            n = iterative_ackermann(m, n - 1)
        m -= 1
    return n + 1
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def formula_ackermann(m, n):
    global calls
    calls += 1
    while m &gt;= 4:
        if n == 0:
            n = 1
        else:
            n = formula_ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return (1 &lt;&lt; n + 3) - 3
    elif m == 2:
        return (n &lt;&lt; 1) + 3
    elif m == 1:
        return n + 2
    else: # m == 0
        return n + 1
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann.py&gt;&gt;=
import sys # for argv

calls = 0

&lt;&lt;ackermann implementations&gt;&gt;

if __name__ == &quot;__main__&quot;:
    m = long(sys.argv[1])
    n = long(sys.argv[2])

    calls = 0
    result = naive_ackermann(m, n)
    print &quot;Naive:     %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = iterative_ackermann(m, n)
    print &quot;Iterative: %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = formula_ackermann(m, n)
    print &quot;Formula:   %d (%d calls)&quot; % (result, calls)
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ python ackermann.py 3 6
Naive:     509 (172233 calls)
Iterative: 509 (85866 calls)
Formula:   509 (1 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ python ackermann.py 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16428</id>
      <timestamp>2009-05-09T13:33:04Z</timestamp>
      <contributor>
        <username>Totoro</username>
        <id>1819</id>
      </contributor>
      <comment>Removed comment on signum() method (appearently a leftover from the Java version)</comment>
      <text xml:space="preserve">{{Category:Ackermann function}}

This article explains a few different methods of computing the Ackermann function in Python. We use Python's &lt;code&gt;long&lt;/code&gt; type for arbitrary-precision integer arithmetic, which allows us to handle more of the very large integer values generated by the Ackermann function (although due to its rapid growth we are still quickly limited by available memory).

==Directly from definition==

The most basic implementation is based directly on the definition above, resembling it nearly identically, except that the greater-than-zero conditions are implicit due to previous conditions being false. We assume that the inputs are non-negative.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def naive_ackermann(m, n):
    global calls
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))
&lt;/codeblock&gt;

==Partially iterative==

For compilers that do not eliminate tail recursion, we can turn two of the recursive calls above into iterative constructs. This greatly reduces the number of recursive calls, although the number is still prohibitive even for small inputs.

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def iterative_ackermann(m, n):
    global calls
    calls += 1
    while m != 0:
        if n == 0:
            n = 1
        else:
            n = iterative_ackermann(m, n - 1)
        m -= 1
    return n + 1
&lt;/codeblock&gt;

==Precomputed for small ''m''==

It is possible to prove the following useful formulas for small values of the input ''m'':

&lt;math&gt;A(0, n) = n + 1&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(1, n) = n + 2&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(2, n) = 2n + 3&lt;/math&gt;&lt;br&gt;
&lt;math&gt;A(3, n) = 2^{n+3} - 3&lt;/math&gt;

Using these, we can drastically reduce runtime not only for these inputs, but for larger inputs which make recursive calls with these inputs. We perform the exponentiation using shifting:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann implementations&gt;&gt;=
def formula_ackermann(m, n):
    global calls
    calls += 1
    while m &gt;= 4:
        if n == 0:
            n = 1
        else:
            n = formula_ackermann(m, n - 1)
        m -= 1
    if m == 3:
        return (1 &lt;&lt; n + 3) - 3
    elif m == 2:
        return (n &lt;&lt; 1) + 3
    elif m == 1:
        return n + 2
    else: # m == 0
        return n + 1
&lt;/codeblock&gt;

== Test main ==

We write a test driver that prints a requested value of the Ackermann function using all three implementations, as well as the number of calls made by each:

&lt;codeblock language=python&gt;
&lt;&lt;ackermann.py&gt;&gt;=
import sys # for argv

calls = 0

&lt;&lt;ackermann implementations&gt;&gt;

if __name__ == &quot;__main__&quot;:
    m = long(sys.argv[1])
    n = long(sys.argv[2])

    calls = 0
    result = naive_ackermann(m, n)
    print &quot;Naive:     %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = iterative_ackermann(m, n)
    print &quot;Iterative: %d (%d calls)&quot; % (result, calls)

    calls = 0
    result = formula_ackermann(m, n)
    print &quot;Formula:   %d (%d calls)&quot; % (result, calls)
&lt;/codeblock&gt;

Here's some sample input/output:

&lt;pre&gt;
$ python ackermann.py 3 6
Naive:     509 (172233 calls)
Iterative: 509 (85866 calls)
Formula:   509 (1 calls)
&lt;/pre&gt;

If we comment out all except ''Formula'', we can compute some impressively large values of the Ackermann function quite quickly, such as A(4,2), which has over 19000 digits (omitted here for space):

&lt;pre&gt;
$ python ackermann.py 4 2
Formula:   200352993040684646497907235156025[...]905719156733 (3 calls)
&lt;/pre&gt;

[[Category:Ackermann function|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Ada Hello World</title>
    <id>1353</id>
    <revision>
      <id>1536</id>
      <timestamp>2006-03-03T00:15:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Ada Hello World moved to Hello World (Ada): Emerging convention</comment>
      <text xml:space="preserve">#redirect [[Hello World (Ada)]]</text>
    </revision>
  </page>
  <page>
    <title>Apply button handling in dialog windows</title>
    <id>1734</id>
    <revision>
      <id>2962</id>
      <timestamp>2006-03-08T20:12:31Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>Apply button handling in dialog windows moved to Apply button handling in dialog windows (Delphi): Consistent with emerging convention of &quot;Pattern/algorithm/program (Language)&quot; for article titles</comment>
      <text xml:space="preserve">#redirect [[Apply button handling in dialog windows (Delphi)]]</text>
    </revision>
  </page>
  <page>
    <title>Apply button handling in dialog windows (Delphi)</title>
    <id>1733</id>
    <revision>
      <id>2957</id>
      <timestamp>2006-03-08T19:08:57Z</timestamp>
      <contributor>
        <username>Joe</username>
        <id>36</id>
      </contributor>
      <comment>Please somebody proofread my English, it's awfull :(</comment>
      <text xml:space="preserve">Apply button handling in dialog windows.
The purpose of this unit is to automatically control an enabled/disabled state of
&quot;Apply&quot; button in dialog windows.
The main idea is that if certain controls' properties changed from its defaults,
then &quot;Apply&quot; button becomes enabled, otherwise it stays disabled.

&lt;codeblock language=delphi&gt;
&lt;&lt;ChangeFinder.pas&gt;&gt;=

{
Usage.
--------------------------------------
You have dialog form with some controls on it and OK, Cancel, Apply buttons.
Also, place TActionList on the form. Create an action in TActionList
for Apply button and associate it with this button. 

Sample code follows.

uses ..., ChangeFinder;

// This code was generated by IDE for our Form
type
  TForm17 = class(TForm)
    Button1: TButton;
    ActionList1: TActionList;
    acApply: TAction;
    Edit1: TEdit;
    Edit2: TEdit;
    CheckBox1: TCheckBox;
    CheckBox2: TCheckBox;
    procedure ActionList1Update(Action: TBasicAction; var Handled: Boolean);
    procedure FormCreate(Sender: TObject);
    procedure acApplyExecute(Sender: TObject);
  private
    FStateHolder: IStateHolder; // an instance of interface implementation
  end;

  imlpementation

// OnCreate event handler
// Executes once on form instance creation
procedure TForm17.FormCreate(Sender: TObject);
begin
  // Create an instance of state holder
  FStateHolder := CreateStateHolder;

  // Here you may set default values for some controls.
  // Or just set them in Object Inspector at design time.

  with FStateHolder do
  begin
    // Save values of Text property
    // for all TEdit controls (and its descedants) on form
    SaveStatesFor(Self,TEdit,'Text');

    // the same for all TCheckBoxes
    SaveStatesFor(Self,TCheckBox,'Checked');

    // do the same for all other controls' classes

    // or you may use SaveState to save state
    // of individual controls instead of specifying a class
  end;
end;

procedure TForm17.acApplyExecute(Sender: TObject);
begin
  // Place here appropriate code
  // to apply changes made in dialog
end;

// OnUpdate event handler
// Executes when application is idle
procedure TForm17.ActionList1Update(Action: TBasicAction; var Handled: Boolean);
begin
  // if control values changed since form creation
  // then &quot;Apply&quot; button becames enabled,
  // otherwise it stays disabled
  acApply.Enabled :=
    FStateHolder.IsChanged;
end;
}

// ------------------------
// actual unit code follows
// ------------------------
unit ChangeFinder;

interface
uses SysUtils, Classes, Controls, Forms, Contnrs;

type

  IStateHolder = interface
    ['{335B2FA7-678D-4B3B-976A-9D139590575B}']
    procedure SaveState (AComponent: TComponent; PropName: string);
    procedure SaveStatesFor (AForm: TForm; AComponentClass: TComponentClass;
      PropName: string);
    function IsChanged: Boolean;
  end;

function CreateStateHolder: IStateHolder;

implementation
uses TypInfo;

type
  TComponentState = class
  private
    FComponent: TComponent;
    FPropertyName: string;
    FValue: Variant;
  public
    constructor Create (AComponent: TComponent; APropertyName: string); reintroduce;
    property Component: TComponent read FComponent;
    property PropertyName: string read FPropertyName;
    function Equal (Another: TComponentState): Boolean;
  end;

  TStateHolder = class (TInterfacedObject, IStateHolder)
  private
    FList: TObjectList;
  public
    constructor Create;
    destructor Destroy; override;
    procedure SaveState (AComponent: TComponent; PropName: string);
    function IsChanged: Boolean;
    procedure SaveStatesFor (Form: TForm; ComponentClass: TComponentClass;
      PropName: string);
  end;

function CreateStateHolder: IStateHolder;
begin
  Result := TStateHolder.Create
end;

function GetPropertyValue (Component: TComponent; PropertyName: string): Variant;
begin
 if GetPropInfo(Component,PropertyName) = nil then
   raise Exception.CreateFmt ('Property %s not found',[PropertyName]);

 Result := GetPropValue (Component,PropertyName);
end;

constructor TStateHolder.Create;
begin
  inherited Create();
  FList := TComponentList.Create(True);
end;

destructor TStateHolder.Destroy;
begin
  FList.Free;
  inherited;
end;

function TStateHolder.IsChanged: Boolean;
var
  I: Integer;
  State1,
  State2: TComponentState;
begin
  Result := False;
  for I := 0 to FList.Count - 1 do
  begin
    State1 := TComponentState(FList[I]);
    State2 := TComponentState.Create(State1.Component,State1.PropertyName);
    try
       if not State1.Equal(State2) then
       begin
         Result := True;
         Break
       end
    finally
      State2.Free
    end
  end
end;

procedure TStateHolder.SaveState(AComponent: TComponent; PropName: string);
begin
  FList.Add( TComponentState.Create(AComponent,PropName))
end;

procedure TStateHolder.SaveStatesFor(Form: TForm;
  ComponentClass: TComponentClass; PropName: string);
var
  I: Integer;
begin
  for I := 0 to Form.ComponentCount-1 do
    if Form.Components[I] is ComponentClass then
      SaveState (Form.Components[I], PropName)
end;

constructor TComponentState.Create(AComponent: TComponent;
  APropertyName: string);
begin
  inherited Create();

  FValue := GetPropertyValue(AComponent,APropertyName);
  FComponent := AComponent;
  FPropertyName := APropertyName;
end;

function TComponentState.Equal(Another: TComponentState): Boolean;
begin
  Result := (FComponent=Another.FComponent) and
            (FPropertyName=Another.FPropertyName) and
            (FValue=Another.FValue);
end;

end.

&lt;/codeblock&gt;

[[Category:Programming language:Delphi]]</text>
    </revision>
    <revision>
      <id>2961</id>
      <timestamp>2006-03-08T20:12:31Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <minor/>
      <comment>Apply button handling in dialog windows moved to Apply button handling in dialog windows (Delphi)</comment>
      <text xml:space="preserve">Apply button handling in dialog windows.
The purpose of this unit is to automatically control an enabled/disabled state of
&quot;Apply&quot; button in dialog windows.
The main idea is that if certain controls' properties changed from its defaults,
then &quot;Apply&quot; button becomes enabled, otherwise it stays disabled.

&lt;codeblock language=delphi&gt;
&lt;&lt;ChangeFinder.pas&gt;&gt;=

{
Usage.
--------------------------------------
You have dialog form with some controls on it and OK, Cancel, Apply buttons.
Also, place TActionList on the form. Create an action in TActionList
for Apply button and associate it with this button. 

Sample code follows.

uses ..., ChangeFinder;

// This code was generated by IDE for our Form
type
  TForm17 = class(TForm)
    Button1: TButton;
    ActionList1: TActionList;
    acApply: TAction;
    Edit1: TEdit;
    Edit2: TEdit;
    CheckBox1: TCheckBox;
    CheckBox2: TCheckBox;
    procedure ActionList1Update(Action: TBasicAction; var Handled: Boolean);
    procedure FormCreate(Sender: TObject);
    procedure acApplyExecute(Sender: TObject);
  private
    FStateHolder: IStateHolder; // an instance of interface implementation
  end;

  imlpementation

// OnCreate event handler
// Executes once on form instance creation
procedure TForm17.FormCreate(Sender: TObject);
begin
  // Create an instance of state holder
  FStateHolder := CreateStateHolder;

  // Here you may set default values for some controls.
  // Or just set them in Object Inspector at design time.

  with FStateHolder do
  begin
    // Save values of Text property
    // for all TEdit controls (and its descedants) on form
    SaveStatesFor(Self,TEdit,'Text');

    // the same for all TCheckBoxes
    SaveStatesFor(Self,TCheckBox,'Checked');

    // do the same for all other controls' classes

    // or you may use SaveState to save state
    // of individual controls instead of specifying a class
  end;
end;

procedure TForm17.acApplyExecute(Sender: TObject);
begin
  // Place here appropriate code
  // to apply changes made in dialog
end;

// OnUpdate event handler
// Executes when application is idle
procedure TForm17.ActionList1Update(Action: TBasicAction; var Handled: Boolean);
begin
  // if control values changed since form creation
  // then &quot;Apply&quot; button becames enabled,
  // otherwise it stays disabled
  acApply.Enabled :=
    FStateHolder.IsChanged;
end;
}

// ------------------------
// actual unit code follows
// ------------------------
unit ChangeFinder;

interface
uses SysUtils, Classes, Controls, Forms, Contnrs;

type

  IStateHolder = interface
    ['{335B2FA7-678D-4B3B-976A-9D139590575B}']
    procedure SaveState (AComponent: TComponent; PropName: string);
    procedure SaveStatesFor (AForm: TForm; AComponentClass: TComponentClass;
      PropName: string);
    function IsChanged: Boolean;
  end;

function CreateStateHolder: IStateHolder;

implementation
uses TypInfo;

type
  TComponentState = class
  private
    FComponent: TComponent;
    FPropertyName: string;
    FValue: Variant;
  public
    constructor Create (AComponent: TComponent; APropertyName: string); reintroduce;
    property Component: TComponent read FComponent;
    property PropertyName: string read FPropertyName;
    function Equal (Another: TComponentState): Boolean;
  end;

  TStateHolder = class (TInterfacedObject, IStateHolder)
  private
    FList: TObjectList;
  public
    constructor Create;
    destructor Destroy; override;
    procedure SaveState (AComponent: TComponent; PropName: string);
    function IsChanged: Boolean;
    procedure SaveStatesFor (Form: TForm; ComponentClass: TComponentClass;
      PropName: string);
  end;

function CreateStateHolder: IStateHolder;
begin
  Result := TStateHolder.Create
end;

function GetPropertyValue (Component: TComponent; PropertyName: string): Variant;
begin
 if GetPropInfo(Component,PropertyName) = nil then
   raise Exception.CreateFmt ('Property %s not found',[PropertyName]);

 Result := GetPropValue (Component,PropertyName);
end;

constructor TStateHolder.Create;
begin
  inherited Create();
  FList := TComponentList.Create(True);
end;

destructor TStateHolder.Destroy;
begin
  FList.Free;
  inherited;
end;

function TStateHolder.IsChanged: Boolean;
var
  I: Integer;
  State1,
  State2: TComponentState;
begin
  Result := False;
  for I := 0 to FList.Count - 1 do
  begin
    State1 := TComponentState(FList[I]);
    State2 := TComponentState.Create(State1.Component,State1.PropertyName);
    try
       if not State1.Equal(State2) then
       begin
         Result := True;
         Break
       end
    finally
      State2.Free
    end
  end
end;

procedure TStateHolder.SaveState(AComponent: TComponent; PropName: string);
begin
  FList.Add( TComponentState.Create(AComponent,PropName))
end;

procedure TStateHolder.SaveStatesFor(Form: TForm;
  ComponentClass: TComponentClass; PropName: string);
var
  I: Integer;
begin
  for I := 0 to Form.ComponentCount-1 do
    if Form.Components[I] is ComponentClass then
      SaveState (Form.Components[I], PropName)
end;

constructor TComponentState.Create(AComponent: TComponent;
  APropertyName: string);
begin
  inherited Create();

  FValue := GetPropertyValue(AComponent,APropertyName);
  FComponent := AComponent;
  FPropertyName := APropertyName;
end;

function TComponentState.Equal(Another: TComponentState): Boolean;
begin
  Result := (FComponent=Another.FComponent) and
            (FPropertyName=Another.FPropertyName) and
            (FValue=Another.FValue);
end;

end.

&lt;/codeblock&gt;

[[Category:Programming language:Delphi]]</text>
    </revision>
    <revision>
      <id>2979</id>
      <timestamp>2006-03-08T20:46:44Z</timestamp>
      <contributor>
        <username>Joe</username>
        <id>36</id>
      </contributor>
      <minor/>
      <comment>Reformatting sample code</comment>
      <text xml:space="preserve">Apply button handling in dialog windows.
The purpose of this unit is to automatically control an enabled/disabled state of
&quot;Apply&quot; button in dialog windows.
The main idea is that if certain controls' properties changed from its defaults,
then &quot;Apply&quot; button becomes enabled, otherwise it stays disabled.

===Main unit===

&lt;codeblock language=delphi&gt;
&lt;&lt;ChangeFinder.pas&gt;&gt;=

unit ChangeFinder;

interface
uses SysUtils, Classes, Controls, Forms, Contnrs;

type
  IStateHolder = interface
    ['{335B2FA7-678D-4B3B-976A-9D139590575B}']
    procedure SaveState (AComponent: TComponent; PropName: string);
    procedure SaveStatesFor (AForm: TForm; AComponentClass: TComponentClass;
      PropName: string);
    function IsChanged: Boolean;
  end;

function CreateStateHolder: IStateHolder;

implementation
uses TypInfo;

type
  TComponentState = class
  private
    FComponent: TComponent;
    FPropertyName: string;
    FValue: Variant;
  public
    constructor Create (AComponent: TComponent; APropertyName: string); reintroduce;
    property Component: TComponent read FComponent;
    property PropertyName: string read FPropertyName;
    function Equal (Another: TComponentState): Boolean;
  end;

  TStateHolder = class (TInterfacedObject, IStateHolder)
  private
    FList: TObjectList;
  public
    constructor Create;
    destructor Destroy; override;
    procedure SaveState (AComponent: TComponent; PropName: string);
    function IsChanged: Boolean;
    procedure SaveStatesFor (Form: TForm; ComponentClass: TComponentClass;
      PropName: string);
  end;

function CreateStateHolder: IStateHolder;
begin
  Result := TStateHolder.Create
end;

function GetPropertyValue (Component: TComponent; PropertyName: string): Variant;
begin
 if GetPropInfo(Component,PropertyName) = nil then
   raise Exception.CreateFmt ('Property %s not found',[PropertyName]);

 Result := GetPropValue (Component,PropertyName);
end;

constructor TStateHolder.Create;
begin
  inherited Create();
  FList := TComponentList.Create(True);
end;

destructor TStateHolder.Destroy;
begin
  FList.Free;
  inherited;
end;

function TStateHolder.IsChanged: Boolean;
var
  I: Integer;
  State1,
  State2: TComponentState;
begin
  Result := False;
  for I := 0 to FList.Count - 1 do
  begin
    State1 := TComponentState(FList[I]);
    State2 := TComponentState.Create(State1.Component,State1.PropertyName);
    try
       if not State1.Equal(State2) then
       begin
         Result := True;
         Break
       end
    finally
      State2.Free
    end
  end
end;

procedure TStateHolder.SaveState(AComponent: TComponent; PropName: string);
begin
  FList.Add( TComponentState.Create(AComponent,PropName))
end;

procedure TStateHolder.SaveStatesFor(Form: TForm;
  ComponentClass: TComponentClass; PropName: string);
var
  I: Integer;
begin
  for I := 0 to Form.ComponentCount-1 do
    if Form.Components[I] is ComponentClass then
      SaveState (Form.Components[I], PropName)
end;

constructor TComponentState.Create(AComponent: TComponent;
  APropertyName: string);
begin
  inherited Create();

  FValue := GetPropertyValue(AComponent,APropertyName);
  FComponent := AComponent;
  FPropertyName := APropertyName;
end;

function TComponentState.Equal(Another: TComponentState): Boolean;
begin
  Result := (FComponent=Another.FComponent) and
            (FPropertyName=Another.FPropertyName) and
            (FValue=Another.FValue);
end;

end.

&lt;/codeblock&gt;


===Usage===
--------------------------------------
You have dialog form with some controls on it and OK, Cancel, Apply buttons.
Also, place TActionList on the form. Create an action in TActionList
for Apply button and associate it with this button. 

The test unit for main form:
&lt;codeblock language=delphi&gt;
&lt;&lt;Unit17.pas&gt;&gt;=
unit Unit17;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ActnList, StdCtrls, ChangeFinder;

type
  TForm17 = class(TForm)
    Button1: TButton;
    ActionList1: TActionList;
    acApply: TAction;
    Edit1: TEdit;
    Edit2: TEdit;
    CheckBox1: TCheckBox;
    CheckBox2: TCheckBox;
    Button2: TButton;
    Button3: TButton;
    procedure ActionList1Update(Action: TBasicAction; var Handled: Boolean);
    procedure FormCreate(Sender: TObject);
    procedure acApplyExecute(Sender: TObject);
  private
    FStateHolder: IStateHolder; // an instance of interface implementation
  public
  end;

var
  Form17: TForm17;

implementation

{$R *.dfm}

procedure TForm17.acApplyExecute(Sender: TObject);
begin
  //
  // Place appropriate code for apply changes
  //
end;

procedure TForm17.ActionList1Update(Action: TBasicAction; var Handled: Boolean);
begin
  acApply.Enabled :=
    FStateHolder.IsChanged;
end;

procedure TForm17.FormCreate(Sender: TObject);
begin
  // Create an instance of state holder
  FStateHolder := CreateStateHolder;

  //
  // Here you may set default values for some controls.
  // Or just set them in Object Inspector at design time.
  //

  with FStateHolder do
  begin
    // Save values of Text property
    // for all TEdit controls (and its descedants) on form
    SaveStatesFor(Self,TEdit,'Text');

    // the same for all TCheckBoxes
    SaveStatesFor(Self,TCheckBox,'Checked');

    // do the same for all other controls' classes

    // or you may use SaveState to save state
    // of individual controls instead of specifying a class

  end;
end;

end.
&lt;/codeblock&gt;

DFM-file for main form:
&lt;codeblock language=delphi&gt;
&lt;&lt;Unit17.dfm&gt;&gt;=
object Form17: TForm17
  Left = 355
  Top = 349
  Caption = 'Form17'
  ClientHeight = 174
  ClientWidth = 378
  Color = clBtnFace
  Font.Charset = DEFAULT_CHARSET
  Font.Color = clWindowText
  Font.Height = -11
  Font.Name = 'Tahoma'
  Font.Style = []
  OldCreateOrder = False
  OnCreate = FormCreate
  PixelsPerInch = 96
  TextHeight = 13
  object Button1: TButton
    Left = 295
    Top = 141
    Width = 75
    Height = 25
    Action = acApply
    TabOrder = 0
  end
  object Edit1: TEdit
    Left = 16
    Top = 16
    Width = 121
    Height = 21
    TabOrder = 1
    Text = 'Edit1'
  end
  object Edit2: TEdit
    Left = 16
    Top = 43
    Width = 121
    Height = 21
    TabOrder = 2
    Text = 'Edit2'
  end
  object CheckBox1: TCheckBox
    Left = 16
    Top = 70
    Width = 97
    Height = 17
    Caption = 'CheckBox1'
    TabOrder = 3
  end
  object CheckBox2: TCheckBox
    Left = 16
    Top = 93
    Width = 97
    Height = 17
    Caption = 'CheckBox2'
    TabOrder = 4
  end
  object Button2: TButton
    Left = 133
    Top = 141
    Width = 75
    Height = 25
    Caption = 'OK'
    TabOrder = 5
  end
  object Button3: TButton
    Left = 214
    Top = 141
    Width = 75
    Height = 25
    Caption = 'Cancel'
    TabOrder = 6
  end
  object ActionList1: TActionList
    OnUpdate = ActionList1Update
    Left = 200
    Top = 24
    object acApply: TAction
      Caption = 'Apply'
      OnExecute = acApplyExecute
    end
  end
end

&lt;/codeblock&gt;




[[Category:Programming language:Delphi]]</text>
    </revision>
  </page>
  <page>
    <title>Arbitrary-precision elementary mathematical functions (Python)</title>
    <id>1790</id>
    <revision>
      <id>3285</id>
      <timestamp>2006-03-12T23:45:05Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>stub</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponentials and logarithms==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test():
    getcontext().prec = 31
    assert exp(4) == Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == Decimal(&quot;0.0003354626279025118388213891257809&quot;)

&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==</text>
    </revision>
    <revision>
      <id>3287</id>
      <timestamp>2006-03-12T23:46:56Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>cats</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponentials and logarithms==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test():
    getcontext().prec = 31
    assert exp(4) == Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == Decimal(&quot;0.0003354626279025118388213891257809&quot;)

&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3288</id>
      <timestamp>2006-03-12T23:56:04Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>/* Exponentials and logarithms */ another test</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponentials and logarithms==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test():
    getcontext().prec = 31
    assert exp(4) == Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2

&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4158</id>
      <timestamp>2006-04-17T14:37:13Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>add implementation of natural logarithm, in need of more work</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2

&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            print w, a
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4159</id>
      <timestamp>2006-04-17T14:42:14Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>filename</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;hpfuncs.py&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2

&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            print w, a
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4160</id>
      <timestamp>2006-04-17T14:48:17Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>let's see if i can get code blocks to work</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2
&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
&lt;&lt;log series&gt;&gt;=
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
&lt;&lt;log 10 constant&gt;&gt;=
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
&lt;&lt;log main&gt;&gt;=
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
&lt;&lt;test log&gt;&gt;=
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            print w, a
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;log&gt;&gt;=
&lt;&lt;log series&gt;&gt;
&lt;&lt;log 10 constant&gt;&gt;
&lt;&lt;log main&gt;&gt;
&lt;&lt;log test&gt;&gt;
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

==Wrapping it up==
&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;
&lt;&lt;log&gt;&gt;

if __name__ == &quot;__main__&quot;:
    test_exp()
    test_log()

&lt;/codeblock&gt;

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4161</id>
      <timestamp>2006-04-17T14:49:22Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>filename</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2
&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
&lt;&lt;log series&gt;&gt;=
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
&lt;&lt;log 10 constant&gt;&gt;=
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
&lt;&lt;log main&gt;&gt;=
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
&lt;&lt;test log&gt;&gt;=
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            print w, a
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;log&gt;&gt;=
&lt;&lt;log series&gt;&gt;
&lt;&lt;log 10 constant&gt;&gt;
&lt;&lt;log main&gt;&gt;
&lt;&lt;log test&gt;&gt;
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

==Wrapping it up==
&lt;codeblock language=python&gt;
&lt;&lt;hpfunc.py&gt;&gt;=
&lt;&lt;exp&gt;&gt;
&lt;&lt;log&gt;&gt;

if __name__ == &quot;__main__&quot;:
    test_exp()
    test_log()

&lt;/codeblock&gt;

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4162</id>
      <timestamp>2006-04-17T14:50:01Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>/* Natural logarithm */ typo</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2
&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
&lt;&lt;log series&gt;&gt;=
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
&lt;&lt;log 10 constant&gt;&gt;=
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
&lt;&lt;log main&gt;&gt;=
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
&lt;&lt;log test&gt;&gt;=
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            print w, a
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;log&gt;&gt;=
&lt;&lt;log series&gt;&gt;
&lt;&lt;log 10 constant&gt;&gt;
&lt;&lt;log main&gt;&gt;
&lt;&lt;log test&gt;&gt;
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

==Wrapping it up==
&lt;codeblock language=python&gt;
&lt;&lt;hpfunc.py&gt;&gt;=
&lt;&lt;exp&gt;&gt;
&lt;&lt;log&gt;&gt;

if __name__ == &quot;__main__&quot;:
    test_exp()
    test_log()

&lt;/codeblock&gt;

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4163</id>
      <timestamp>2006-04-17T14:51:13Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>/* Natural logarithm */ remove debug print statement</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2
&lt;/codeblock&gt;

==Natural logarithm==

The natural logarithm can be computed using the Mercator series:

:&lt;math&gt;\log x = (x - 1) - \frac{(x-1)^2}{2} + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + \cdots.&lt;/math&gt;

A simple implementation follows:

&lt;codeblock language=python&gt;
&lt;&lt;log series&gt;&gt;=
def logser(x):
    getcontext().prec += 3
    x -= 1
    s = 1
    ns = 0
    n = 1
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
    while abs(s - ns) &gt; eps:
        s = ns
        ns += (-1)**(n+1) * (x**n) / n
        n += 1
    getcontext().prec -= 3
    return s
&lt;/codeblock&gt;

Unfortunately, this series is only convergent when 0 &lt; ''x'' &amp;le; 2. However, it is a simple matter to reduce any argument to this range by dividing a power of 10, using the formula

:&lt;math&gt;\log(10^n x) = n \log 10 + \log x.\,&lt;/math&gt;

(The choice of base 10 is arbitrary, but simplifies calculation with decimals. When binary floating-point arithmetic is used, powers of 2 should be used instead.) Thus we need to be able to calculate the constant log 10 with high precision. This can be done by computing log 0.1, which is simply &amp;minus;log 10, using the series. The following function returns log 10 with the current precision, and caches results to avoid re-computation unless a higher level of precision is sought:

&lt;codeblock language=python&gt;
&lt;&lt;log 10 constant&gt;&gt;=
log10const_cached = Decimal(&quot;2.30259&quot;)
log10const_digits = 5

def log10const():
    global log10const_value, log10const_digits
    if getcontext().prec &lt; log10const_digits:
        return +log10const_value
    else:
        getcontext().prec += 3
        x = -logser(Decimal(&quot;0.1&quot;))
        log10const_value = x
        log10const_digits = getcontext().prec
        getcontext().prec -= 3
        return +x
&lt;/codeblock&gt;

Finally, we implement a log function that reduces its argument to the correct range before evaluating the series, and handles the special cases:

&lt;codeblock language=python&gt;
&lt;&lt;log main&gt;&gt;=
def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    x = Decimal(x)
    n = 0
    # XXX: do this more cleverly
    while x &lt; Decimal(&quot;0.1&quot;):
        x *= 10
        n -= 1
    while x &gt; Decimal(&quot;1&quot;):
        x /= 10
        n += 1
    y = logser(x) + log10const()*n
    getcontext().prec -= 3
    return +y
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
&lt;&lt;log test&gt;&gt;=
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;log&gt;&gt;=
&lt;&lt;log series&gt;&gt;
&lt;&lt;log 10 constant&gt;&gt;
&lt;&lt;log main&gt;&gt;
&lt;&lt;log test&gt;&gt;
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

==Wrapping it up==
&lt;codeblock language=python&gt;
&lt;&lt;hpfunc.py&gt;&gt;=
&lt;&lt;exp&gt;&gt;
&lt;&lt;log&gt;&gt;

if __name__ == &quot;__main__&quot;:
    test_exp()
    test_log()

&lt;/codeblock&gt;

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4313</id>
      <timestamp>2006-04-30T00:08:47Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>ok, screw that. newton's method is about 30x faster (!)</comment>
      <text xml:space="preserve">{{develop}}

The aim of this program is to implement elementary mathematical functions, in particular those all functions in Python's standard math module, for use with the &lt;tt&gt;Decimal&lt;/tt&gt; class. The functions should ideally handle arbitrary precision and always return a correctly rounded result.

==General notes==
To avoid rounding errors, the functions must temporarily increase the working precision for intermediate calculations. This is done by incrementing &lt;tt&gt;getcontext().prec&lt;/tt&gt;. After a calculation has finished, the precision is decremented and the value to be returned is normalized to this precision with &lt;tt&gt;+x&lt;/tt&gt;.

==Exponential function==
The exponential function is most easily calculated from its Taylor series,

:&lt;math&gt;e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots&lt;/math&gt;

&lt;codeblock language=python&gt;
&lt;&lt;exp&gt;&gt;=
from decimal import *

def exp(x):
    getcontext().prec += 3
    if x &lt; 0:
        s = 1 / exp(abs(x))
    else:
        xpower = 1
        ns = 0
        s = 1
        n = 0
        factorial = 1
        while s != ns:
            s = ns
            term = Decimal(xpower) / factorial
            ns = s + term
            xpower *= x
            n += 1
            factorial *= n
    getcontext().prec -= 3
    return +s

def test_exp():
    assert exp(4) == +Decimal(&quot;54.59815003314423907811026120286&quot;)
    assert exp(0) == 1
    assert exp(-8) == +Decimal(&quot;0.0003354626279025118388213891257809&quot;)
    assert exp(Decimal(&quot;0.6931471805599453094172321214582&quot;)) == 2
&lt;/codeblock&gt;

==Natural logarithm==

With the exponential function available, the natural logarithm can be computed easily using Newton's method.

&lt;codeblock language=python&gt;
&lt;&lt;log main&gt;&gt;=
from math import log as _flog

def log(x):
    if x &lt; 0:
        return Decimal(&quot;NaN&quot;)
    if x == 0:
        return Decimal(&quot;-inf&quot;)
    getcontext().prec += 3
    eps = Decimal(&quot;10&quot;)**(-getcontext().prec+2)
    # A good initial estimate is needed
    r = Decimal(repr(_flog(float(x))))
    while 1:
        r2 = r - 1 + x/exp(r)
        if abs(r2-r) &lt; eps:
            break
        else:
            r = r2
    getcontext().prec -= 3
    return +r
&lt;/codeblock&gt;

To test the function, we can calculate the logarithms of a few values and feed them to exp to hopefully obtain the original values. Since two separate operations are performed, a tiny epsilon must be allowed to account for rounding error.

&lt;codeblock language=python&gt;
&lt;&lt;log test&gt;&gt;=
def test_log():
    A = [4, 1, Decimal(&quot;0.67753892&quot;)]
    for p in [5, 40, 28]:
        getcontext().prec = p
        eps = Decimal(&quot;10&quot;)**(-getcontext().prec + 2)
        for a in A:
            w = exp(log(a))
            assert abs(w - a) &lt; eps
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;log&gt;&gt;=
&lt;&lt;log main&gt;&gt;
&lt;&lt;log test&gt;&gt;
&lt;/codeblock&gt;

==Trigonometric functions==

==Hyperbolic functions==

==Constants==

==Wrapping it up==
&lt;codeblock language=python&gt;
&lt;&lt;hpfunc.py&gt;&gt;=
&lt;&lt;exp&gt;&gt;
&lt;&lt;log&gt;&gt;

if __name__ == &quot;__main__&quot;:
    test_exp()
    test_log()

&lt;/codeblock&gt;

[[Category:Arbitrary-precision arithmetic]]
[[Category:Numerical special functions]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Arbitrary-precision integer arithmetic (C)</title>
    <id>2291</id>
    <revision>
      <id>6046</id>
      <timestamp>2006-06-09T02:23:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial article describing addition, subtraction, stubbed out multiplication, shift, and remainder</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/code&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    for(int i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    for(int i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is very similar to addition except that we consider ''all'' pairs of components in the two inputs instead of just ''aligned'' pairs:

&lt;codeblock&gt;
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_mod(integer a, integer b) {
    
}
&lt;/codeblock&gt;

TODO: finish

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6047</id>
      <timestamp>2006-06-09T03:03:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix sup</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    for(int i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    for(int i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is very similar to addition except that we consider ''all'' pairs of components in the two inputs instead of just ''aligned'' pairs:

&lt;codeblock&gt;
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_mod(integer a, integer b) {
    
}
&lt;/codeblock&gt;

TODO: finish

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6048</id>
      <timestamp>2006-06-09T03:46:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Implement multiply</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock&gt;
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            if (lidx &gt;= left.num_components) continue;
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6049</id>
      <timestamp>2006-06-09T03:46:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Multiplication */ language=c</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            if (lidx &gt;= left.num_components) continue;
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6050</id>
      <timestamp>2006-06-09T03:47:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Multiplication */ Don't need continue anymore</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6051</id>
      <timestamp>2006-06-09T03:57:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Files</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BITS */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
#include &quot;integer.h&quot;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6052</id>
      <timestamp>2006-06-09T03:58:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix chunks</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;multiply integer function&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BITS */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6053</id>
      <timestamp>2006-06-09T03:59:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Multiplication */ Match naming pattern</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BITS */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6054</id>
      <timestamp>2006-06-09T04:00:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Malloc header</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* components;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.components = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left[i];
        if (i &lt; right.num_components) partial_sum += right[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right[i];
        result[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left[0]*right[2] + left[1]*right[1] + left[2]*right[0] + the carry from result[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left[lidx])*right[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BITS */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6055</id>
      <timestamp>2006-06-09T04:01:56Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Syntax</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(int i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BITS&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BITS)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BITS */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6056</id>
      <timestamp>2006-06-09T04:04:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Compiler error fixes</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6059</id>
      <timestamp>2006-06-09T08:40:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add set to zero and set result initially to zero in each arithmetic function</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1:

TODO: finish

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6060</id>
      <timestamp>2006-06-09T09:00:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Compare integers, shift left one</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer multiplication&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. The result may be larger than ''n''; if so, a recursive call is made to reduce it again.

TODO: finish

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6061</id>
      <timestamp>2006-06-09T10:02:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Remainder */ Initial implementation</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer multiplication&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2^3 + 2^2 + 2^0
:13 mod ''n'' = ((2^3 mod ''n'') + (2^2 mod ''n'') + (2^0 mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    integer mod_two_power = create_integer(right.num_components + 1);
    int i;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6062</id>
      <timestamp>2006-06-09T10:03:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Remainder */ Syntax</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer multiplication&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    integer mod_two_power = create_integer(right.num_components + 1);
    int i;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6063</id>
      <timestamp>2006-06-09T10:05:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix chunks</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6064</id>
      <timestamp>2006-06-09T10:06:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Kill unused var</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6074</id>
      <timestamp>2006-06-09T17:31:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>&lt;&lt;integer shift left one&gt;&gt;</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
    return 0;
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6075</id>
      <timestamp>2006-06-09T17:32:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Delete copy paste error return</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    set_zero_integer(result);
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    set_zero_integer(result);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6076</id>
      <timestamp>2006-06-09T17:41:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Modify zeroing out in addition/subtraction to allow for target equal to an argument</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6077</id>
      <timestamp>2006-06-09T17:54:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Forgot to reset carry flag</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction will also have this property, but multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6078</id>
      <timestamp>2006-06-09T18:29:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+integer division by a small number</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction will also have this property, but multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = arg.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6079</id>
      <timestamp>2006-06-09T19:00:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Some string conversion stuff and small number multiplication/division</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_10 n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is &lt;math&gt;\ceil{\log_10 n}&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_10 n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(integer x) {
    int result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10));
    /* TODO: finish */
    &lt;&lt;reverse string&gt;&gt;
    return result;
}
&lt;/codeblock&gt;

Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6080</id>
      <timestamp>2006-06-09T19:02:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Conversion to/from string */ Fix math syntax</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder ==

Next, we need a function to find the remainder of an integer after division by another integer. The simplest way to do this is to look at the binary representation of the number. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying heavily on operations we've already written. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(integer x) {
    int result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10));
    /* TODO: finish */
    &lt;&lt;reverse string&gt;&gt;
    return result;
}
&lt;/codeblock&gt;

Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6081</id>
      <timestamp>2006-06-09T19:25:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Finish integer to string, add mod_small_integer</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 1);
    integer ten = create_integer(1);
    ten.s[0] = 10;

    for (i = 0; !is_zero_integer(x); i++) {
        s[i] = (char)mod_small_integer(x, 10) + '0';
        divide_small_integer(x, 10, x);
    }
    s[i] = '\0';

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;
&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6082</id>
      <timestamp>2006-06-09T19:25:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Add conversion chunks to source file</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 1);
    integer ten = create_integer(1);
    ten.s[0] = 10;

    for (i = 0; !is_zero_integer(x); i++) {
        s[i] = (char)mod_small_integer(x, 10) + '0';
        divide_small_integer(x, 10, x);
    }
    s[i] = '\0';

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6083</id>
      <timestamp>2006-06-09T19:30:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Special case zero</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;string to integer conversion&gt;&gt;=
char* string_to_integer(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.s[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            s[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        s[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6084</id>
      <timestamp>2006-06-09T19:33:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Copy paste error</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(result.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.s[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            s[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        s[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6085</id>
      <timestamp>2006-06-09T19:39:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, forgot to finish writing helper function</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= arg.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.s[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.s[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            s[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        s[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6086</id>
      <timestamp>2006-06-09T19:42:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Header, other compiler fixes</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt; right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt; right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt; 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt; 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6087</id>
      <timestamp>2006-06-09T20:55:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Off by one error (we're out of range if equal to the modulus)</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - temp - 1];
    result[result_len - temp - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6088</id>
      <timestamp>2006-06-09T20:57:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix bug</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    return 0;
}
&lt;/codeblock&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6089</id>
      <timestamp>2006-06-09T21:12:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Sample code */ Fill this in</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6090</id>
      <timestamp>2006-06-09T21:37:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix out of bounds access</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        if (i &lt; right.num_components) partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6091</id>
      <timestamp>2006-06-09T21:38:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>One more</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (i &lt; right.num_components &amp;&amp; partial_diff &lt; right.c[i]) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        if (i &lt; right.num_components) partial_diff -= right.c[i];
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= right.c[i]) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6092</id>
      <timestamp>2006-06-09T21:41:24Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Okay, really fix this time</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t partial_diff = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (partial_diff &lt; rhs) {
            borrow = 1;
            partial_diff += MAX_COMPONENT + 1;
        }
        partial_diff -= rhs;
        result.c[i] = partial_diff;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (partial_diff &lt;= rhs) {
        /* leave borrow set to 1 */
        partial_diff += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        partial_diff--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6093</id>
      <timestamp>2006-06-09T21:42:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Subtraction */ Make this clearer</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6094</id>
      <timestamp>2006-06-09T21:44:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Small warning fixes in test main</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset() */
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6095</id>
      <timestamp>2006-06-09T21:59:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+integer copy</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6096</id>
      <timestamp>2006-06-09T22:10:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Shift right one</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6108</id>
      <timestamp>2006-06-09T23:59:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Potential improvements</comment>
      <text xml:space="preserve">{{develop}}

In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6109</id>
      <timestamp>2006-06-09T23:59:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Remove develop - it works, although no division right now</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6114</id>
      <timestamp>2006-06-10T00:45:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix free_integer prototype</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry = (left.num_components-1) + (right.num_components-1);
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left.num_components - 1);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt; right.num_components) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6222</id>
      <timestamp>2006-06-13T09:42:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Improve multiplication time by clipping leading zero components</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6704</id>
      <timestamp>2006-07-11T12:43:11Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Arbitrary-precision integer arithmetic (C)]] moved to [[Arbitrary-precision integer arithmetic (C) on Wheels]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6878</id>
      <timestamp>2006-07-11T14:18:50Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Arbitrary-precision integer arithmetic (C) on Wheels]] moved to [[Arbitrary-precision integer arithmetic (C)]]: revert</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy or rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7039</id>
      <timestamp>2006-07-19T22:43:01Z</timestamp>
      <contributor>
        <ip>81.58.69.2</ip>
      </contributor>
      <comment>/* Shift left/right */ Typo fixed</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7227</id>
      <timestamp>2006-08-11T19:18:23Z</timestamp>
      <contributor>
        <ip>70.230.148.65</ip>
      </contributor>
      <comment>bug in string_to_integer</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13349</id>
      <timestamp>2008-05-14T21:07:04Z</timestamp>
      <contributor>
        <ip>203.162.2.133</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13351</id>
      <timestamp>2008-05-14T23:53:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/203.162.2.133|203.162.2.133]] ([[User_talk:203.162.2.133|203.162.2.133]]); changed back to last version by [[User:70.230.148.65|70.230.148.65]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13676</id>
      <timestamp>2008-06-17T10:46:30Z</timestamp>
      <contributor>
        <ip>221.128.220.155</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13677</id>
      <timestamp>2008-06-17T11:12:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13854</id>
      <timestamp>2008-07-02T23:07:28Z</timestamp>
      <contributor>
        <ip>221.222.38.137</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13856</id>
      <timestamp>2008-07-03T02:42:37Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.222.38.137|221.222.38.137]] ([[User_talk:221.222.38.137|221.222.38.137]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13858</id>
      <timestamp>2008-07-03T05:22:14Z</timestamp>
      <contributor>
        <ip>82.228.204.180</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13860</id>
      <timestamp>2008-07-03T05:23:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/82.228.204.180|82.228.204.180]] ([[User_talk:82.228.204.180|82.228.204.180]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13861</id>
      <timestamp>2008-07-03T16:01:08Z</timestamp>
      <contributor>
        <ip>72.27.197.178</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13862</id>
      <timestamp>2008-07-03T17:38:47Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/72.27.197.178|72.27.197.178]] ([[User_talk:72.27.197.178|72.27.197.178]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13875</id>
      <timestamp>2008-07-05T03:37:08Z</timestamp>
      <contributor>
        <ip>88.159.77.253</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13876</id>
      <timestamp>2008-07-05T04:02:56Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/88.159.77.253|88.159.77.253]] ([[User_talk:88.159.77.253|88.159.77.253]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13877</id>
      <timestamp>2008-07-05T14:47:36Z</timestamp>
      <contributor>
        <ip>92.243.5.31</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13878</id>
      <timestamp>2008-07-05T20:09:23Z</timestamp>
      <contributor>
        <ip>92.243.5.31</ip>
      </contributor>
      <comment>/* Subtraction */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13879</id>
      <timestamp>2008-07-05T22:00:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/92.243.5.31|92.243.5.31]] ([[User_talk:92.243.5.31|92.243.5.31]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13881</id>
      <timestamp>2008-07-06T04:04:58Z</timestamp>
      <contributor>
        <ip>222.255.31.82</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13884</id>
      <timestamp>2008-07-06T13:26:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13891</id>
      <timestamp>2008-07-07T10:09:15Z</timestamp>
      <contributor>
        <ip>125.135.15.181</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13892</id>
      <timestamp>2008-07-07T12:19:54Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13893</id>
      <timestamp>2008-07-07T16:06:58Z</timestamp>
      <contributor>
        <ip>80.251.112.137</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13894</id>
      <timestamp>2008-07-07T17:08:52Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13895</id>
      <timestamp>2008-07-07T21:32:36Z</timestamp>
      <contributor>
        <ip>81.74.236.38</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13897</id>
      <timestamp>2008-07-07T23:42:08Z</timestamp>
      <contributor>
        <ip>222.47.88.14</ip>
      </contributor>
      <comment>/* Subtraction */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13898</id>
      <timestamp>2008-07-08T03:40:52Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Revert to last version by 213.31.11.24</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13899</id>
      <timestamp>2008-07-08T04:29:07Z</timestamp>
      <contributor>
        <ip>123.236.166.45</ip>
      </contributor>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

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== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13900</id>
      <timestamp>2008-07-08T04:47:50Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16868</id>
      <timestamp>2010-09-23T13:17:16Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">I drove my tractor through your haystack last night
I threw me pitch fork at your dog to keep quiet
Now something's telling me that you've avoiding me,
Come on now darling,
You got something i need.

(Chorus)

'Cause I got a brand new combine harvester and I'll give you the key
Come on now, let's get together
In perfect harmony
I got 20 acres and you got 43
Now I got a brand new combine harvester and I'll give you the key.

She might well laugh.

I'll stick by you and give you all that you need
We'll have twins and triplets
I'm a man built for speed
And you know I'll love you darling
So give me your hand
Oh, the thing I want the most is all that acres of land.

(Chorus)

For seven long years I've been alone in this place
Pigs sleep in the kitchen
It's a proper disgrace
Now if I cleaned it up, would you change your mind?
I'll give up drinking Scrumpy
And that lager and lime.

Course.

Who loves you baby?

Weren't we a grand couple at that last Wurzel dance?
I wore brand new gaiters and me corduroy pants
In your new Sunday dress
With your perfume smelling grand
We had our photos taken, us holding hands.

Now I got a brand new combine harvester and I'll give you the key
Now that we're both past our 50's I think that you and me should stop this gallivanting
And will you marry me?
'Cause I got a brand new combine harvester and I'll give you the key.

Arr, you're a fine looking woman
And I can't wait to get me hands on your land.

You're a fine looking woman.</text>
    </revision>
    <revision>
      <id>16902</id>
      <timestamp>2010-09-23T15:50:04Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">In many applications in number theory and other areas, it's convenient to be able to perform simple arithmetic operations (addition, subtraction, multiplication, division, remainder) on arbitrarily large integers. This article describes some very simple algorithms for computing these in C.

We will represent our datatype with a structure &lt;code&gt;integer&lt;/code&gt; that encodes large integers as arrays of unsigned 16-bit integers, with the least significant component first:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned short component_t;
typedef unsigned long double_component_t;

&lt;&lt;integer type&gt;&gt;=
typedef struct {
    component_t* c;    /* least-significant word first */
    int num_components;
} integer;

&lt;&lt;prototypes&gt;&gt;=
integer create_integer(int components);
&lt;&lt;integer constructor&gt;&gt;=
integer create_integer(int components) {
    integer result;
    result.num_components = components;
    result.c = (component_t*)malloc(sizeof(component_t)*components);
    return result;
}

&lt;&lt;prototypes&gt;&gt;=
void free_integer(integer i);
&lt;&lt;integer destructor&gt;&gt;=
void free_integer(integer i) {
    free(i.c);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* for malloc() */
&lt;/codeblock&gt;

The precise definition of a component_t may vary from platform to platform, but a short is guaranteed to be at least 16 bits. Why do we use 16-bit components? Because to perform our operations efficiently we need a datatype &lt;code&gt;double_component_t&lt;/code&gt; twice as wide as the component datatype, and C does not guarantee that any 64-bit integer datatype is supplied. On platforms supporting these, it is only necessary to modify the typedefs.

We'll find this small function helpful, which zeros out an integer using &lt;code&gt;memset()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void set_zero_integer(integer i);
&lt;&lt;integer set to zero&gt;&gt;=
void set_zero_integer(integer i) {
    memset(i.c, 0, sizeof(component_t)*i.num_components);
}

&lt;&lt;header files&gt;&gt;=
#include &lt;string.h&gt;   /* for memset(), memmove() */
&lt;/codeblock&gt;

Similar is the function for copying an integer, which has the slight
complication that it must either truncate or zero-extend if the lengths differ:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void copy_integer(integer source, integer target);
&lt;&lt;integer copy&gt;&gt;=
void copy_integer(integer source, integer target) {
    memmove(target.c, source.c,
            sizeof(component_t)*MIN(source.num_components, target.num_components));
    if (target.num_components &gt; source.num_components) {
        memset(target.c + source.num_components, 0,
               sizeof(component_t)*(target.num_components - source.num_components));
    }
}
&lt;/codeblock&gt;

== Addition ==

We can now define an addition function; this is the same addition used in grade-school methods, except that we're working with digits in base 2&lt;sup&gt;16&lt;/sup&gt; (the components of the number). Keep in mind that the least significant component is at index zero. To avoid unnecessary costly allocations, the structure for the result is passed in to the method, and must have at least one more component than the larger of the two inputs to prevent overflow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void add_integer(integer left, integer right, integer result);
&lt;&lt;integer addition&gt;&gt;=
void add_integer(integer left, integer right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || i&lt;right.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i];
        if (i &lt; right.num_components) partial_sum += right.c[i];
        if (partial_sum &gt; MAX_COMPONENT) {
            partial_sum &amp;= MAX_COMPONENT;
            carry = 1;
        }
        result.c[i] = (component_t)partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

We must be careful to account for the case where either number is shorter, or where there is a carry beyond the end of both input numbers. MAX_COMPONENT is the maximum value of a component, which we define using a trick with &amp;minus;1 that works for unsigned types:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define MAX_COMPONENT  ((component_t)(-1))
&lt;/codeblock&gt;

The above implementation also has the useful property that, because we never read index ''i'' of either input after writing index ''i'' of the result, we can specify the same integer for the result as for one of the inputs. Subtraction and multiplication by a small number will also have this property, but full multiplication will not.

== Subtraction ==

For subtraction we again use the grade school method, but this is a bit trickier because borrowing is involved. If we find ourselves trying to subtract a larger component from a smaller component, we have to borrow:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void subtract_integer(integer left, integer right, integer result);
&lt;&lt;integer subtraction&gt;&gt;=
void subtract_integer(integer left, integer right, integer result) {
    int borrow = 0;
    int i;
    for(i=0; i&lt;left.num_components; i++) {
        double_component_t lhs = left.c[i];
        double_component_t rhs = (i &lt; right.num_components) ? right.c[i] : 0;
        &lt;&lt;deal with borrowing from previous step&gt;&gt;
        if (lhs &lt; rhs) {
            borrow = 1;
            lhs += MAX_COMPONENT + 1;
        }
        result.c[i] = lhs - rhs;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

When we borrow, we just set a flag. When we reach the next step, we try to subtract one from &lt;code&gt;partial_diff&lt;/code&gt; for the borrow. If &lt;code&gt;left.c[i]&lt;/code&gt;&amp;nbsp;&amp;le;&amp;nbsp;&lt;code&gt;right.c[i]&lt;/code&gt; however, this will require another borrow from the next step up:

&lt;codeblock language=c&gt;
&lt;&lt;deal with borrowing from previous step&gt;&gt;=
if (borrow) {
    if (lhs &lt;= rhs) {
        /* leave borrow set to 1 */
        lhs += (MAX_COMPONENT + 1) - 1;
    } else {
        borrow = 0;
        lhs--;
    }
}
&lt;/codeblock&gt;

== Multiplication by a small number ==

Multiplying by a small number, no larger than one component, is straightforward. We multiply by each component, set the result to the low &lt;code&gt;COMPONENT_BITS&lt;/code&gt; bits, and add the higher bits to the next component as carry:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer multiplication by a small number&gt;&gt;=
void multiply_small_integer(integer left, component_t right, integer result) {
    double_component_t carry = 0;
    int i;
    for(i=0; i&lt;left.num_components || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        if (i &lt; left.num_components)  partial_sum += left.c[i]*right;
        carry = partial_sum &gt;&gt; COMPONENT_BITS;
        result.c[i] = (component_t)(partial_sum &amp; MAX_COMPONENT);
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

== Multiplication ==

The multiplication algorithm is again based on grade-school algorithms, and is similar to addition. As in addition, we compute the columns of the result right-to-left, and any carry from a column is added to the next column to its left. However, the numbers we're adding are different: to get these numbers, we must multiply components of the input number whose indexes add to a fixed value. For example, the component &lt;code&gt;result.c[2]&lt;/code&gt; is given by the low 16 bits of this expression:

:&lt;code&gt;left.c[0]*right.c[2] + left.c[1]*right.c[1] + left.c[2]*right.c[0] + the carry from result.c[1]&lt;/code&gt;

Notice that in all these products, the indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; add to 2.

The code works by first fixing the result column index and then iterating over all possible pairs of indexes into &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt; that sum to that index - the bounds are a bit tricky and depend on the sizes of &lt;code&gt;left&lt;/code&gt; and &lt;code&gt;right&lt;/code&gt;. Also, because the multiplications above produce double-size values, we must separate out the upper half often to prevent overflow.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void multiply_integer(integer left, integer right, integer result);
&lt;&lt;integer multiplication&gt;&gt;=
void multiply_integer(integer left, integer right, integer result) {
    int i, lidx, ridx;
    double_component_t carry = 0;
    int max_size_no_carry;
    int left_max_component  = left.num_components - 1;
    int right_max_component = right.num_components - 1;
    &lt;&lt;minimize max component indexes&gt;&gt;
    max_size_no_carry = left_max_component + right_max_component;
    for(i=0; i &lt;= max_size_no_carry || carry != 0; i++) {
        double_component_t partial_sum = carry;
        carry = 0;
        lidx = MIN(i, left_max_component);
        ridx = i - lidx;
        while(lidx &gt;= 0 &amp;&amp; ridx &lt;= right_max_component) {
            partial_sum += ((double_component_t)left.c[lidx])*right.c[ridx];
            carry += partial_sum &gt;&gt; COMPONENT_BITS;
            partial_sum &amp;= MAX_COMPONENT;
            lidx--; ridx++;
        }
        result.c[i] = partial_sum;
    }
    for ( ; i &lt; result.num_components; i++) { result.c[i] = 0; }
}
&lt;/codeblock&gt;

Above, &lt;code&gt;COMPONENT_BITS&lt;/code&gt; is the number of bits in a component, which can be computed at compile time using &lt;code&gt;sizeof&lt;/code&gt; and &lt;code&gt;CHAR_BIT&lt;/code&gt;, since C guarantees &lt;code&gt;sizeof(char) == 1&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define COMPONENT_BITS  (sizeof(component_t)*CHAR_BIT)

&lt;&lt;type definition headers&gt;&gt;=
#include &lt;limits.h&gt;  /* for CHAR_BIT */
&lt;/codeblock&gt;

&lt;code&gt;MIN()&lt;/code&gt; is just the obvious macro finding the minimum of two side-effect free expressions, which we use to ensure that &lt;code&gt;lidx&lt;/code&gt; is in range at the beginning of the loop. We similarly define MAX, which we'll use later.

&lt;codeblock language=c&gt;
&lt;&lt;macros&gt;&gt;=
#define MIN(x,y)  ((x)&lt;(y) ? (x) : (y))
#define MAX(x,y)  ((x)&gt;(y) ? (x) : (y))
&lt;/codeblock&gt;

Since the time required increases rapidly as we add more components, we want to ensure the max left and right component indexes are as small as possible. We do this by ignoring leading zero components, pointing the indexes at the most significant nonzero component:

&lt;codeblock language=c&gt;
&lt;&lt;minimize max component indexes&gt;&gt;=
while(left.c[left_max_component]   == 0) left_max_component--;
while(right.c[right_max_component] == 0) right_max_component--;
&lt;/codeblock&gt;

== Comparison operator ==

It's helpful in many algorithms to be able to determine whether an integer is less than, equal to, or greater than another integer. Much like comparing strings, we simply compare the integers lexicographically by their components, starting with the most significant component. Any components beyond the end of an integer are treated as zero.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int compare_integers(integer left, integer right);
&lt;&lt;integer comparison&gt;&gt;=
int compare_integers(integer left, integer right) {
    int i = MAX(left.num_components - 1, right.num_components - 1);
    for ( ; i &gt;= 0; i--) {
        component_t left_comp =
            (i &lt; left.num_components) ? left.c[i] : 0;
        component_t right_comp =
            (i &lt; right.num_components) ? right.c[i] : 0;
        if (left_comp &lt; right_comp)
            return -1;
        else if (left_comp &gt; right_comp)
            return  1;
    }
    return 0;
}
&lt;/codeblock&gt;

Like the comparators passed to library routines like &lt;code&gt;qsort()&lt;/code&gt;, we return a negative, zero, or positive value depending on whether &lt;code&gt;left&lt;/code&gt; is less than, equal to, or greater than &lt;code&gt;right&lt;/code&gt;, respectively.

== Shift left/right ==

Performing a bit shift on a larger integer is handy for rapidly multiplying or dividing it by a power of 2. The easiest operation is shifting left by 1. We shift each component left by one, but also make sure to propagate the high bit of each component into the low bit of the next component up. In this implementation we discard the highest bit.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_left_one_integer(integer arg);
&lt;&lt;integer shift left one&gt;&gt;=
void shift_left_one_integer(integer arg) {
    int i;
    arg.c[arg.num_components - 1] &lt;&lt;= 1;
    for (i = arg.num_components - 2; i &gt;= 0; i--) {
        arg.c[i + 1] |= arg.c[i] &gt;&gt; (COMPONENT_BITS - 1);
        arg.c[i] &lt;&lt;= 1;
    }
}
&lt;/codeblock&gt;

Shifting right by one is similar, but propagating from the lowest to the highest bit and moving right to left instead of left to right:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void shift_right_one_integer(integer arg);
&lt;&lt;integer shift right one&gt;&gt;=
void shift_right_one_integer(integer arg) {
    int i;
    arg.c[0] &gt;&gt;= 1;
    for (i = 1; i &lt; arg.num_components; i++) {
        arg.c[i - 1] |= (arg.c[i] &amp; 1) &lt;&lt; (COMPONENT_BITS - 1);
        arg.c[i] &gt;&gt;= 1;
    }
}
&lt;/codeblock&gt;

== Remainder with a small divisor ==

Next, we need a function to find the remainder of an integer after division by a small divisor, no larger than one component. The simplest way to do this is to look at the binary representation of the dividend. This expresses it as a sum of powers of 2. For example, for 13 we have:

:13 = 1101&lt;sub&gt;2&lt;/sub&gt; = 2&lt;sup&gt;3&lt;/sup&gt; + 2&lt;sup&gt;2&lt;/sup&gt; + 2&lt;sup&gt;0&lt;/sup&gt;
:13 mod ''n'' = ((2&lt;sup&gt;3&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;2&lt;/sup&gt; mod ''n'') + (2&lt;sup&gt;0&lt;/sup&gt; mod ''n'')) mod ''n''

Here we're using &quot;mod&quot; in the sense of &quot;remainder&quot;. As it turns out, computing the sequence &lt;math&gt;2^i&lt;/math&gt; mod ''n'' is relatively easy:
* Start with ''k''=1. Multiply ''k'' by 2 repeatedly (we can effect this with &lt;code&gt;shift_left_integer&lt;/code&gt;).
* If ever ''k'' &amp;ge; ''n'',  subtract ''n'' from ''k'' (using &lt;code&gt;subtract_integer&lt;/code&gt;).
This works because if ''k'' &lt; ''n'', it follows that 2''k'' &lt; 2''n'', and so we cannot subtract out more than one ''n''. This doesn't work for larger bases. As we produce the sequence, we add together the sum of powers of 2 above. Since each value we add is also less than ''n'', by subtracting ''n'' whenever the value exceeds ''n'' the result will be less than ''n''.

Here's some C code for this algorithm, relying on operations we've already written.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
component_t mod_small_integer(integer left, component_t right);
&lt;&lt;integer remainder with a small divisor&gt;&gt;=
component_t mod_small_integer(integer left, component_t right) {
    double_component_t mod_two_power = 1;
    double_component_t result = 0;
    int i, bit;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                result += mod_two_power;
                if (result &gt;= right) {
                    result -= right;
                }
            }
            mod_two_power &lt;&lt;= 1;
            if (mod_two_power &gt;= right) {
                mod_two_power -= right;
            }
        }
    }
    return (component_t)result;
}
&lt;/codeblock&gt;

== Remainder ==

Generalizing the above to a remainder by a large integer is straightforward, just replacing some of the component-sized operations with previously implemented arbitrary-precision operations. Note that we assume for convenience that result has one more component than &lt;code&gt;right&lt;/code&gt;, the modulus.

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void mod_integer(integer left, integer right, integer result);
&lt;&lt;integer remainder&gt;&gt;=
void mod_integer(integer left, integer right, integer result) {
    integer mod_two_power = create_integer(right.num_components + 1);
    int i, bit;
    set_zero_integer(result);
    set_zero_integer(mod_two_power);
    mod_two_power.c[0] = 1;
    for(i=0; i&lt;left.num_components; i++) {
        for(bit=0; bit&lt;COMPONENT_BITS; bit++) {
            if ((left.c[i] &amp; (1 &lt;&lt; bit)) != 0) {
                add_integer(result, mod_two_power, result);
                if (compare_integers(result, right) &gt;= 0) {
                    subtract_integer(result, right, result);
                }
            }
            shift_left_one_integer(mod_two_power);
            if (compare_integers(mod_two_power, right) &gt;= 0) {
                subtract_integer(mod_two_power, right, mod_two_power);
            }
        }
    }
    free_integer(mod_two_power);
}
&lt;/codeblock&gt;

== Division by a small number ==

Dividing by a small number, the size of one component, is simple using the grade-school method of division. We simply proceed left-to-right, dividing each component by the divisor. The quotient becomes the corresponding component of the result, and the remainder becomes the high 16 bits of the dividend in the next component's division:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result);
&lt;&lt;integer division by a small number&gt;&gt;=
void divide_small_integer(integer left, component_t right, integer result) {
    double_component_t dividend = 0;
    int i;
    for (i = left.num_components - 1; i &gt;= 0; i--) {
        dividend |= left.c[i];
        result.c[i] = dividend/right;
        dividend = (dividend % right) &lt;&lt; COMPONENT_BITS;
    }
}
&lt;/codeblock&gt;

== Conversion to/from string ==

Producing an integer from a decimal string is a simple matter of repeatedly alternating between multiplying by 10 and adding the next digit. To determine how many components we need, we use this formula, where ''b'' is &lt;code&gt;COMPONENT_BITS&lt;/code&gt;:

:&lt;math&gt;\log_{2^b} n = (\log_2 10 \cdot \log_{10} n)/b&lt;/math&gt;

This follows from basic laws of exponents. Noting that the string length is the ceiling of &lt;math&gt;\log_{10} n&lt;/math&gt;, this allows us to find a fairly tight upper bound on &lt;math&gt;\log_{2^b} n&lt;/math&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
integer string_to_integer(char* s);
&lt;&lt;string to integer conversion&gt;&gt;=
integer string_to_integer(char* s) {
    integer result = create_integer((int)ceil(LOG_2_10*strlen(s)/COMPONENT_BITS));
    set_zero_integer(result);
    integer digit = create_integer(1);
    int i;
    for (i = 0; s[i] != '\0'; i++) {
        multiply_small_integer(result, 10, result);
        digit.c[0] = s[i] - '0';
        add_integer(result, digit, result);
    }
    free_integer(digit);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for ceil */
&lt;/codeblock&gt;

The constant &lt;code&gt;LOG_2_10&lt;/code&gt; is precomputed:

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define LOG_2_10    3.3219280948873623478703194294894
&lt;/codeblock&gt;

To convert in the other direction, we alternate between dividing by 10 and using modulus to extract the next digit, making a special case for zero. To determine how large a string to allocate we rearrange the formula above to obtain:

:&lt;math&gt;\log_{10} n = (b\log_{2^b} n)/(\log_2 10)&lt;/math&gt;

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
char* integer_to_string(integer x);
&lt;&lt;integer to string conversion&gt;&gt;=
char* integer_to_string(integer x) {
    int i, result_len;
    char* result =
        (char*)malloc((int)ceil(COMPONENT_BITS*x.num_components/LOG_2_10) + 2);
    integer ten = create_integer(1);
    ten.c[0] = 10;

    if (is_zero_integer(x)) {
        strcpy(result, &quot;0&quot;);
    } else {
        for (i = 0; !is_zero_integer(x); i++) {
            result[i] = (char)mod_small_integer(x, 10) + '0';
            divide_small_integer(x, 10, x);
        }
        result[i] = '\0';
    }

    &lt;&lt;reverse string&gt;&gt;

    free_integer(ten);
    return result;
}
&lt;/codeblock&gt;

This particular implementation destroys the integer x in the process, to avoid copying. Since the digits are extracted in reverse order, we must reverse the string at the end to get the usual printing order:

&lt;codeblock language=c&gt;
&lt;&lt;reverse string&gt;&gt;=
result_len = strlen(result);
for(i=0; i &lt; result_len/2; i++) {
    char temp = result[i];
    result[i] = result[result_len - i - 1];
    result[result_len - i - 1] = temp;
}
&lt;/codeblock&gt;

The helper function &lt;code&gt;is_zero_integer&lt;/code&gt; tests whether an integer is zero by comparing each component to zero:

&lt;codeblock language=c&gt;
&lt;&lt;prototypes&gt;&gt;=
int is_zero_integer(integer x);
&lt;&lt;test if integer is zero&gt;&gt;=
int is_zero_integer(integer x) {
    int i;
    for(i=0; i &lt; x.num_components; i++) {
        if (x.c[i] != 0) return 0;
    }
    return 1;
}
&lt;/codeblock&gt;

== Files ==

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
#ifndef _INTEGER_H_
#define _INTEGER_H_

&lt;&lt;type definition headers&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;

&lt;&lt;macros&gt;&gt;

&lt;&lt;integer type&gt;&gt;

&lt;&lt;prototypes&gt;&gt;

#endif /* #ifndef _INTEGER_H_ */
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;integer.h&quot;

&lt;&lt;integer constructor&gt;&gt;

&lt;&lt;integer destructor&gt;&gt;

&lt;&lt;integer set to zero&gt;&gt;

&lt;&lt;test if integer is zero&gt;&gt;

&lt;&lt;integer copy&gt;&gt;

&lt;&lt;integer addition&gt;&gt;

&lt;&lt;integer subtraction&gt;&gt;

&lt;&lt;integer multiplication by a small number&gt;&gt;

&lt;&lt;integer multiplication&gt;&gt;

&lt;&lt;integer comparison&gt;&gt;

&lt;&lt;integer shift left one&gt;&gt;

&lt;&lt;integer shift right one&gt;&gt;

&lt;&lt;integer remainder with a small divisor&gt;&gt;

&lt;&lt;integer remainder&gt;&gt;

&lt;&lt;integer division by a small number&gt;&gt;

&lt;&lt;string to integer conversion&gt;&gt;

&lt;&lt;integer to string conversion&gt;&gt;

&lt;/codeblock&gt;

== Sample code ==

This sample code allows a user to interactively use several of the functions above, as well as some new ones built using them. It also incidentally stresses a number of other functions through string conversion, which depends on mod, which in turn depends on several others.

&lt;codeblock language=c&gt;
&lt;&lt;integer_sample.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;  /* for atoi */
#include &quot;integer.h&quot;

int main(int argc, char* argv[]) {
    integer a1, a2, result;
    a1.num_components = a2.num_components = 0; /* quelch compiler warnings */
    if (argc &gt; 2) a1 = string_to_integer(argv[2]);
    if (argc &gt; 3) a2 = string_to_integer(argv[3]);
    if (strcmp(argv[1], &quot;add&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        add_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;subtract&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        subtract_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;multiply&quot;) == 0) {
        result = create_integer(a1.num_components + a2.num_components + 1);
        multiply_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;mod&quot;) == 0) {
        result = create_integer(a2.num_components + 1);
        mod_integer(a1, a2, result);
    } else if (strcmp(argv[1], &quot;factorial&quot;) == 0) {
        int i, n = atoi(argv[2]);
        result = create_integer(n*n + 1);
        set_zero_integer(result);
        result.c[0] = 1;
        for(i=2; i&lt;=n; i++) {
            multiply_small_integer(result, i, result);
        }
    }
    puts(integer_to_string(result));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample input and output (some lines have been split using \ for readability):

&lt;pre&gt;
$ ./integer_sample add 5000000000000 4000000000000
9000000000000
$ ./integer_sample subtract 5000000000000 4000000000000
1000000000000
$ ./integer_sample multiply 123456789 987654321
121932631112635269
$ ./integer_sample factorial 100
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000
&lt;/pre&gt;

== Potential improvements ==

Although simple, the algorithms described in this article are too inefficient for very large numbers with millions of digits. There are a number of better multiplication algorithms, the most well known of which runs in O(''n'' log ''n'') time and is based on the Fast Fourier Transform. The addition and subtraction algorithms are hard to beat on a single processor, but these implementations parallelize poorly. Finally, the modulus depends on many integer-size computations, and could be written more efficiently in terms of component-sized operations like the others.

[[Category:Arbitrary-precision integer arithmetic]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Asian Option Pricing (MATLAB)</title>
    <id>2162</id>
    <revision>
      <id>5102</id>
      <timestamp>2006-05-23T06:59:49Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

%---------------------------------------------------
%---Description of PDE---
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

%---Initial Condition---
function u0 = pdeic(x)
u0 = max(x, 0);

%---Boundary Condition---
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>5104</id>
      <timestamp>2006-05-23T07:05:37Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

%---------------------------------------------------
%---Description of PDE---
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

%---Initial Condition---
function u0 = pdeic(x)
u0 = max(x, 0);

%---Boundary Condition---
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5105</id>
      <timestamp>2006-05-23T07:06:31Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

%---------------------------------------------------
%---Description of PDE---
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

%---Initial Condition---
function u0 = pdeic(x)
u0 = max(x, 0);

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5106</id>
      <timestamp>2006-05-23T07:08:01Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5107</id>
      <timestamp>2006-05-23T07:09:55Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5108</id>
      <timestamp>2006-05-23T07:10:52Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5109</id>
      <timestamp>2006-05-23T07:12:12Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The MAtlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5110</id>
      <timestamp>2006-05-23T07:13:03Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5111</id>
      <timestamp>2006-05-23T07:35:03Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5112</id>
      <timestamp>2006-05-23T07:38:47Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
global vol r T;
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5113</id>
      <timestamp>2006-05-23T07:44:21Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Description of PDE */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5114</id>
      <timestamp>2006-05-23T07:44:30Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Initial Condition */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5115</id>
      <timestamp>2006-05-23T07:44:39Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Boundary Condition */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5116</id>
      <timestamp>2006-05-23T07:44:51Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function asiancontinuous(S0,K,r,vol,T)

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5117</id>
      <timestamp>2006-05-23T08:00:47Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5118</id>
      <timestamp>2006-05-23T08:01:22Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Boundary Condition */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 


%%%%%%%%%%%%%%%%%%% MESH %%%%%%%%%%%%%%%%%%%%%%%

N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5119</id>
      <timestamp>2006-05-23T08:02:34Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems.

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5120</id>
      <timestamp>2006-05-23T08:03:24Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5121</id>
      <timestamp>2006-05-23T08:04:54Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5122</id>
      <timestamp>2006-05-23T08:06:00Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Main function */</comment>
      <text xml:space="preserve">{{develop}}

__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5123</id>
      <timestamp>2006-05-23T08:07:59Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Use of the pricing function==

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5125</id>
      <timestamp>2006-05-23T08:13:04Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Use of the pricing function */</comment>
      <text xml:space="preserve">__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Use of the pricing function==

[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5126</id>
      <timestamp>2006-05-23T08:13:46Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5127</id>
      <timestamp>2006-05-23T08:14:49Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used too.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5129</id>
      <timestamp>2006-05-23T09:01:33Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Comute price value */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Comute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5130</id>
      <timestamp>2006-05-23T09:01:44Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Comupte price value */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5131</id>
      <timestamp>2006-05-23T09:03:32Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Plot function */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how MAtlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>5132</id>
      <timestamp>2006-05-23T09:03:43Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Plot function */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:Matlab]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7445</id>
      <timestamp>2006-08-21T16:48:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Category:Programming language:MATLAB]]</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7491</id>
      <timestamp>2006-08-26T02:54:01Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <minor/>
      <comment>[[Asian Option Pricing (Matlab)]] moved to [[Asian Option Pricing (MATLAB)]]</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==Matlab function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The Matlab [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7495</id>
      <timestamp>2006-08-26T02:54:39Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>/* Matlab function for pricing */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==MATLAB function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with matlab===

The MATLAB [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7496</id>
      <timestamp>2006-08-26T02:55:45Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>/* PDE Solving with matlab */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==MATLAB function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with MATLAB===

The MATLAB [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The Matlab [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7497</id>
      <timestamp>2006-08-26T02:55:57Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>/* Compute price value */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==MATLAB function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with MATLAB===

The MATLAB [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The MATLAB [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how Matlab embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7498</id>
      <timestamp>2006-08-26T02:56:08Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>/* Plot function */</comment>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==MATLAB function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with MATLAB===

The MATLAB [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The MATLAB [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how MATLAB embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7915</id>
      <timestamp>2006-11-05T06:52:58Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">[[Image:Asiancontinuous.png|thumb|right|Plot of internal values of asiancontinuous]]__TOC__

Here is the [[Asian Option Pricing (Matlab)|MATLAB implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 (some minor changes have been made by [[USer:Lehalle|Charles-Albert Lehalle]]).

==Use of the pricing function==

This function is easy to use, it returns the price of the option and the way to plot some internal results.

&lt;codeblock language=matlab&gt;
&lt;&lt;test_asiancontinuous.m&gt;&gt;=
[price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
pde_sol.plot()
&lt;/codeblock&gt;

The result of the last line is quite simple (see figure).

==MATLAB function for pricing==

===Main function===

&lt;codeblock language=matlab&gt;
&lt;&lt;asiancontinuous.m&gt;&gt;=
function [price, pde_sol] = asiancontinuous(S0,K,r,vol,T)
% ASIANCONTINUOUS - implementation of Vecer's PDE Method for Asion Option
% Pricing, minor modifications by Charles-Albert Lehalle.
% use:
% [price, pde_sol] = asiancontinuous(100, 110, .04, .12, .5)
% pde_sol.plot()

%Implementation of Vecer's PDE Method
%Vecer, J. (2002): &quot;Unified Asian Pricing&quot;,  Risk, Vol. 15, No. 6, 113-116 

&lt;&lt;mesh building&gt;&gt;

&lt;&lt;solve pde&gt;&gt;

&lt;&lt;price value&gt;&gt;

fprintf( '\n\nPrice of Asian Option is %8.6f\n\n', price);

&lt;&lt;description of PDE&gt;&gt;

&lt;&lt;initial condition&gt;&gt;

&lt;&lt;boundary condition&gt;&gt;

&lt;&lt;plot function&gt;&gt;

end
&lt;/codeblock&gt;

===PDE Solving with MATLAB===

The MATLAB [http://www.mathworks.com.au/access/helpdesk/help/techdoc/ref/pdepe.html pdepe function] is used to solve parabolic-elliptic initial-boundary value problems. 

&lt;codeblock language=matlab&gt;
&lt;&lt;solve pde&gt;&gt;=
m = 0;
sol = pdepe(m, @pdef, @pdeic, @pdebc, x, t);
pde_sol = struct('x', x, 't', t, 'u', sol(:,:,1), 'plot', @plot_sol);
&lt;/codeblock&gt;

===Mesh building===

&lt;codeblock language=matlab&gt;
&lt;&lt;mesh building&gt;&gt;=
N = 200;       %number of subintervals in space 
M = 200;       %number of subintervals in time

%more points -&gt; higher precision, but slower

%Xmesh  x
xmin = -1;
xmax = 1;
x = linspace(xmin, xmax, N+1);

%Tspan
t = linspace(0, T, M+1);
&lt;/codeblock&gt;

===Description of PDE===

&lt;codeblock language=matlab&gt;
&lt;&lt;description of PDE&gt;&gt;=
function [c, f, s] = pdef(x, t, u, DuDx)
c = 1;

    f = 0.5*vol^2*( (1-exp(-r*t))/(r*T) - x )^2*DuDx;
    s = vol^2*((1-exp(-r*t))/(r*T) - x)*DuDx;

end
&lt;/codeblock&gt;

===Initial Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;initial condition&gt;&gt;=
function u0 = pdeic(x)
u0 = max(x, 0);
end
&lt;/codeblock&gt;

===Boundary Condition===

&lt;codeblock language=matlab&gt;
&lt;&lt;boundary condition&gt;&gt;=
function [pl, ql, pr, qr] = pdebc(xl, ul, xr, ur, t)
pl = ul;
ql = 0;
pr = ur - xr;
qr = 0;
end
&lt;/codeblock&gt;

===Compute price value===

The MATLAB [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdeval.html pdeval] function is used here.

&lt;codeblock language=matlab&gt;
&lt;&lt;price value&gt;&gt;=
%Output of the value of the option
X_0 = (1-exp(-r*T))*S0/r/T - exp(-r*T)*K;
x0 = X_0/S0;

uout = pdeval(m,x,sol(M+1,:),x0);
price = uout*S0;
&lt;/codeblock&gt;

===Plot function===

You can see here how MATLAB embedded functions can be used to implicitly create some internal variables (here the |pde_sol| variable become implicitly stored into the results of the |asiancontinuous.m| function).

&lt;codeblock language=matlab&gt;
&lt;&lt;plot function&gt;&gt;=
function h = plot_sol
figure('Color',[0.9412 0.9412 0.9412 ]);
surf(pde_sol.x, pde_sol.t, pde_sol.u, 'edgecolor', 'none');
axis([min(pde_sol.x) max(pde_sol.x) min(pde_sol.t) max(pde_sol.t) min(min(pde_sol.u)) max(max(pde_sol.u))]);
xlabel('X');ylabel('t');
end
&lt;/codeblock&gt;


[[Category:Programming language:MATLAB]]
[[Category:Quantitative finance]]</text>
    </revision>
  </page>
  <page>
    <title>Asian Option Pricing (Matlab)</title>
    <id>2664</id>
    <revision>
      <id>7492</id>
      <timestamp>2006-08-26T02:54:01Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>[[Asian Option Pricing (Matlab)]] moved to [[Asian Option Pricing (MATLAB)]]</comment>
      <text xml:space="preserve">#REDIRECT [[Asian Option Pricing (MATLAB)]]</text>
    </revision>
  </page>
  <page>
    <title>Average (J)</title>
    <id>3237</id>
    <revision>
      <id>11271</id>
      <timestamp>2007-10-25T21:48:42Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;code language=&quot;j&quot;&gt;
&lt;average.ijs&gt;=
avr=:&lt;definition&gt;&lt;/code&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;code language=&quot;j&quot;&gt;
&lt;definition&gt;=&lt;sum&gt;%#&lt;/code&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;code language=&quot;j&quot;&gt;&lt;sum&gt;=+/&lt;/code&gt;</text>
    </revision>
    <revision>
      <id>11272</id>
      <timestamp>2007-10-25T21:49:34Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;code language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;definition&gt;&lt;/code&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;code language=&quot;j&quot;&gt;
&lt;definition&gt;=&lt;sum&gt;%#&lt;/code&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;code language=&quot;j&quot;&gt;&lt;sum&gt;=+/&lt;/code&gt;</text>
    </revision>
    <revision>
      <id>11273</id>
      <timestamp>2007-10-25T21:50:32Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;definition&gt;&lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;definition&gt;=&lt;sum&gt;%#&lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt;&lt;sum&gt;=+/&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11274</id>
      <timestamp>2007-10-25T21:51:22Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;&lt;definition&gt;&gt;&lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;=&lt;&lt;sum&gt;&gt;%#&lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt;&lt;&lt;sum&gt;&gt;=+/&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11275</id>
      <timestamp>2007-10-25T21:56:45Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= &lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; &lt;&lt;sum&gt;&gt;= +/ &lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11276</id>
      <timestamp>2007-10-25T21:57:36Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; &lt;&lt;sum&gt;&gt;= 
+/ &lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11277</id>
      <timestamp>2007-10-25T21:58:19Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>Computing an average in J</comment>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; &lt;&lt;sum&gt;&gt;= 
+/ 
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11278</id>
      <timestamp>2007-10-25T21:59:51Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= 
+/ 
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11279</id>
      <timestamp>2007-10-25T22:00:20Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= +/ 
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11280</id>
      <timestamp>2007-10-25T22:01:18Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr =: &lt;&lt;definition&gt;&gt; &lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt; %# &lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= 
+/ &lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11281</id>
      <timestamp>2007-10-25T22:01:58Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;&lt;definition&gt;&gt;&lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt;%#&lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= 
+/&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11282</id>
      <timestamp>2007-10-25T22:14:33Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">We want to define a functon, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;&lt;definition&gt;&gt;&lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt;%#&lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= 
+/&lt;/codeblock&gt;


[[Category:Programming language:J]]</text>
    </revision>
    <revision>
      <id>11283</id>
      <timestamp>2007-10-25T22:24:15Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <comment>fixed spelling</comment>
      <text xml:space="preserve">We want to define a function, named &quot;avr&quot;, to find the average of a vector.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;average.ijs&gt;&gt;=
avr=:&lt;&lt;definition&gt;&gt;&lt;/codeblock&gt;

To get the average we need to sum the elements of the vector, and divide it by the number of elements.

&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definition&gt;&gt;= 
&lt;&lt;sum&gt;&gt;%#&lt;/codeblock&gt;

We get the sum by inserting the verb &quot;+&quot; between each pair of elements with the adverb &quot;/&quot;

&lt;codeblock language=&quot;j&quot;&gt; 
&lt;&lt;sum&gt;&gt;= 
+/&lt;/codeblock&gt;


[[Category:Programming language:J]]</text>
    </revision>
  </page>
  <page>
    <title>BMP decoder (C)</title>
    <id>1739</id>
    <revision>
      <id>3008</id>
      <timestamp>2006-03-09T07:26:24Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add initial sections on endianness, reading primitives, and reading the header</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* It's negative */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type = read_u16(in);
    header-&gt;size = read_u32(in);
    header-&gt;reserved = read_u32(in);
    header-&gt;bitmap_offset = read_u32(in);
    header-&gt;header_size = read_u32(in);
    header-&gt;width = read_s32(in);
    header-&gt;height = read_s32(in);
    header-&gt;planes = read_u16(in);
    header-&gt;bits_per_pixel = read_u16(in); 
    header-&gt;compression = read_u32(in);
    header-&gt;bitmap_size = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution = read_u32(in);
    header-&gt;num_colors = read_u32(in);
    header-&gt;num_important_colors = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:BMP encoders and decoders]]</text>
    </revision>
    <revision>
      <id>3009</id>
      <timestamp>2006-03-09T07:27:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Reading primitives */ Small fixes</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type = read_u16(in);
    header-&gt;size = read_u32(in);
    header-&gt;reserved = read_u32(in);
    header-&gt;bitmap_offset = read_u32(in);
    header-&gt;header_size = read_u32(in);
    header-&gt;width = read_s32(in);
    header-&gt;height = read_s32(in);
    header-&gt;planes = read_u16(in);
    header-&gt;bits_per_pixel = read_u16(in); 
    header-&gt;compression = read_u32(in);
    header-&gt;bitmap_size = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution = read_u32(in);
    header-&gt;num_colors = read_u32(in);
    header-&gt;num_important_colors = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:BMP encoders and decoders]]</text>
    </revision>
    <revision>
      <id>3010</id>
      <timestamp>2006-03-09T07:28:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix cat</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type = read_u16(in);
    header-&gt;size = read_u32(in);
    header-&gt;reserved = read_u32(in);
    header-&gt;bitmap_offset = read_u32(in);
    header-&gt;header_size = read_u32(in);
    header-&gt;width = read_s32(in);
    header-&gt;height = read_s32(in);
    header-&gt;planes = read_u16(in);
    header-&gt;bits_per_pixel = read_u16(in); 
    header-&gt;compression = read_u32(in);
    header-&gt;bitmap_size = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution = read_u32(in);
    header-&gt;num_colors = read_u32(in);
    header-&gt;num_important_colors = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3011</id>
      <timestamp>2006-03-09T07:29:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>More cats</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type = read_u16(in);
    header-&gt;size = read_u32(in);
    header-&gt;reserved = read_u32(in);
    header-&gt;bitmap_offset = read_u32(in);
    header-&gt;header_size = read_u32(in);
    header-&gt;width = read_s32(in);
    header-&gt;height = read_s32(in);
    header-&gt;planes = read_u16(in);
    header-&gt;bits_per_pixel = read_u16(in); 
    header-&gt;compression = read_u32(in);
    header-&gt;bitmap_size = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution = read_u32(in);
    header-&gt;num_colors = read_u32(in);
    header-&gt;num_important_colors = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3012</id>
      <timestamp>2006-03-09T07:31:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Preliminary source file</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type = read_u16(in);
    header-&gt;size = read_u32(in);
    header-&gt;reserved = read_u32(in);
    header-&gt;bitmap_offset = read_u32(in);
    header-&gt;header_size = read_u32(in);
    header-&gt;width = read_s32(in);
    header-&gt;height = read_s32(in);
    header-&gt;planes = read_u16(in);
    header-&gt;bits_per_pixel = read_u16(in); 
    header-&gt;compression = read_u32(in);
    header-&gt;bitmap_size = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution = read_u32(in);
    header-&gt;num_colors = read_u32(in);
    header-&gt;num_important_colors = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3013</id>
      <timestamp>2006-03-09T07:33:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Reading the header */ Line up</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = c[size-1 - i];
            c[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, size_t size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3014</id>
      <timestamp>2006-03-09T07:35:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>More fixes</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
} bmp_file_header;
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3015</id>
      <timestamp>2006-03-09T07:36:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Kill trailing junk from copy-paste</comment>
      <text xml:space="preserve">{{develop}}

This articles describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3019</id>
      <timestamp>2006-03-09T08:41:49Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>sp</comment>
      <text xml:space="preserve">{{develop}}

This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3022</id>
      <timestamp>2006-03-09T09:51:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix link</comment>
      <text xml:space="preserve">{{develop}}

This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3023</id>
      <timestamp>2006-03-09T10:10:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Reading primitives */ Compiler warning</comment>
      <text xml:space="preserve">{{develop}}

This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3151</id>
      <timestamp>2006-03-10T23:18:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Overview, reading the palette</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
int read_palette(read_func in, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3152</id>
      <timestamp>2006-03-10T23:19:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add new chunks to code</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3153</id>
      <timestamp>2006-03-10T23:20:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add header arg to read_palette</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. The decoder is:
* Stream-based: It reads its input and produces its output sequentially on demand.
* Incremental: It always produces as many output pixels as are known from the input bytes read so far. The alternative would be a monolithic approach that reads the entire file before decoding it.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3160</id>
      <timestamp>2006-03-11T05:30:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Some stuff on decoding uncompressed indexed pixels</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
    UNCOMPRESSED = 0,
    RLE4 = 1,
    RLE8 = 2,
    BITFIELDS = 3
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out. We then look up the index in the table

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a pixel, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3161</id>
      <timestamp>2006-03-11T05:30:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Reading pixel data */ Oops, take out stuff not supposed to be shown yet</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out. We then look up the index in the table

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a pixel, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3162</id>
      <timestamp>2006-03-11T05:31:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Uncompressed indexed */ Oops, dangling comment</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a pixel, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3163</id>
      <timestamp>2006-03-11T05:32:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Uncompressed indexed */ Middle of a byte</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>3444</id>
      <timestamp>2006-03-18T14:22:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Noweb syntax fix</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>4757</id>
      <timestamp>2006-05-14T21:06:14Z</timestamp>
      <contributor>
        <ip>86.143.39.217</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
//herst penna
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>4758</id>
      <timestamp>2006-05-14T21:12:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert strange comment</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>6792</id>
      <timestamp>2006-07-11T12:46:42Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[BMP decoder (C)]] moved to [[BMP decoder (C) on Wheels]]</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>6958</id>
      <timestamp>2006-07-11T14:28:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[BMP decoder (C) on Wheels]] moved to [[BMP decoder (C)]]: revert</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>15627</id>
      <timestamp>2008-12-17T20:58:12Z</timestamp>
      <contributor>
        <ip>211.115.218.116</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

FIELD_MESSAGE_limondartr

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
    <revision>
      <id>15641</id>
      <timestamp>2008-12-17T21:34:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">{{develop}}

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
|height=50|&lt;center&gt;Header&lt;/center&gt;
|-
|&lt;center&gt;Palette&lt;/center&gt;
|-
|height=150|&lt;center&gt;Pixel data&lt;/center&gt;
|}
&lt;/div&gt;
This article describes a portable decoder for BMP image files, a program for converting a BMP file into a raw bitmap of RGB triples. For simplicity, the decoder is monolithic: it reads in its entire input at once sequentially and produces its entire output at once sequentially.

Because version 4 and version 5 BMP files support embedding of very complex JPEG and PNG files, and because most BMP readers do not read these versions, we do not currently support them in this implementation.

The BMP file has 3 main parts as shown to the right: the header, the palette (only present for indexed images), and the bitmap or pixel data, which may or may not be compressed.

== Endianness ==

Because BMP files were designed for use on IBM PC-compatible machines, all multibyte values are stored in a little-endian fashion, least significant byte first. In order for this decoder to be portable to big-endian machines, we must ensure that on these machines we perform byte reversal on any multibyte values subsequent to reading them in raw. For the purposes of this article we use a simple in-place algorithm that reinterprets the value as a byte array and swaps each pair of elements equally far from the middle:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
void fix_endian_func(void* data, int size) {
    &lt;&lt;if running on a big endian machine&gt;&gt; {
        unsigned char* cdata = data;
        int i;
        for (i=0; i&lt;size/2; i++) {
            unsigned char temp = cdata[i];
            cdata[i] = cdata[size-1 - i];
            cdata[size-1 - i] = temp;
        }
    }
}
&lt;/codeblock&gt;

On a machine without byte addressing, other approaches can be more efficient; see [[:Category:Byte reversal]]. To test if we're running on a big endian machine, we simply place the value &quot;1&quot; in an ''int'' and see if the first byte ends up being zero or not:

&lt;codeblock language=c&gt;
&lt;&lt;if running on a big endian machine&gt;&gt;=
int endian_test = 1;
unsigned char* endian_test_bytes = (unsigned char *)&amp;endian_test;
if (endian_test_bytes[0] == '\0')
&lt;/codeblock&gt;

Finally, we add a convenient macro for invoking the function on static-sized objects:

&lt;codeblock language=c&gt;
&lt;&lt;fix endianness&gt;&gt;=
#define fix_endian(x)  (fix_endian_func(&amp;(x), sizeof(x)))
&lt;/codeblock&gt;

== Reading primitives ==

To be as generic as possible, all of our functions will perform input via a function pointer that behaves similarly to the standard &lt;code&gt;fread()&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Reads up to size bytes into the buffer, returning number of bytes read */
typedef int (*read_func)(void* buffer, int size);
&lt;/codeblock&gt;

=== Reading integers ===

The BMP file format is limited to three types of integer fields: unsigned 1-byte, unsigned 2-byte, unsigned 4-byte, and signed 4-byte integers. We define primitive read functions for each of these, each taking a read_func. We assume any end of file condition is unexpected and exit the program, which simplifies calling code (in C++, exception handling would be used). The C89 standard guarantees that a char is one byte, making the first primitive easy:

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned char read_u8(read_func read) {
    unsigned char result;
    if (read(&amp;result, 1) &lt; 1) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return result;
}
&lt;/codeblock&gt;

We add the necessary headers for printf() and exit():

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

For the others, the standard only guarantees that shorts and longs will be ''at least'' long enough to hold 2-byte and 4-byte quantities, respectively (ref section 5.2.4.2, Numerical limits). To deal with this, we intialize them to zero; since we're reading in little endian quantities, the most significant bytes are left as zero. We then perform byte reversal if necessary on the entire integer, not just the first 2 or 4 bytes.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
unsigned short read_u16(read_func read) {
    unsigned short result = 0;
    if (read(&amp;result, 2) &lt; 2) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}

unsigned long read_u32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    return result;
}
&lt;/codeblock&gt;

Finally, the signed s32 adds a twist: we must sign extend it if it is negative. We do this by ORing it with a bitmask, where the bitmask is computed by shifting -1 (all 1 bits) left by 32 bits. On a platform with 32-bit longs, this operation has no effect.

&lt;codeblock language=c&gt;
&lt;&lt;reading primitives&gt;&gt;=
signed long read_s32(read_func read) {
    unsigned long result = 0;
    if (read(&amp;result, 4) &lt; 4) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    fix_endian(result);
    if ((result &gt;&gt; 31) &amp; 1) { /* If it's negative... */
        result |= ((unsigned long)(-1)) &lt;&lt; 32;
    }
    return (long)result;
}
&lt;/codeblock&gt;

While portable, this does introduce a warning in some compilers which see the shift as useless. The next section will demonstrate the use of these functions.

== Reading the header ==

&lt;div class=&quot;floatright&quot;&gt;
{|border=&quot;1&quot;
!Field!!Bytes!!Signed
|-
|Type||2||N
|-
|Size||4||N
|-
|Reserved||4||N
|-
|Bitmap offset||4||N
|-
|Header size||4||N
|-
|Width||4||Y
|-
|Height||4||Y
|-
|Planes||2||N
|-
|Bits per pixel||2||N
|-
|Compression||4||N
|-
|Bitmap size||4||N
|-
|Horizontal res||4||Y
|-
|Vertical res||4||Y
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; colors||4||N
|-
|&lt;nowiki&gt;#&lt;/nowiki&gt; important colors||4||N
|}
&lt;/div&gt;

Next, we focus on reading the header. The header has a simple fixed layout as shown in the table to the right. The two structures composing it are documented Windows structures called [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_62uq.asp BITMAPFILEHEADER] and [http://msdn.microsoft.com/library/en-us/gdi/bitmaps_1rw2.asp BITMAPINFOHEADER], both of which are documented at MSDN. On Windows, these are included in Windows header files, but since they're not available on any other platform and we desire uniform presentation, we choose not to use these structures.

We use a single header structure for the whole header with longs, shorts, and chars for the fields. Some of these fields may be larger than in the file, but because we're going to read them field by field this doesn't matter:

&lt;codeblock language=c&gt;
&lt;&lt;bitmap header structure&gt;&gt;=
struct bmp_file_header { 
    unsigned short   type; 
    unsigned long    size; 
    unsigned long    reserved; 
    unsigned long    bitmap_offset;
    unsigned long    header_size; 
    signed   long    width; 
    signed   long    height; 
    unsigned short   planes; 
    unsigned short   bits_per_pixel; 
    unsigned long    compression; 
    unsigned long    bitmap_size;
    signed   long    horizontal_resolution;
    signed   long    vertical_resolution;
    unsigned long    num_colors; 
    unsigned long    num_important_colors; 
}; 
&lt;/codeblock&gt;

We'll explain these fields as we use them later. Reading in this structure field by field with our reading primitives is straightforward. We read field by field partly due to our inability to determine the sizes of integer types and partly to avoid issues with structure element alignment.

&lt;codeblock language=c&gt;
&lt;&lt;read bitmap header function&gt;&gt;=
void read_bitmap_header(read_func in, struct bmp_file_header* header) {
    header-&gt;type                  = read_u16(in);
    header-&gt;size                  = read_u32(in);
    header-&gt;reserved              = read_u32(in);
    header-&gt;bitmap_offset         = read_u32(in);
    header-&gt;header_size           = read_u32(in);
    header-&gt;width                 = read_s32(in);
    header-&gt;height                = read_s32(in);
    header-&gt;planes                = read_u16(in);
    header-&gt;bits_per_pixel        = read_u16(in); 
    header-&gt;compression           = read_u32(in);
    header-&gt;bitmap_size           = read_u32(in);
    header-&gt;horizontal_resolution = read_s32(in);
    header-&gt;vertical_resolution   = read_u32(in);
    header-&gt;num_colors            = read_u32(in);
    header-&gt;num_important_colors  = read_u32(in);
}
&lt;/codeblock&gt;

== Reading the palette ==

For the palette we'll define a simple static 2-dimensional array data structure containing up to 256 red-green-blue triples:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
enum color_component {
    BLUE,
    GREEN,
    RED
};

#define PALETTE_ENTRY_SIZE   4
#define MAX_PALETTE_SIZE     256

typedef unsigned char palette[MAX_PALETTE_SIZE][PALETTE_ENTRY_SIZE];
&lt;/codeblock&gt;

Although the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;num_colors&lt;/code&gt; are related to the size of the palette, the easiest way to determine its size is to use the &lt;code&gt;bitmap_offset&lt;/code&gt; property. This is the offset of the pixel data in the file; if we just subtract the header size, we have the palette size in bytes. We'll need to define a constant for the header size, since the &lt;code&gt;bmp_file_header&lt;/code&gt; structure may be larger.

&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
#define HEADER_SIZE (2 + 6*4 + 2*2 + 6*4)

&lt;&lt;compute size of palette&gt;&gt;=
int palette_size = header-&gt;bitmap_offset - HEADER_SIZE;
&lt;/codeblock&gt;

To read the palette, we can simply read in a block of bytes, since our array elements are guaranteed to be contiguous and in row-major order. We return the number of palette entries by simply dividing the size by the size of a palette entry:

&lt;codeblock language=c&gt;
&lt;&lt;read palette function&gt;&gt;=
int read_palette(read_func in, struct bmp_file_header* header, palette palette) {
    &lt;&lt;compute size of palette&gt;&gt;
    if (in(&amp;palette[0][0], palette_size) &lt; palette_size) {
        printf(&quot;Unexpected end of file&quot;);
        exit(-1);
    }
    return palette_size/PALETTE_ENTRY_SIZE;
}
&lt;/codeblock&gt;

== Reading pixel data ==

The encoding of the pixel data depends on the header members &lt;code&gt;bits_per_pixel&lt;/code&gt; and &lt;code&gt;compression&lt;/code&gt;. The main bitmap reading function will just dispatch based on these values. We will output pixel data in a very simple format: a two-dimensional array with 3 bytes for each pixel, one per RGB component.

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
typedef unsigned char raw_pixels[][3];

&lt;&lt;read pixel data function&gt;&gt;=
raw_pixels convert_pixel_data(reader_func in, struct bmp_file_header* header,
                              palette palette)
{
    raw_pixels output = malloc(3 * header-&gt;width * header-&gt;height;
    &lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;
    return output;
}
&lt;/codeblock&gt;

We'll need an enumeration for values of the compression field:
&lt;codeblock language=c&gt;
&lt;&lt;constants&gt;&gt;=
enum compression_values {
    &lt;&lt;compression field values&gt;&gt;
};
&lt;/codeblock&gt;

These will be explained in more detail below. Reading uncompressed BMP files is relatively straightforward, so we begin with this.

=== Uncompressed indexed ===

In the uncompressed format, BMP pixel data simply has a fixed number of bits for each pixel, specified by the &lt;code&gt;bits_per_pixel&lt;/code&gt; member of the header. If this is less than 16 (in other words, at most 8), then each value is an index into the palette.

&lt;codeblock language=c&gt;
&lt;&lt;compression field values&gt;&gt;=
UNCOMPRESSED = 0,

&lt;&lt;dispatch based on bits per pixel and compression&gt;&gt;=
if (header-&gt;compression == UNCOMPRESSED &amp;&amp; header-&gt;bits_per_pixel &lt; 16) {
    convert_uncompressed_indexed_pixels(in, header, palette, output);
} &lt;/codeblock&gt;

Since each scanline is aligned to the nearest 4 byte boundary, we can determine the number of bytes in a scanline like this:

&lt;codeblock language=c&gt;
&lt;&lt;scanline bytes calculation&gt;&gt;=
int scanline_bits = header-&gt;width * header-&gt;bits_per_pixel;
int scanline_bytes = ((scanline_bits + 31)/32)*4;
&lt;/codeblock&gt;

The effect of adding 31 and then dividing by 32 is to find the ceiling of scanline_bits divided by 32, which is the smallest number of 4-byte blocks containing that many bits. We then multiply by 4 to get a byte count.

Keeping in mind that BMP files list scanlines from the bottom up, we're now ready to read in the pixel data:

&lt;codeblock language=c&gt;
&lt;&lt;convert uncompressed indexed pixels function&gt;&gt;=
void convert_uncompressed_indexed_pixels(
    reader_func in, struct bmp_file_header* header,
    palette palette, raw_pixels output)
{
    &lt;&lt;scanline bytes calculation&gt;&gt;
    for(int row = header-&gt;height-1; row &gt;= 0; row--) {
        int out_offset = header-&gt;width*row*3;
        int column = 0;
        for (int bytenum=0; bytenum &lt; scanline_bytes; bytenum++) {
            &lt;&lt;read and decode a byte full of pixels&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

Just how we decode each byte depends on the number of bits per pixel. We loop over the pixels in the byte, shifting it left to keep the current pixel in the highest bits so that we can use &lt;code&gt;extract_high_bits()&lt;/code&gt; (defined later) to read the index out.

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
unsigned char pixel_byte = read_u8(in);
for (int pixel_num=0; pixel_num &lt; header-&gt;bytes_per_pixel; pixel_num++) {
    int index = extract_high_bits(pixel_byte, header-&gt;bytes_per_pixel);
    &lt;&lt;set output bytes based on palette entry index&gt;&gt;
    pixel_byte &lt;&lt;= header-&gt;bytes_per_pixel;
    &lt;&lt;break if scanline done&gt;&gt;
}
&lt;/codeblock&gt;

Setting the output bytes is a simple matter of calculating the correct position in the output array and filling it with the intensity values from the palette entry indicated by &lt;code&gt;index&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;read and decode a byte full of pixels&gt;&gt;=
output[out_offset + column*3 + 0] = palette[index][0];
output[out_offset + column*3 + 1] = palette[index][1];
output[out_offset + column*3 + 2] = palette[index][2];
&lt;/codeblock&gt;

Because it's possible for a scanline to end in the middle of a byte, we break out of the loop if &lt;code&gt;column&lt;/code&gt; exceeds the bitmap width:

&lt;codeblock language=c&gt;
&lt;&lt;break if scanline done&gt;&gt;=
column++;
if (column &gt; header-&gt;width) break;
&lt;/codeblock&gt;

Finally, we define the helper function &lt;code&gt;extract_high_bits()&lt;/code&gt;, which uses a shift to move the highest ''k'' bits to the lowest ''k'' bits; zeros are left in front of them:

&lt;codeblock language=c&gt;
&lt;&lt;extract high bits helper function&gt;&gt;=
unsigned char extract_high_bits(unsigned char x, int bits) {
    return x &gt;&gt; (8 - bits);
}
&lt;/codeblock&gt;

=== Uncompressed RGB ===

=== Bitfields (16- and 32-bit) ===

=== Run-length encoding (4- and 8-bit) ===

== More to come ==

&lt;codeblock language=c&gt;
&lt;&lt;bmp_decode.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
&lt;&lt;type definitions&gt;&gt;
&lt;&lt;constants&gt;&gt;
&lt;&lt;bitmap header structure&gt;&gt;

&lt;&lt;fix endianness&gt;&gt;
&lt;&lt;reading primitives&gt;&gt;
&lt;&lt;read bitmap header function&gt;&gt;
&lt;&lt;read palette function&gt;&gt;
&lt;/codeblock&gt;

== References ==

* Dr. David Kirby. [http://atlc.sourceforge.net/bmp.html bmp format]. http://atlc.sourceforge.net/bmp.html

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:BMP decoders and encoders]]</text>
    </revision>
  </page>
  <page>
    <title>Base64 (C)</title>
    <id>3000</id>
    <revision>
      <id>8956</id>
      <timestamp>2007-02-09T19:01:18Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>codedump, needs major work</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code, originally hacked as a quick fix on a box without a decent mail reader.  I don't do much in C these days, so you all are invited to fix it up and literate it.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

/* [DL] 10122004 - quick hack*/

unsigned char in[4];
unsigned char out[3];

xlate()
{
	out[0] = in[0] &lt;&lt; 2 | in[1] &gt;&gt; 4;
	out[1] = in[1] &lt;&lt; 4 | in[2] &gt;&gt; 2;
	out[2] = in[2] &lt;&lt; 6 | in[3] &gt;&gt; 0;
}

main()
{
	char base64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;

	int c, phase;
	char *p;
	FILE *fp = fopen(&quot;b64.out&quot;, &quot;wb&quot;);

	phase = 0;
	while((c = getchar()) != EOF)	{
		if(c == '=')	{
			xlate();			
			switch(phase)	{
			case 1:	fwrite(out, 1, 1, fp);	break;
			case 3:	fwrite(out, 2, 1, fp);	break;
			}
			break;
		}
	        p = strchr(base64, c);
		if(p)	{
			in[phase] = p - base64;
			if(phase == 3)	{
				xlate();
				fwrite(out, 3, 1, fp);
				in[0]=in[1]=in[2]=in[3]=0;
			}
			phase = (phase + 1) % 4;
		}
	}
}
&lt;/codedump&gt;&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8957</id>
      <timestamp>2007-02-09T19:02:40Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>C shift operators confusing noweb</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code, originally hacked as a quick fix on a box without a decent mail reader.  I don't do much in C these days, so you all are invited to fix it up and literate it.

maybe not working so well, as noweb doesn't like the shift operators?

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

/* [DL] 10122004 - quick hack*/

unsigned char in[4];
unsigned char out[3];

xlate()
{
	out[0] = in[0] &lt;&lt; 2 | in[1] &gt;&gt; 4;
	out[1] = in[1] &lt;&lt; 4 | in[2] &gt;&gt; 2;
	out[2] = in[2] &lt;&lt; 6 | in[3] &gt;&gt; 0;
}

main()
{
	char base64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;

	int c, phase;
	char *p;
	FILE *fp = fopen(&quot;b64.out&quot;, &quot;wb&quot;);

	phase = 0;
	while((c = getchar()) != EOF)	{
		if(c == '=')	{
			xlate();			
			switch(phase)	{
			case 1:	fwrite(out, 1, 1, fp);	break;
			case 3:	fwrite(out, 2, 1, fp);	break;
			}
			break;
		}
	        p = strchr(base64, c);
		if(p)	{
			in[phase] = p - base64;
			if(phase == 3)	{
				xlate();
				fwrite(out, 3, 1, fp);
				in[0]=in[1]=in[2]=in[3]=0;
			}
			phase = (phase + 1) % 4;
		}
	}
}
&lt;/codedump&gt;&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8960</id>
      <timestamp>2007-02-09T19:11:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>using @ to escape noweb chunk syntax, rm &lt;/codedump&gt; tag</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code, originally hacked as a quick fix on a box without a decent mail reader.  I don't do much in C these days, so you all are invited to fix it up and literate it.

maybe not working so well, as noweb doesn't like the shift operators?

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

/* [DL] 10122004 - quick hack*/

unsigned char in[4];
unsigned char out[3];

xlate()
{
	out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
	out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
	out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
}

main()
{
	char base64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;

	int c, phase;
	char *p;
	FILE *fp = fopen(&quot;b64.out&quot;, &quot;wb&quot;);

	phase = 0;
	while((c = getchar()) != EOF)	{
		if(c == '=')	{
			xlate();			
			switch(phase)	{
			case 1:	fwrite(out, 1, 1, fp);	break;
			case 3:	fwrite(out, 2, 1, fp);	break;
			}
			break;
		}
	        p = strchr(base64, c);
		if(p)	{
			in[phase] = p - base64;
			if(phase == 3)	{
				xlate();
				fwrite(out, 3, 1, fp);
				in[0]=in[1]=in[2]=in[3]=0;
			}
			phase = (phase + 1) % 4;
		}
	}
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8961</id>
      <timestamp>2007-02-09T19:13:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>declare xlate() as void, main() as int</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code, originally hacked as a quick fix on a box without a decent mail reader.  I don't do much in C these days, so you all are invited to fix it up and literate it.

maybe not working so well, as noweb doesn't like the shift operators?

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

/* [DL] 10122004 - quick hack*/

unsigned char in[4];
unsigned char out[3];

void xlate()
{
	out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
	out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
	out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
}

int main()
{
	char base64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;

	int c, phase;
	char *p;
	FILE *fp = fopen(&quot;b64.out&quot;, &quot;wb&quot;);

	phase = 0;
	while((c = getchar()) != EOF)	{
		if(c == '=')	{
			xlate();			
			switch(phase)	{
			case 1:	fwrite(out, 1, 1, fp);	break;
			case 3:	fwrite(out, 2, 1, fp);	break;
			}
			break;
		}
	        p = strchr(base64, c);
		if(p)	{
			in[phase] = p - base64;
			if(phase == 3)	{
				xlate();
				fwrite(out, 3, 1, fp);
				in[0]=in[1]=in[2]=in[3]=0;
			}
			phase = (phase + 1) % 4;
		}
	}

	return 0;
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8972</id>
      <timestamp>2007-02-10T00:16:14Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>+diagram, trimmed code.  still in need of literation.</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code for [http://en.wikipedia.org/wiki/Base64#MIME Base 64 decoding], originally hacked as a quick fix on a box without a decent mail reader.

I don't do much in C these days, so you all are invited to fix it up and literate it.

[[Image:Base64.png]]

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

char b64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
int nbytes[] = { 3, 1, 1, 2 };

void xlate(unsigned char *in, int phase)
{
    unsigned char out[3];
    out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
    out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
    out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
    fwrite(out, nbytes[phase], 1, stdout);
}

int main()
{
    int c, phase;
    unsigned char in[4];
    char *p;

    phase = 0;
    while((c = getchar()) != EOF)    {
        if(c == '=')    {
            xlate(in, phase);
            break;
        }
        p = strchr(b64, c);
        if(p)    {
            in[phase] = p - b64;
            phase = (phase + 1) % 4;
            if(phase == 0)    {
                xlate(in, phase);
                in[0]=in[1]=in[2]=in[3]=0;
            }
        }
    }
    return 0;
}
&lt;/codeblock&gt;
&lt;pre&gt;TGl0ZXJhdGVQcm9ncmFtcw==&lt;/pre&gt;
decodes to
&lt;pre&gt;LiteratePrograms&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>9003</id>
      <timestamp>2007-02-11T18:45:26Z</timestamp>
      <contributor>
        <username>Djura</username>
        <id>141</id>
      </contributor>
      <minor/>
      <comment>Added link to Base64 RFC</comment>
      <text xml:space="preserve">{{codedump}}
some working (albeit rather minimal) code for [http://en.wikipedia.org/wiki/Base64#MIME Base 64 decoding], [http://www.ietf.org/rfc/rfc3548.txt RFC3548], originally hacked as a quick fix on a box without a decent mail reader.

I don't do much in C these days, so you all are invited to fix it up and literate it.

[[Image:Base64.png]]

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

char b64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
int nbytes[] = { 3, 1, 1, 2 };

void xlate(unsigned char *in, int phase)
{
    unsigned char out[3];
    out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
    out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
    out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
    fwrite(out, nbytes[phase], 1, stdout);
}

int main()
{
    int c, phase;
    unsigned char in[4];
    char *p;

    phase = 0;
    while((c = getchar()) != EOF)    {
        if(c == '=')    {
            xlate(in, phase);
            break;
        }
        p = strchr(b64, c);
        if(p)    {
            in[phase] = p - b64;
            phase = (phase + 1) % 4;
            if(phase == 0)    {
                xlate(in, phase);
                in[0]=in[1]=in[2]=in[3]=0;
            }
        }
    }
    return 0;
}
&lt;/codeblock&gt;
&lt;pre&gt;TGl0ZXJhdGVQcm9ncmFtcw==&lt;/pre&gt;
decodes to
&lt;pre&gt;LiteratePrograms&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>9518</id>
      <timestamp>2007-03-19T17:52:03Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>a little literation</comment>
      <text xml:space="preserve">some working (albeit rather minimal) code for [http://en.wikipedia.org/wiki/Base64#MIME Base 64 decoding], [http://www.ietf.org/rfc/rfc3548.txt RFC3548], originally hacked as a quick fix on a box without a decent mail reader.

==theory==
This program is almost not worth writing:
the core of the Base 64 conversion
consists of the isomorphism
between 24-bit bitstrings
(presented on input
as 4 groups of 6 bits
and output
as 3 groups of 8 bits).
[[Image:Base64.png]]

The slight complications are that:
* strings to be coded are not necessarily multiples of 24 bits; we must be prepared to handle a runt conversion for the last few characters.
* the 6-bit groups are injected into regular 8-bit bytes, so it may take an arbitrary number of source characters in order to accumulate 4 coding characters.

Note that this is easier than the general metamorphism;
we may not have 1:1 correspondence between source characters and groups,
but each group is translated independently &amp;mdash; we never have to &quot;carry&quot; bits from the computation of one group to that of the next.
 
==practice==

Translating a 24 bit chunk is a simple matter
of shifting all the bits
into the appropriate places.
(we use &lt;code&gt;nbytes[phase]&lt;/code&gt;
to handle runt conversions)

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;translate chunk&gt;&gt;=
xlate(in,phase);
&lt;&lt;define translation&gt;&gt;=
void xlate(unsigned char *in, int phase)
{
    unsigned char out[3];
    out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
    out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
    out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
    fwrite(out, nbytes[phase], 1, stdout);
}
&lt;/codeblock&gt;

We must process the input a character, '''c''', at a time
even though most of the time we will be translating it
in four-character chunks.

This is because, as mentioned above,
* the last chunk may be less than four characters (signalled by an equals sign, &lt;code&gt;'='&lt;/code&gt;)
* arbitrary non-coding characters are ignored, so accumulating a chunk may require more than four characters of source text.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;process input&gt;&gt;=
if(c == '=')    {
    &lt;&lt;translate chunk&gt;&gt; 
    break;
}
p = strchr(b64, c);
if(p)    {
    in[phase] = p - b64;
    phase = (phase + 1) % 4;
    if(phase == 0)    {
        &lt;&lt;translate chunk&gt;&gt; 
        in[0]=in[1]=in[2]=in[3]=0;
    }
}
&lt;/codeblock&gt;

==wrapping up==

Finally, we put it all together in a small filter program

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

char b64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
int nbytes[] = { 3, 1, 1, 2 };

&lt;&lt;define translation&gt;&gt;

int main()
{
    int c, phase;
    unsigned char in[4];
    char *p;

    phase = 0;
    while((c = getchar()) != EOF)    {
        &lt;&lt;process input&gt;&gt;
    }
    return 0;
}
&lt;/codeblock&gt;

and verify that

&lt;pre&gt;TGl0ZXJhdGVQcm9ncmFtcw==&lt;/pre&gt;
decodes to
&lt;pre&gt;LiteratePrograms&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>10650</id>
      <timestamp>2007-07-07T01:47:26Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cats</comment>
      <text xml:space="preserve">some working (albeit rather minimal) code for [http://en.wikipedia.org/wiki/Base64#MIME Base 64 decoding], [http://www.ietf.org/rfc/rfc3548.txt RFC3548], originally hacked as a quick fix on a box without a decent mail reader.

==theory==
This program is almost not worth writing:
the core of the Base 64 conversion
consists of the isomorphism
between 24-bit bitstrings
(presented on input
as 4 groups of 6 bits
and output
as 3 groups of 8 bits).
[[Image:Base64.png]]

The slight complications are that:
* strings to be coded are not necessarily multiples of 24 bits; we must be prepared to handle a runt conversion for the last few characters.
* the 6-bit groups are injected into regular 8-bit bytes, so it may take an arbitrary number of source characters in order to accumulate 4 coding characters.

Note that this is easier than the general metamorphism;
we may not have 1:1 correspondence between source characters and groups,
but each group is translated independently &amp;mdash; we never have to &quot;carry&quot; bits from the computation of one group to that of the next.
 
==practice==

Translating a 24 bit chunk is a simple matter
of shifting all the bits
into the appropriate places.
(we use &lt;code&gt;nbytes[phase]&lt;/code&gt;
to handle runt conversions)

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;translate chunk&gt;&gt;=
xlate(in,phase);
&lt;&lt;define translation&gt;&gt;=
void xlate(unsigned char *in, int phase)
{
    unsigned char out[3];
    out[0] = in[0] @&lt;&lt; 2 | in[1] &gt;&gt; 4;
    out[1] = in[1] @&lt;&lt; 4 | in[2] &gt;&gt; 2;
    out[2] = in[2] @&lt;&lt; 6 | in[3] &gt;&gt; 0;
    fwrite(out, nbytes[phase], 1, stdout);
}
&lt;/codeblock&gt;

We must process the input a character, '''c''', at a time
even though most of the time we will be translating it
in four-character chunks.

This is because, as mentioned above,
* the last chunk may be less than four characters (signalled by an equals sign, &lt;code&gt;'='&lt;/code&gt;)
* arbitrary non-coding characters are ignored, so accumulating a chunk may require more than four characters of source text.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;process input&gt;&gt;=
if(c == '=')    {
    &lt;&lt;translate chunk&gt;&gt; 
    break;
}
p = strchr(b64, c);
if(p)    {
    in[phase] = p - b64;
    phase = (phase + 1) % 4;
    if(phase == 0)    {
        &lt;&lt;translate chunk&gt;&gt; 
        in[0]=in[1]=in[2]=in[3]=0;
    }
}
&lt;/codeblock&gt;

==wrapping up==

Finally, we put it all together in a small filter program

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;base64.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

char b64[] = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
int nbytes[] = { 3, 1, 1, 2 };

&lt;&lt;define translation&gt;&gt;

int main()
{
    int c, phase;
    unsigned char in[4];
    char *p;

    phase = 0;
    while((c = getchar()) != EOF)    {
        &lt;&lt;process input&gt;&gt;
    }
    return 0;
}
&lt;/codeblock&gt;

and verify that

&lt;pre&gt;TGl0ZXJhdGVQcm9ncmFtcw==&lt;/pre&gt;
decodes to
&lt;pre&gt;LiteratePrograms&lt;/pre&gt;

[[Category:Base64]]
[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (AmigaE)</title>
    <id>2367</id>
    <revision>
      <id>6415</id>
      <timestamp>2006-06-22T00:08:23Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n=0 TO 9
          WriteF('For loop \d\n&quot;,n)
	ENDFOR
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0
	WHILE n&lt;10
          WriteF('While loop \d\n&quot;,n)
	ENDWHILE
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n=0;
        REPEAT
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n=0;
        DO
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;


&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6416</id>
      <timestamp>2006-06-22T00:09:46Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>rough 1st draft for basic constructs in AmigaE</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n=0 TO 9
          WriteF('For loop \d\n&quot;,n)
	ENDFOR
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0
	WHILE n&lt;10
          WriteF('While loop \d\n&quot;,n)
	ENDWHILE
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n=0;
        REPEAT
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n=0;
        DO
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;


&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:AmigaE]]</text>
    </revision>
    <revision>
      <id>6418</id>
      <timestamp>2006-06-22T00:10:51Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Fixed some typos...</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n:=0 TO 9
          WriteF('For loop \d\n&quot;,n)
	ENDFOR
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n:=0
	WHILE n&lt;10
          WriteF('While loop \d\n&quot;,n)
	ENDWHILE
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n:=0;
        REPEAT
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n:=0;
        DO
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;


&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:AmigaE]]</text>
    </revision>
    <revision>
      <id>6419</id>
      <timestamp>2006-06-22T00:13:14Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <minor/>
      <comment>A few more mistakes fixed (When will I learn to use the preview button :P )</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n:=0 TO 9
          WriteF('For loop \d\n&quot;,n)
	ENDFOR
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n:=0
	WHILE n&lt;10
          WriteF('While loop \d\n&quot;,n)
	ENDWHILE
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n:=0;
        REPEAT
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

This is a never ending DO LOOP - exit is done by the AmigaE's &quot;goto&quot; statement JUMP

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n:=0;
        DO
          n=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:AmigaE]]</text>
    </revision>
    <revision>
      <id>6421</id>
      <timestamp>2006-06-22T00:17:32Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Corrected even more typos ( (Yes I'm tired) :'(</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

This is a FOR loop. Will output numbers 0 - 9

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n:=0 TO 9
          WriteF('For loop \d\n&quot;,n)
	ENDFOR
&lt;/codeblock&gt;

Here is an example of a WHILE loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n:=0
	WHILE n&lt;10
          WriteF('While loop \d\n&quot;,n)
          n:=n+1
	ENDWHILE
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n:=0;
        REPEAT
          n:=n+1
          WriteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

This is a never ending DO LOOP - exit is done by the AmigaE's &quot;goto&quot; statement JUMP

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n:=0;
        DO
          n:=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:AmigaE]]</text>
    </revision>
    <revision>
      <id>6452</id>
      <timestamp>2006-06-22T14:52:26Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Fixed wrong cathegory + a few adjustments</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the AmigaE programming language].

== Loops ==

There are 4 standard ways to create a loop in AmigaE.

This is a FOR loop.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;forloop&gt;&gt;=
	FOR n:=0 TO 9
          WriteF('For loop alternative 1: \d\n&quot;,n)
	ENDFOR
        
        FOR n:=0 TO 9 STEP 1 DO WriteF('For loop alternative 2: \d\n&quot;,n)
&lt;/codeblock&gt;

Here is an example of a WHILE loop. The output is exactly the same as in the FOR loop example. In the alternative way of writing this the BUT construct is used to allow for a second expression (sequencing).

&lt;codeblock language=AmigaE&gt;
&lt;&lt;whileloop&gt;&gt;=
	n:=0
	WHILE n&lt;10
          WriteF('While loop alternative 1: \d\n&quot;,n)
          n:=n+1
	ENDWHILE
        
        n:=0
        WHILE n&lt;10 DO n:=n+1 BUT WriteF('While loop alternative 2: \d\n&quot;,n)
&lt;/codeblock&gt;

The REPEAT ... UNTIL works like the WHILE loop, except the test expression is evaluated after the code block.

&lt;codeblock language=AmigaE&gt;
&lt;&lt;repeatuntilloop&gt;&gt;=
	n:=0;
        REPEAT
          n:=n+1
          WriteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
        UNTIL n=9
&lt;/codeblock&gt;

This is a never ending DO LOOP - exit is done by using the Amiga E's &quot;goto&quot; statement JUMP

&lt;codeblock language=AmigaE&gt;
&lt;&lt;doloop&gt;&gt;=
	n:=0;
        DO
          n:=n+1
          WtiteF(&quot;'REPEAT .. UNTIL loop \d\n&quot;,n)
          IF n=9 JUMP exit
        LOOP
exit:
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;loops&gt;&gt;=
PROC loops()
  &lt;&lt;forloop&gt;&gt;
  &lt;&lt;whileloop&gt;&gt;
  &lt;&lt;repeatuntilloop&gt;&gt;
  &lt;&lt;doloop&gt;&gt;
ENDFOR
&lt;/codeblock&gt;

&lt;codeblock language=AmigaE&gt;
&lt;&lt;basic_constructs.e&gt;&gt;=

PROC main()

  loops()

ENDPROC
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Amiga E]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (C Plus Plus)</title>
    <id>3898</id>
    <revision>
      <id>16431</id>
      <timestamp>2009-05-15T17:57:08Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>A start</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets a list of the program arguments and the length of that list. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=char* argc[], int argv
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.c&gt;&gt;=
&lt;&lt;function&gt;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16432</id>
      <timestamp>2009-05-15T17:58:37Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>The line break after the &lt;&lt;...&gt;&gt;= seems to be required</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets a list of the program arguments and the length of that list. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
char* argc[], int argv
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.c&gt;&gt;=
&lt;&lt;function&gt;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16433</id>
      <timestamp>2009-05-15T17:59:31Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets a list of the program arguments and the length of that list. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
char* argc[], int argv
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.c&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16434</id>
      <timestamp>2009-05-15T18:01:15Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>oops, how could I get that wrong ...</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.c&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16441</id>
      <timestamp>2009-05-19T10:44:00Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>#include</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of program&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16442</id>
      <timestamp>2009-05-20T14:29:46Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Includes */ Example with user header</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of program&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16443</id>
      <timestamp>2009-05-20T14:32:30Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>fixed chunk names</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16444</id>
      <timestamp>2009-05-22T17:52:10Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>Basic I/O</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16454</id>
      <timestamp>2009-06-03T16:47:37Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>Some more</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a type can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16455</id>
      <timestamp>2009-06-03T16:49:06Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Basic Input and Output */ Fixed codeblock end tag</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a type can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16466</id>
      <timestamp>2009-06-25T19:30:47Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Variables and types */ C++ basic types</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a variable initialization can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

C++ has a variety of built-in types. The following variable definitions show all basic types of C++:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;basic types&gt;&gt;=
char c = 'a';  // character type, guaranteed to have size of one byte
char c2 = 48;  // the type char actually is a numeric type (on systems using ASCII, this initializes c2 with '0'
signed char sc = -3; // one byte, signed (i.e. can take negative values)
unsigned char uc = 3; // one byte, unsigned (i.e. all values are non-negative)
// note that the type char has the same representation and value range as either signed char or unsigned char,
// but is a distinct type from both

wchar_t wc = L'a'; // wide character type

short s = -300s; // signed short integer; same type as signed short, short int, signed short int
unsigned short us = 300us; // unsigned short integer; same type as unsigned short int

int i = -1000; // signed integer; same type as signed int, signed
unsigned u = 1000u; // unsigned integer; same type as unsigned int

long l = -100000L; // long signed integer; same type as long int, signed long, signed long int
unsigned long ul = 100000UL; // long unsigned integer; same type as unsigned long int

bool b = false; // boolean variable; can only take the values false and true (but implicit conversion from/to int exists)

float f = 1.0f; // floating point variable
double d = 1.0; // floating point variable (usually double precision)
long double d = 1.0L; // floating point value (at least same precision as double, sometimes more)

// the following types are not in the current C++ standard, but a very common extension,
// part of C99, and will be part of next version of the C++ standard
long long ll = -1000000000LL; // very long integer, same as long long int, signed long long, signed long long int
unsigned long long ull = 1000000000ULL; // unsigned version of long long
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16477</id>
      <timestamp>2009-07-09T19:12:03Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Variables and types */ more types</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a variable initialization can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

C++ has a variety of built-in types. The following variable definitions show all basic types of C++:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;basic types&gt;&gt;=
char c = 'a';  // character type, guaranteed to have size of one byte
char c2 = 48;  // the type char actually is a numeric type (on systems using ASCII, this initializes c2 with '0'
signed char sc = -3; // one byte, signed (i.e. can take negative values)
unsigned char uc = 3; // one byte, unsigned (i.e. all values are non-negative)
// note that the type char has the same representation and value range as either signed char or unsigned char,
// but is a distinct type from both

wchar_t wc = L'a'; // wide character type

short s = -300s; // signed short integer; same type as signed short, short int, signed short int
unsigned short us = 300us; // unsigned short integer; same type as unsigned short int

int i = -1000; // signed integer; same type as signed int, signed
unsigned u = 1000u; // unsigned integer; same type as unsigned int

long l = -100000L; // long signed integer; same type as long int, signed long, signed long int
unsigned long ul = 100000UL; // long unsigned integer; same type as unsigned long int

bool b = false; // boolean variable; can only take the values false and true (but implicit conversion from/to int exists)

float f = 1.0f; // floating point variable
double d = 1.0; // floating point variable (usually double precision)
long double d = 1.0L; // floating point value (at least same precision as double, sometimes more)

// the following types are not in the current C++ standard, but a very common extension,
// part of C99, and will be part of next version of the C++ standard
long long ll = -1000000000LL; // very long integer, same as long long int, signed long long, signed long long int
unsigned long long ull = 1000000000ULL; // unsigned version of long long
&lt;/codeblock&gt;
In addition, there's the type &lt;code&gt;void&lt;/code&gt; which is special in that you cannot define variables of that type. However you can use it as return type, and in the following type constructs (with the exception of references and arrays).

For each C++ type T with the exception of reference types (see below), you can create any of the following types:
* &lt;code&gt;T const&lt;/code&gt; = constant T; you cannot modify objects of this type
* &lt;code&gt;T volatile&lt;/code&gt; = volatile T; objects of this type may be externally visible/modifyable
* &lt;code&gt;T*&lt;/code&gt; = pointer to T
* &lt;code&gt;T[n]&lt;/code&gt; (n any constant integer) = array of n Ts
* &lt;code&gt;T&amp;&lt;/code&gt; = reference to T; gives a new name to an existing object
Note that the pointer type (&lt;code&gt;T*&lt;/code&gt;) is a built-in type even if T is not. Also note that for array types, variable names as well as further type specifiers go ''in between'' T and [n]. In some cases parentheses are put around that part in order to remove ambiguities.

The following shows a few examples:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
&lt;&lt;basic types&gt;&gt;
int const ci = 3; // compile time constant
int const ci2 = some_function(); // constant, but initialized at run time
int volatile vi; // This may be visible from outside the program
int const volatile cvi; // The program may not change it, but external processes might
int* pi = &amp;i; // pointer to int, initialized to point to i
int const* pci = &amp;i; // pointer to constant int, initialized to i; cannot be used to change i
int* const cpi = &amp;i; // constant pointer to int, initialized i; can be used to change i,
                     // but not reset to point somewhere else
int const* const cpci = &amp;i; // constant pointer to constant int, pointing to i
int const* cpi2 = &amp;ci; // pointer to constant int can (but need not) point to actually constant int
void* pv = pi; // pointer to void pointing to i; stores address, but loses type information
void const* pcv = pci; // constness matters also for pointer to void
int ai[3] = { 1, 2, 3 }; // array of 3 ints
int* api[3]; // array of 3 pointers to int
int (*pai)[3]; // pointer to array of 3 ints
int* (*pai)[5]; // pointer to array of 5 pointers to int
int a2[3][4]; // two-dimensional array; actually an array of 3 arrays of 4 ints each
int&amp; ri = i; // gives a new name to i
int const&amp; rci = ai[1]; // gives a name to the second member of the array ai;
                        // the name cannot be used to modify ai[1].
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16482</id>
      <timestamp>2009-07-16T17:11:44Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Variables and types */ again a bit more</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a variable initialization can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

C++ has a variety of built-in types. The following variable definitions show all basic types of C++:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;basic types&gt;&gt;=
char c = 'a';  // character type, guaranteed to have size of one byte
char c2 = 48;  // the type char actually is a numeric type (on systems using ASCII, this initializes c2 with '0'
signed char sc = -3; // one byte, signed (i.e. can take negative values)
unsigned char uc = 3; // one byte, unsigned (i.e. all values are non-negative)
// note that the type char has the same representation and value range as either signed char or unsigned char,
// but is a distinct type from both

wchar_t wc = L'a'; // wide character type

short s = -300s; // signed short integer; same type as signed short, short int, signed short int
unsigned short us = 300us; // unsigned short integer; same type as unsigned short int

int i = -1000; // signed integer; same type as signed int, signed
unsigned u = 1000u; // unsigned integer; same type as unsigned int

long l = -100000L; // long signed integer; same type as long int, signed long, signed long int
unsigned long ul = 100000UL; // long unsigned integer; same type as unsigned long int

bool b = false; // boolean variable; can only take the values false and true (but implicit conversion from/to int exists)

float f = 1.0f; // floating point variable
double d = 1.0; // floating point variable (usually double precision)
long double d = 1.0L; // floating point value (at least same precision as double, sometimes more)

// the following types are not in the current C++ standard, but a very common extension,
// part of C99, and will be part of next version of the C++ standard
long long ll = -1000000000LL; // very long integer, same as long long int, signed long long, signed long long int
unsigned long long ull = 1000000000ULL; // unsigned version of long long
&lt;/codeblock&gt;
In addition, there's the type &lt;code&gt;void&lt;/code&gt; which is special in that you cannot define variables of that type. However you can use it as return type, and in the following type constructs (with the exception of references and arrays).

For each C++ type T with the exception of reference types (see below), you can create any of the following types:
* &lt;code&gt;T const&lt;/code&gt; = constant T; you cannot modify objects of this type
* &lt;code&gt;T volatile&lt;/code&gt; = volatile T; objects of this type may be externally visible/modifyable
* &lt;code&gt;T*&lt;/code&gt; = pointer to T
* &lt;code&gt;T[n]&lt;/code&gt; (n any constant integer) = array of n Ts
* &lt;code&gt;T&amp;&lt;/code&gt; = reference to T; gives a new name to an existing object
Note that the pointer type (&lt;code&gt;T*&lt;/code&gt;) is a built-in type even if T is not. Also note that for array types, variable names as well as further type specifiers go ''in between'' T and [n]. In some cases parentheses are put around that part in order to remove ambiguities.

The following shows a few examples:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
&lt;&lt;basic types&gt;&gt;
int const ci = 3; // compile time constant
int const ci2 = some_function(); // constant, but initialized at run time
int volatile vi; // This may be visible from outside the program
int const volatile cvi; // The program may not change it, but external processes might
int* pi = &amp;i; // pointer to int, initialized to point to i
int const* pci = &amp;i; // pointer to constant int, initialized to i; cannot be used to change i
int* const cpi = &amp;i; // constant pointer to int, initialized i; can be used to change i,
                     // but not reset to point somewhere else
int const* const cpci = &amp;i; // constant pointer to constant int, pointing to i
int const* cpi2 = &amp;ci; // pointer to constant int can (but need not) point to actually constant int
void* pv = pi; // pointer to void pointing to i; stores address, but loses type information
void const* pcv = pci; // constness matters also for pointer to void
int ai[3] = { 1, 2, 3 }; // array of 3 ints
int* api[3]; // array of 3 pointers to int
int (*pai)[3]; // pointer to array of 3 ints
int* (*pai)[5]; // pointer to array of 5 pointers to int
int a2[3][4]; // two-dimensional array; actually an array of 3 arrays of 4 ints each
int&amp; ri = i; // gives a new name to i
int const&amp; rci = ai[1]; // gives a name to the second member of the array ai;
                        // the name cannot be used to modify ai[1].
&lt;/codeblock&gt;
In addition to that, there are function types, of the form ''return type''(''arguments''). While you cannot define variables of that type (the corresponding syntax defines functions), you can create pointers and references to functions, and those can be used to define variables. Like with arrays, the function name or further type specifiers go in the middle, just after the return type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
void foo(int);          // not a variable, but a function declaration
void (*pf)(int) = foo;  // a function pointer pointing to foo
void (**pf)(int) = &amp;pf; // a pointer to pointer to function, pointing to pf
void (&amp;rf)(int) = foo;  // a function reference to foo; seldom used,
                        // works identical to a const pointer
&lt;/codeblock&gt;
In addition to those built-in types (and a few more to be introduced later), there are various user-defined types. The simplest one is the enumeration type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum color { red, orange, yellow, green, blue, violet }; // defines type &quot;color&quot;
color background = green; // a variable of type color
&lt;/codeblock&gt;
Enumeration values implicitly convert to integer values; by default, the first enumerator (&lt;code&gt;red&lt;/code&gt; in the example above) is given the value 0, the second enumerator gets 1, and so on. However, it's also possible to explicitly give values:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum flags { flag0 = 1, flag1 = 2, flag3 = 4, flag4 = 8, flag5 = 16 };
&lt;/codeblock&gt;
Note however that despite the implicit conversion, an enumeration is still a separate type. For example, you cannot assign an int to a variable of enumeration type (without explicit typecast), and you can overload operators on enumeration types.

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16498</id>
      <timestamp>2009-08-25T19:23:12Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Variables and types */ again a bit more</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==

=== Variable definition ===
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a variable initialization can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

=== Built-in types ===
C++ has a variety of built-in types. The following variable definitions show all basic types of C++:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;basic types&gt;&gt;=
char c = 'a';  // character type, guaranteed to have size of one byte
char c2 = 48;  // the type char actually is a numeric type (on systems using ASCII, this initializes c2 with '0'
signed char sc = -3; // one byte, signed (i.e. can take negative values)
unsigned char uc = 3; // one byte, unsigned (i.e. all values are non-negative)
// note that the type char has the same representation and value range as either signed char or unsigned char,
// but is a distinct type from both

wchar_t wc = L'a'; // wide character type

short s = -300s; // signed short integer; same type as signed short, short int, signed short int
unsigned short us = 300us; // unsigned short integer; same type as unsigned short int

int i = -1000; // signed integer; same type as signed int, signed
unsigned u = 1000u; // unsigned integer; same type as unsigned int

long l = -100000L; // long signed integer; same type as long int, signed long, signed long int
unsigned long ul = 100000UL; // long unsigned integer; same type as unsigned long int

bool b = false; // boolean variable; can only take the values false and true (but implicit conversion from/to int exists)

float f = 1.0f; // floating point variable
double d = 1.0; // floating point variable (usually double precision)
long double d = 1.0L; // floating point value (at least same precision as double, sometimes more)

// the following types are not in the current C++ standard, but a very common extension,
// part of C99, and will be part of next version of the C++ standard
long long ll = -1000000000LL; // very long integer, same as long long int, signed long long, signed long long int
unsigned long long ull = 1000000000ULL; // unsigned version of long long
&lt;/codeblock&gt;
In addition, there's the type &lt;code&gt;void&lt;/code&gt; which is special in that you cannot define variables of that type. However you can use it as return type, and in the following type constructs (with the exception of references and arrays).

For each C++ type T with the exception of reference types (see below), you can create any of the following types:
* &lt;code&gt;T const&lt;/code&gt; = constant T; you cannot modify objects of this type
* &lt;code&gt;T volatile&lt;/code&gt; = volatile T; objects of this type may be externally visible/modifyable
* &lt;code&gt;T*&lt;/code&gt; = pointer to T
* &lt;code&gt;T[n]&lt;/code&gt; (n any constant integer) = array of n Ts
* &lt;code&gt;T&amp;&lt;/code&gt; = reference to T; gives a new name to an existing object
Note that the pointer type (&lt;code&gt;T*&lt;/code&gt;) is a built-in type even if T is not. Also note that for array types, variable names as well as further type specifiers go ''in between'' T and [n]. In some cases parentheses are put around that part in order to remove ambiguities.

The following shows a few examples:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
&lt;&lt;basic types&gt;&gt;
int const ci = 3; // compile time constant
int const ci2 = some_function(); // constant, but initialized at run time
int volatile vi; // This may be visible from outside the program
int const volatile cvi; // The program may not change it, but external processes might
int* pi = &amp;i; // pointer to int, initialized to point to i
int const* pci = &amp;i; // pointer to constant int, initialized to i; cannot be used to change i
int* const cpi = &amp;i; // constant pointer to int, initialized i; can be used to change i,
                     // but not reset to point somewhere else
int const* const cpci = &amp;i; // constant pointer to constant int, pointing to i
int const* cpi2 = &amp;ci; // pointer to constant int can (but need not) point to actually constant int
void* pv = pi; // pointer to void pointing to i; stores address, but loses type information
void const* pcv = pci; // constness matters also for pointer to void
int ai[3] = { 1, 2, 3 }; // array of 3 ints
int* api[3]; // array of 3 pointers to int
int (*pai)[3]; // pointer to array of 3 ints
int* (*pai)[5]; // pointer to array of 5 pointers to int
int a2[3][4]; // two-dimensional array; actually an array of 3 arrays of 4 ints each
int&amp; ri = i; // gives a new name to i
int const&amp; rci = ai[1]; // gives a name to the second member of the array ai;
                        // the name cannot be used to modify ai[1].
&lt;/codeblock&gt;
In addition to that, there are function types, of the form ''return type''(''arguments''). While you cannot define variables of that type (the corresponding syntax defines functions), you can create pointers and references to functions, and those can be used to define variables. Like with arrays, the function name or further type specifiers go in the middle, just after the return type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
void foo(int);          // not a variable, but a function declaration
void (*pf)(int) = foo;  // a function pointer pointing to foo
void (**pf)(int) = &amp;pf; // a pointer to pointer to function, pointing to pf
void (&amp;rf)(int) = foo;  // a function reference to foo; seldom used,
                        // works identical to a const pointer
&lt;/codeblock&gt;

=== User-defined types ===
In addition to those built-in types (and a few more to be introduced later), there are various user-defined types. User-defined types have to be defined in every file where they are used. Those definitions have to be the same. This is usually achieved by defining it in a header which then gets included in all files needing the definition.

The simplest one is the enumeration type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum color { red, orange, yellow, green, blue, violet }; // defines type &quot;color&quot;
color background = green; // a variable of type color
&lt;/codeblock&gt;
Enumeration values implicitly convert to integer values; by default, the first enumerator (&lt;code&gt;red&lt;/code&gt; in the example above) is given the value 0, the second enumerator gets 1, and so on. However, it's also possible to explicitly give values:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum flags { flag0 = 1, flag1 = 2, flag3 = 4, flag4 = 8, flag5 = 16 };
&lt;/codeblock&gt;
Note however that despite the implicit conversion, an enumeration is still a separate type. For example, you cannot assign an int to a variable of enumeration type (without explicit typecast), and you can overload operators on enumeration types.

The next type is the class type. Class types can be written with the keyword &lt;code&gt;struct&lt;/code&gt; or &lt;code&gt;class&lt;/code&gt;. The only difference between both is that with &lt;code&gt;struct&lt;/code&gt; access is public by default, while with &lt;code&gt;class&lt;/code&gt; it's private. The following defines a simple class type &lt;code&gt;node&lt;/code&gt; which has two public member variables: An integer named &lt;code&gt;value&lt;/code&gt; and a pointer to &lt;code&gt;node&lt;/code&gt; named &lt;code&gt;next&lt;/code&gt;:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct node
{
  int value;
  node* next;
};
&lt;/codeblock&gt;
This also shows that the type's name already can be used inside the type definition, although in restricted ways: It can be used to define pointer and reference members, and to declare member functions (see below). Such a type is called ''incomplete type.'' After the end of the definition, the type is complete, and there's no restriction as to how it can be used.

If somewhere you only need the incomplete type, you can also just declare that type. Such a declaration looks like this:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct node;
&lt;/codeblock&gt;
After that declaration, the name &lt;code&gt;node&lt;/code&gt; is recognized by the compiler as incomplete type (unless a complete definition has been seen before).

The following defines a variable of type &lt;code&gt;node&lt;/code&gt; (this requires the type to be complete):
&lt;codeblock&gt;
&lt;&lt;vars&gt;&gt;=
node some_node;
&lt;/codeblock&gt;
For C compatibility, also the following definition is allowed:
&lt;codeblock&gt;
&lt;&lt;vars&gt;&gt;=
struct node some_other_node;
&lt;/codeblock&gt;
But this latter form is unidiomatic in C++.

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16513</id>
      <timestamp>2009-09-20T10:02:32Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* User-defined types */ expanded a bit</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of the C++ programming language.

== Functions ==
A function generally has the following structure:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function&gt;&gt;=
&lt;&lt;return type&gt;&gt; &lt;&lt;function name&gt;&gt;(&lt;&lt;argument list&gt;&gt;)
{
  &lt;&lt;function body&gt;&gt;
}
&lt;/codeblock&gt;

Each program has at least one function:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function name&gt;&gt;=
main
&lt;/codeblock&gt;

The function &lt;code&gt;main&lt;/code&gt; is called at program startup. As arguments it gets the number of arguments and a list of the program arguments. Those are traditionally named &lt;code&gt;argc&lt;/code&gt; and &lt;code&gt;argv&lt;/code&gt;, but that's just convention, not demanded by the language.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;argument list&gt;&gt;=
int argc, char* argv[]
&lt;/codeblock&gt;
Note that if the program doesn't need program arguments, the argument list may also be empty instead.

The return type of the main function is always
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;return type&gt;&gt;=
int
&lt;/codeblock&gt;
The returned integer is given back to the operating system in order to indicate success or failure. Returning 0 always indicates success:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function body&gt;&gt;=
return 0;
&lt;/codeblock&gt;
Note that for the main function (and only for the main function), not having a return statement is equivalent to returning 0.

The main function is the only thing which absolutely must be written. Therefore this function alone is already a complete program (which in this case does nothing):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;do_nothing.cc&gt;&gt;=
&lt;&lt;function&gt;&gt;
&lt;/codeblock&gt;

==Includes==
A typical C++ program needs to use libraries (including the C++ standard library), and usually consists of more than one file. To make declarations visible in more than one file, they are written in separate files, usually called headers. The naming of header files is completely arbitrary (as far as the compiler is concerned; some editors automatically switch to appropriate C++ editing modes if the file has a recogniced extension). Typically header files get one of the extensions &quot;.h&quot; (like C headers), &quot;.H&quot;, &quot;.hh&quot;, &quot;.hpp&quot;, &quot;.hxx&quot; or &quot;.h++&quot; (note that some file systems don't allow the last one as file name). An exception are the standard library headers which don't have an extension at all (but for compatibility, the C headers are also available in the traditional &quot;.h&quot; form).

Header files are included with the preprocessor directive &lt;code&gt;#include&lt;/code&gt;. For standard headers (or headers provided by the system), the file name is enclosed in angle brackets, which causes the compiler only to search the system directories. For self-written headers, the name is enclosed in quotes. Note that include directives provide pure textual inclusion, therefore they should not be used inside any program construct (unless the header is specially designed for that, but that's extremely unusual).

By convention, the include directives are usually collected at the beginning of the C++ file:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example2.cc&gt;&gt;=
&lt;&lt;includes of example 2&gt;&gt;

&lt;&lt;rest of example 2&gt;&gt;
&lt;/codeblock&gt;

The example program unconditionally tells the operating system that the program has failed. For that, there exists a special value, &lt;code&gt;EXIT_FAILURE&lt;/code&gt;. Note that this is the only truly portable way to signal failure; different operating systems have different conventions to indicate success or failure.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;rest of example 2&gt;&gt;=
int main()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;
The value &lt;code&gt;EXIT_FAILURE&lt;/code&gt; is defined in the header &lt;code&gt;cstdlib&lt;/code&gt; (and the corresponding C header &lt;code&gt;stdlib.h&lt;/code&gt;). Therefore this header must be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes of example 2&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The following example program implements a helper function &lt;code&gt;failure&lt;/code&gt; (which just returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;) in a separate file. The complete program consists of ''three'' files: The header file declaring the function, the implementation file defining it, and the main file calling it.

Since header files might be included (indirectly) several times into the same main file, but certain constructs may not be repeated, header files should always get an include guard (although in this simple case, it would not be needed):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h&gt;&gt;=
#ifndef FAILURE_H_INCLUDED
#define FAILURE_H_INCLUDED

&lt;&lt;failure.h contents&gt;&gt;

#endif
&lt;/codeblock&gt;
The include guard tests if a header-specific macro is defined, and only if not, passes the rest of the header to the compiler. The first thing it does in that conditional part is to define the macro, so if the same header is included again, the macro will be defined. Note that for this to work, the macro name may not be used otherwise, therefore it should be derived from the file name.

In this case, the header just forward declares the function &lt;code&gt;failure&lt;/code&gt;, which takes no arguments and returns an int:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.h contents&gt;&gt;=
int failure();
&lt;/codeblock&gt;

The function is implemented in the file failure.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc&gt;&gt;=
&lt;&lt;failure.cc includes&gt;&gt;

&lt;&lt;function failure implementation&gt;&gt;
&lt;/codeblock&gt;

By convention, the first thing an implementation file should do is to include the corresponding header. For one, inclusion of the header is usually necessary anyway to get definitions from there. In addition, including it first gives a nice test that the header is self-contained.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;

The implementation of the function is quite simple: It just (again) returns &lt;code&gt;EXIT_FAILURE&lt;/code&gt;.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;function failure implementation&gt;&gt;=
int failure()
{
  return EXIT_FAILURE;
}
&lt;/codeblock&gt;

To make &lt;code&gt;EXIT_FAILURE&lt;/code&gt; available, failure.cc must include cstdlib.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;failure.cc includes&gt;&gt;=
#include &lt;cstdlib&gt;
&lt;/codeblock&gt;

The main program is implemented in the file example3.cc:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc&gt;&gt;=
&lt;&lt;example3.cc includes&gt;&gt;

&lt;&lt;example 3 main function&gt;&gt;
&lt;/codeblock&gt;

The main function just calls &lt;code&gt;failure&lt;/code&gt; to get the value to return:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example 3 main function&gt;&gt;=
int main()
{
  return failure();
}
&lt;/codeblock&gt;
To do so, the header failure.h has to be included:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example3.cc includes&gt;&gt;=
#include &quot;failure.h&quot;
&lt;/codeblock&gt;
Note that there's no need to include cstdlib, since &lt;code&gt;EXIT_FAILURE&lt;/code&gt; isn't used in this file.

The program example3 of course does exactly the same as example2: just report failure to the operating system.

== Basic Input and Output ==
Input and output in C++ are done with streams. The standard output stream is &lt;code&gt;std::cout&lt;/code&gt;. Output is done with the &lt;code&gt;&lt;&lt;&lt;/code&gt; operator. A hello world program could therefore read:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc&gt;&gt;=
&lt;&lt;hello.cc includes&gt;&gt;

int main()
{
  std::cout &lt;&lt; &quot;Hello world!&quot; &lt;&lt; std::endl;
}
&lt;/codeblock&gt;
The &lt;code&gt;std::endl&lt;/code&gt; outputs a newline and makes sure the line is actually output.

The stream &lt;code&gt;std::cout&lt;/code&gt; is found in the standard header iostream:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;hello.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;/codeblock&gt;

Input is done by using the &lt;code&gt;&gt;&gt;&lt;/code&gt; operator on &lt;code&gt;std::cin&lt;/code&gt;, which is found in the same standard header. The following program reads an integer and then prints it again:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc&gt;&gt;=
#include &lt;iostream&gt;

int main()
{
  &lt;&lt;io.cc ask for integer&gt;&gt;
  &lt;&lt;io.cc read integer&gt;&gt;
  &lt;&lt;io.cc output message about integer&gt;&gt;
}
&lt;/codeblock&gt;
First, we output a message that we want an integer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc ask for integer&gt;&gt;=
std::cout &lt;&lt; &quot;Please enter an integer value: &quot;;
&lt;/codeblock&gt;

Then we read an integer. For this, we need an integer variable. Note that in C++ a common style rule is that a variable should be defined as close to its initialization as possible. In the ideal case, it would be initialized directly at the definition, but for input that's not posible. However, we deferred the definition until directly before the input statement:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer&gt;&gt;=
&lt;&lt;io.cc define integer variable&gt;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;
&lt;/codeblock&gt;

The variable is named &lt;code&gt;value&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;. It is defined as follows:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc define integer variable&gt;&gt;=
int value;
&lt;/codeblock&gt;
Finally we can read the integer value.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc read integer into variable&gt;&gt;=
std::cin &gt;&gt; value;
&lt;/codeblock&gt;
The stream &lt;code&gt;std::cin&lt;/code&gt; is tied to the stream &lt;code&gt;std::cout&lt;/code&gt;, so that the text of the previous output statement is guaranteed to be output before waiting for the input.

Finally, we output a message telling which value was input.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;io.cc output message about integer&gt;&gt;=
std::cout &lt;&lt; &quot;The number you typed was &quot; &lt;&lt; value &lt;&lt; std::endl;
&lt;/codeblock&gt;

== Variables and types ==

=== Variable definition ===
In C++, variables are typically defined by writing its type followed by the variable name and an (usually) optional initialization. For example, the following defines a variable named &lt;code&gt;v&lt;/code&gt; of type &lt;code&gt;int&lt;/code&gt;, which gets initialized with 3:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v as int and initialize with 3&gt;&gt;=
int v(3);
&lt;/codeblock&gt;
There's another syntax, called copy initialization, which often looks more natural, but isn't always allowed (and in some cases has subtly different meaning, but not for simple types like &lt;code&gt;int&lt;/code&gt;):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;=
int v2 = 3;
&lt;/codeblock&gt;
Sometimes a variable initialization can have more than one argument, e.g. thew following defines a double-precision complex number variable named z with the initial value (2+3i):
&lt;codeblock&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;complex&gt;
&lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;=
std::complex&lt;double&gt; z(2,3);
&lt;/codeblock&gt;
However, some types don't follow the simple rule above. One example is the array type, where the size of the array comes to the right:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;=
int primes[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
&lt;/codeblock&gt;
Note that if an initialization is given, the compiler can figure out the length by itself:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;define array a without explicitly giving length&gt;&gt;=
int a[] = { 1, 2, 3, 4, 5 };
&lt;/codeblock&gt;

Variable definitions can be both at global scope or at function scope:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
&lt;&lt;variables.cc includes&gt;&gt;

// variables at global scope
&lt;&lt;define v as int and initialize with 3&gt;&gt;
&lt;&lt;define v2 as int and copy-initialize with 3&gt;&gt;
&lt;&lt;define primes as array of 10 ints and initialize it with the first 10 primes&gt;&gt;

void f()
{
  // variables at function scope
  &lt;&lt;define c as std::complex&amp;lt;double&amp;gt; and initialize it with (2+3i)&gt;&gt;
  &lt;&lt;define array a without explicitly giving length&gt;&gt;
}
&lt;/codeblock&gt;
Global variables exist as long as the program runs, function scope variables only exist during the execution of the function. However, the lifetime of local variables can be extended by prefixing with static. In that case, initialization occurs the first time the the definition is executed:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc&gt;&gt;=
int remember(int init)
{
  static int var = init;
  return var;
}
&lt;/codeblock&gt;

The main function demonstrates this by calling the function twice with different values, and showing the result each time:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;variables.cc includes&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;variables.cc&gt;&gt;=
int main()
{
  std::cout &lt;&lt; remember(42) &lt;&lt; &quot;\n&quot;;
  std::cout &lt;&lt; remember(39) &lt;&lt; &quot;\n&quot;; // outputs 42 again
}
&lt;/codeblock&gt;

=== Built-in types ===
C++ has a variety of built-in types. The following variable definitions show all basic types of C++:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;basic types&gt;&gt;=
char c = 'a';  // character type, guaranteed to have size of one byte
char c2 = 48;  // the type char actually is a numeric type (on systems using ASCII, this initializes c2 with '0'
signed char sc = -3; // one byte, signed (i.e. can take negative values)
unsigned char uc = 3; // one byte, unsigned (i.e. all values are non-negative)
// note that the type char has the same representation and value range as either signed char or unsigned char,
// but is a distinct type from both

wchar_t wc = L'a'; // wide character type

short s = -300s; // signed short integer; same type as signed short, short int, signed short int
unsigned short us = 300us; // unsigned short integer; same type as unsigned short int

int i = -1000; // signed integer; same type as signed int, signed
unsigned u = 1000u; // unsigned integer; same type as unsigned int

long l = -100000L; // long signed integer; same type as long int, signed long, signed long int
unsigned long ul = 100000UL; // long unsigned integer; same type as unsigned long int

bool b = false; // boolean variable; can only take the values false and true (but implicit conversion from/to int exists)

float f = 1.0f; // floating point variable
double d = 1.0; // floating point variable (usually double precision)
long double d = 1.0L; // floating point value (at least same precision as double, sometimes more)

// the following types are not in the current C++ standard, but a very common extension,
// part of C99, and will be part of next version of the C++ standard
long long ll = -1000000000LL; // very long integer, same as long long int, signed long long, signed long long int
unsigned long long ull = 1000000000ULL; // unsigned version of long long
&lt;/codeblock&gt;
In addition, there's the type &lt;code&gt;void&lt;/code&gt; which is special in that you cannot define variables of that type. However you can use it as return type, and in the following type constructs (with the exception of references and arrays).

For each C++ type T with the exception of reference types (see below), you can create any of the following types:
* &lt;code&gt;T const&lt;/code&gt; = constant T; you cannot modify objects of this type
* &lt;code&gt;T volatile&lt;/code&gt; = volatile T; objects of this type may be externally visible/modifyable
* &lt;code&gt;T*&lt;/code&gt; = pointer to T
* &lt;code&gt;T[n]&lt;/code&gt; (n any constant integer) = array of n Ts
* &lt;code&gt;T&amp;&lt;/code&gt; = reference to T; gives a new name to an existing object
Note that the pointer type (&lt;code&gt;T*&lt;/code&gt;) is a built-in type even if T is not. Also note that for array types, variable names as well as further type specifiers go ''in between'' T and [n]. In some cases parentheses are put around that part in order to remove ambiguities.

The following shows a few examples:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
&lt;&lt;basic types&gt;&gt;
int const ci = 3; // compile time constant
int const ci2 = some_function(); // constant, but initialized at run time
int volatile vi; // This may be visible from outside the program
int const volatile cvi; // The program may not change it, but external processes might
int* pi = &amp;i; // pointer to int, initialized to point to i
int const* pci = &amp;i; // pointer to constant int, initialized to i; cannot be used to change i
int* const cpi = &amp;i; // constant pointer to int, initialized i; can be used to change i,
                     // but not reset to point somewhere else
int const* const cpci = &amp;i; // constant pointer to constant int, pointing to i
int const* cpi2 = &amp;ci; // pointer to constant int can (but need not) point to actually constant int
void* pv = pi; // pointer to void pointing to i; stores address, but loses type information
void const* pcv = pci; // constness matters also for pointer to void
int ai[3] = { 1, 2, 3 }; // array of 3 ints
int* api[3]; // array of 3 pointers to int
int (*pai)[3]; // pointer to array of 3 ints
int* (*pai)[5]; // pointer to array of 5 pointers to int
int a2[3][4]; // two-dimensional array; actually an array of 3 arrays of 4 ints each
int&amp; ri = i; // gives a new name to i
int const&amp; rci = ai[1]; // gives a name to the second member of the array ai;
                        // the name cannot be used to modify ai[1].
&lt;/codeblock&gt;
In addition to that, there are function types, of the form ''return type''(''arguments''). While you cannot define variables of that type (the corresponding syntax defines functions), you can create pointers and references to functions, and those can be used to define variables. Like with arrays, the function name or further type specifiers go in the middle, just after the return type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
void foo(int);          // not a variable, but a function declaration
void (*pf)(int) = foo;  // a function pointer pointing to foo
void (**pf)(int) = &amp;pf; // a pointer to pointer to function, pointing to pf
void (&amp;rf)(int) = foo;  // a function reference to foo; seldom used,
                        // works identical to a const pointer
&lt;/codeblock&gt;

=== User-defined types ===
In addition to those built-in types (and a few more to be introduced later), there are various user-defined types. User-defined types have to be defined in every file where they are used. Those definitions have to be the same. This is usually achieved by defining it in a header which then gets included in all files needing the definition.

The simplest one is the enumeration type:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum color { red, orange, yellow, green, blue, violet }; // defines type &quot;color&quot;
color background = green; // a variable of type color
&lt;/codeblock&gt;
Enumeration values implicitly convert to integer values; by default, the first enumerator (&lt;code&gt;red&lt;/code&gt; in the example above) is given the value 0, the second enumerator gets 1, and so on. However, it's also possible to explicitly give values:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
enum flags { flag0 = 1, flag1 = 2, flag3 = 4, flag4 = 8, flag5 = 16 };
&lt;/codeblock&gt;
Note however that despite the implicit conversion, an enumeration is still a separate type. For example, you cannot assign an int to a variable of enumeration type (without explicit typecast), and you can overload operators on enumeration types.

The next type is the class type. Class types can be written with the keyword &lt;code&gt;struct&lt;/code&gt; or &lt;code&gt;class&lt;/code&gt;. The only difference between both is that with &lt;code&gt;struct&lt;/code&gt; access is public by default, while with &lt;code&gt;class&lt;/code&gt; it's private. The following defines a simple class type &lt;code&gt;node&lt;/code&gt; which has two public member variables: An integer named &lt;code&gt;value&lt;/code&gt; and a pointer to &lt;code&gt;node&lt;/code&gt; named &lt;code&gt;next&lt;/code&gt;:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct node
{
  int value;
  node* next;
};
&lt;/codeblock&gt;
This also shows that the type's name already can be used inside the type definition, although in restricted ways: It can be used to define pointer and reference members, and to declare member functions (see below). Such a type is called ''incomplete type.'' After the end of the definition, the type is complete, and there's no restriction as to how it can be used.

If somewhere you only need the incomplete type, you can also just declare that type. Such a declaration looks like this:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct node;
&lt;/codeblock&gt;
After that declaration, the name &lt;code&gt;node&lt;/code&gt; is recognized by the compiler as incomplete type (unless a complete definition has been seen before).

The following defines a variable of type &lt;code&gt;node&lt;/code&gt; (this requires the type to be complete):
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vars&gt;&gt;=
node some_node;
&lt;/codeblock&gt;
For C compatibility, also the following definition is allowed:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vars&gt;&gt;=
struct node some_other_node;
&lt;/codeblock&gt;
But this latter form is unidiomatic in C++.

User defined variables can also be initialized at definition time (and it is encouraged to do so). Types like &lt;code&gt;node&lt;/code&gt; which don't have user-defined constructors (see below) can be initialized by giving the values of the members in braces:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vars&gt;&gt;=
node initialized_node = { 7, &amp;some_node };
&lt;/codeblock&gt;
Here &lt;code&gt;&amp;&lt;/code&gt; is the adress-of operator, which gives a pointer to the object it is applied to (i.e. &lt;code&gt;some_node&lt;/code&gt;).

Besides data members, classes can also have member functions. For example:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct vector3d
{
  double x, y, z;
  double length();
};

double vector3d::length()
{
  return std::sqrt(x*x+y*y+z*z);
}

&lt;&lt;vars&gt;&gt;=
vector3d diagonal = { 1, 1, 1 };
double diagonal_length = diagonal.length(); // sqrt(3)
&lt;/codeblock&gt;

There are some member functions which have special syntax and/or semantics. One important example are constructors and destructors. Constructors are written by just appending an argument list to the class name. Those are demonstrated with the following example class:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;types&gt;&gt;=
struct example_class
{
  &lt;&lt;example class constructor declarations&gt;&gt;
  int i;
};

&lt;&lt;example class constructor definitions&gt;&gt;
&lt;/codeblock&gt;

The simplest constructor is the default constructor. It can be used to initialize an object without giving an explicit initializer:
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;example class constructor declarations&gt;&gt;=
example_class();
&lt;&lt;example class constructor definitions&gt;&gt;=
example_class::example_class():
  i(3)
{
  std::cout &lt;&lt; &quot;default-initialized an object. i = &quot; &lt;&lt; i &lt;&lt; &quot;\n&quot;;
}
&lt;/codeblock&gt;
The part starting with &quot;:&quot; is the constructor initializer list; it tells how to initialize the members (in this case, initialize i with 3).

With this constructor, if you write
&lt;codeblock language=&quot;c++&quot;&gt;
example_class example_variable;
&lt;/codeblock&gt;
then the above constructor will be called.

Indeed, if you don't implement any constructor yourself, the compiler will always generate a default-constructor for you; however that default constructor will just call the default constructors of the contained members of user-defined type and let the non-initialized members of built-in type uninitialized.

[[Category:Programming language:C Plus Plus]]
[[Category:Basic constructs]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (C)</title>
    <id>2362</id>
    <revision>
      <id>6382</id>
      <timestamp>2006-06-21T14:27:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Variables ==

== Functions ==

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;loops&gt;&gt;

int main(int argc, char *argv[])
{
	loops();
	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>6383</id>
      <timestamp>2006-06-21T14:29:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Category:Programming language:C</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Variables ==

== Functions ==

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;loops&gt;&gt;

int main(int argc, char *argv[])
{
	loops();
	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6387</id>
      <timestamp>2006-06-21T20:40:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Command line arguments */ Filename chunk header</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Variables ==

== Functions ==

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;loops&gt;&gt;

int main(int argc, char *argv[])
{
	loops();
	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6393</id>
      <timestamp>2006-06-21T22:11:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>simple i/o, rm empty sections</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char b[80];

	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

int main(int argc, char *argv[])
{
	loops();

	io();

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6394</id>
      <timestamp>2006-06-21T22:12:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* File reading writing */ s/b/line/</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

int main(int argc, char *argv[])
{
	loops();

	io();

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6395</id>
      <timestamp>2006-06-21T22:13:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Simple I/O */ fix chunk name</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

int main(int argc, char *argv[])
{
	loops();

	io();

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6405</id>
      <timestamp>2006-06-21T23:10:54Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <minor/>
      <comment>Added a quick note about infinite loops</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

int main(int argc, char *argv[])
{
	loops();

	io();

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6462</id>
      <timestamp>2006-06-23T17:08:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Command line arguments */ + example of argument handling</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, argv[0]);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6463</id>
      <timestamp>2006-06-23T17:09:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Command line arguments */ s/argv[0]/cmd/</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>7413</id>
      <timestamp>2006-08-18T12:31:43Z</timestamp>
      <contributor>
        <username>Ruediger Hanke</username>
        <id>16</id>
      </contributor>
      <minor/>
      <comment>Spelling</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11077</id>
      <timestamp>2007-10-08T15:36:43Z</timestamp>
      <contributor>
        <ip>85.17.186.161</ip>
      </contributor>
      <text xml:space="preserve">daracel
{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11094</id>
      <timestamp>2007-10-08T16:57:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11203</id>
      <timestamp>2007-10-13T07:46:17Z</timestamp>
      <contributor>
        <ip>200.1.123.30</ip>
      </contributor>
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{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11216</id>
      <timestamp>2007-10-13T07:57:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>12017</id>
      <timestamp>2008-01-10T05:25:43Z</timestamp>
      <contributor>
        <ip>217.172.56.174</ip>
      </contributor>
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{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>12021</id>
      <timestamp>2008-01-10T07:18:46Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{develop}}

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/C/Tutorials/ This page] at Google Directory provide links to some C tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the difference in the assembly code generated for the two different loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'' when the end of the file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write them to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and write to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (Java)</title>
    <id>2396</id>
    <revision>
      <id>6556</id>
      <timestamp>2006-06-30T11:26:32Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Getting started: Straight copy of Basic Constructs (C)</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic Constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/Java/Tutorials/ This page] at Google Directory provide links to some Java tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (C)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6557</id>
      <timestamp>2006-06-30T11:27:17Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* See also */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic Constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/Java/Tutorials/ This page] at Google Directory provide links to some Java tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6558</id>
      <timestamp>2006-06-30T11:28:17Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>corrected an internal link</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://directory.google.com/Top/Computers/Programming/Languages/Java/Tutorials/ This page] at Google Directory provide links to some Java tutorials.

== Loops ==

There are 3 standard ways to create a loop in C.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=c&gt;
&lt;&lt;forloop&gt;&gt;=
	for(n=0; n&lt;10; ++n) {
		printf(&quot;%d\n&quot;, n);
	}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=c&gt;
&lt;&lt;whileloop&gt;&gt;=
	n=0;
	while(n&lt;10) {
		printf(&quot;%d\n&quot;, n);
		++n;
	}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=c&gt;
&lt;&lt;dowhileloop&gt;&gt;=
	n=0;
	do {
		printf(&quot;%d\n&quot;, n);
		++n;
	} while(n&lt;10);

&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;loops&gt;&gt;=
void loops()
{
	int n;

&lt;&lt;forloop&gt;&gt;

&lt;&lt;whileloop&gt;&gt;

&lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as for(;;) , while(1) . For embedded systems where wasted CPU cycles are undesirable there might be a small speed advantage in using the for(;;) as it causes no evaluation. A (do{ }) while(1) will evaluate the expression depending on how smart the compiler is. It might be worth it to check the diffrence in the assembly code generated for the two diffrent loops.

== Simple I/O ==

Most programs dealing with input/output include the stdio.h header file.

&lt;codeblock language=c&gt;
&lt;&lt;include stdio.h&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.

&lt;codeblock language=c&gt;
&lt;&lt;stdio&gt;&gt;=
	while((ch=getchar())!=EOF) {
		putchar(ch);
	}
&lt;/codeblock&gt;

=== File reading writing ===

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=c&gt;
&lt;&lt;fileio&gt;&gt;=

	if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
		return;
	}

	line[79]='\0';
	fgets(line, 80, fp);

	fclose(fp);

	if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
		fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
		return;
	}

	fputs(line, fp);

	fclose(fp);

&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;io&gt;&gt;=

void io()
{
	FILE *fp;
	char line[80];
	int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

The ''argc'' argument to ''main()'' is the number of arguments specified when invoking the command. This number includes the command itself. ''argv'' is an array of the arguments itself. When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=c&gt;
&lt;&lt;basic_constructs.c&gt;&gt;=
#include&lt;stdio.h&gt;

&lt;&lt;include stdio.h&gt;&gt;
#include&lt;string.h&gt;
#include&lt;stdlib.h&gt;

&lt;&lt;loops&gt;&gt;

&lt;&lt;io&gt;&gt;

void usage(const char *cmd)
{
	fprintf(stderr, &quot;Usage %s loops|io\n&quot;, cmd);
	exit(1);
}

int main(int argc, char *argv[])
{
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: Wrong number of arguments\n&quot;);
		usage(argv[0]);
		return 1;
	}

	if(!strcmp(argv[1], &quot;loops&quot;)) loops();
	else if(!strcmp(argv[1], &quot;io&quot;)) io();
	else {
		fprintf(stderr, &quot;ERROR: Unknown command: \&quot;%s\&quot;\n&quot;, argv[1]);
		usage(argv[0]);
	}

	return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6559</id>
      <timestamp>2006-06-30T12:10:34Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>First draft: class definition and loop examples are probably correct. But IO needs conversion from C to Java</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;forloop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;whileloop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;dowhileloop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;forloop&gt;&gt;

    &lt;&lt;whileloop&gt;&gt;

    &lt;&lt;dowhileloop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;stdio&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;fileio&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;io&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

&lt;&lt;stdio&gt;&gt;

&lt;&lt;fileio&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;io&gt;&gt;

    private void usage()
    {
        System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
        System.exit(1);
    }

    public static void main(String[] args)
    {
        if (args.length &lt; 1) {
            System.err(&quot;ERROR: Wrong number of arguments&quot;);
            usage();
        }

        BasicConstructs bc = new BasicConstructs();

        for (int i = 0; i &lt; args.length; i++) {
            if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
            else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
            else {
                System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
                usage();
            }

            System.exit(0);

        }
    }
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6560</id>
      <timestamp>2006-06-30T12:14:01Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>improved names of chuncks (no need to run words together)</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file I/O&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input/output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

&lt;&lt;standard input/output&gt;&gt;

&lt;&lt;file I/O&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;io&gt;&gt;

    private void usage()
    {
        System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
        System.exit(1);
    }

    public static void main(String[] args)
    {
        if (args.length &lt; 1) {
            System.err(&quot;ERROR: Wrong number of arguments&quot;);
            usage();
        }

        BasicConstructs bc = new BasicConstructs();

        for (int i = 0; i &lt; args.length; i++) {
            if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
            else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
            else {
                System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
                usage();
            }

            System.exit(0);

        }
    }
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6561</id>
      <timestamp>2006-06-30T12:18:18Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>code corrections</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

&lt;&lt;standard input and output&gt;&gt;

&lt;&lt;file input and output&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    private void usage()
    {
        System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
        System.exit(1);
    }

    public static void main(String[] args)
    {
        if (args.length &lt; 1) {
            System.err(&quot;ERROR: Wrong number of arguments&quot;);
            usage();
        }

        BasicConstructs bc = new BasicConstructs();

        for (int i = 0; i &lt; args.length; i++) {
            if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
            else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
            else {
                System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
                usage();
            }

            System.exit(0);

        }
    }
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6562</id>
      <timestamp>2006-06-30T12:19:29Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* File reading writing */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). When wrong arguments are specified, programs normally display an error mesage, along with a usage message showing the allowed arguments.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    private void usage()
    {
        System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
        System.exit(1);
    }

    public static void main(String[] args)
    {
        if (args.length &lt; 1) {
            System.err(&quot;ERROR: Wrong number of arguments&quot;);
            usage();
        }

        BasicConstructs bc = new BasicConstructs();

        for (int i = 0; i &lt; args.length; i++) {
            if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
            else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
            else {
                System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
                usage();
            }

            System.exit(0);

        }
    }
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6563</id>
      <timestamp>2006-06-30T12:29:59Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Refactored explanation of command line arguments</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
       usage();
    }

    System.exit(0);

}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program, or incorrect or unexpected arguments are encountered while processing the command-line arguments, programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6564</id>
      <timestamp>2006-06-30T12:34:19Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Command line arguments */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }

    System.exit(0);

}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6565</id>
      <timestamp>2006-06-30T12:37:47Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Code correction</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java */
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java */
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}

&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6566</id>
      <timestamp>2006-06-30T12:47:22Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Commented IO so we can test rest of program</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java */
while((ch = getchar())!= EOF) {
    putchar(ch);
}
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java 
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
*/
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6567</id>
      <timestamp>2006-06-30T12:48:09Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Commented out more IO</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
/* Rewrite this C code for Java 
void io()
{
  FILE *fp;
  char line[80];
  int ch;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
*/
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6568</id>
      <timestamp>2006-06-30T12:49:56Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* File reading writing */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6569</id>
      <timestamp>2006-06-30T12:52:03Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>corrected calls to usage</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6570</id>
      <timestamp>2006-06-30T12:54:30Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>more corrections of compiler errors</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    &lt;&lt;validate command-line arguments&gt;&gt;

    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6571</id>
      <timestamp>2006-06-30T12:56:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Another compiler error</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
'''TODO: rewrite this in Java'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6572</id>
      <timestamp>2006-06-30T12:59:51Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Standard input/output */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;. 

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6573</id>
      <timestamp>2006-06-30T13:02:21Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Improved output a little</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will read characters from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
/* This won't work in Java 
while((ch = getchar())!= EOF) {
    putchar(ch);
}
*/
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6575</id>
      <timestamp>2006-06-30T13:22:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Code for STDIO</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will a line from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Enter a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
}
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6576</id>
      <timestamp>2006-06-30T13:23:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Standard input/output */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will a line from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Enter a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6577</id>
      <timestamp>2006-06-30T13:24:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Standard input/output */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will a line from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6578</id>
      <timestamp>2006-06-30T13:26:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added &quot;throws Exception&quot; to main method</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will a line from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io()
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6579</id>
      <timestamp>2006-06-30T13:27:05Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added &quot;throws IOException&quot; to io method</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
'''TODO: rewrite this in Java'''

''getchar()'' is used to read one character from the standard input stream (stdin). It returns ''EOF'', when end of file is reached. We use ''putchar()'' to write to the standard output stream (stdout). The following code will a line from stdin, and write it to stdout.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6580</id>
      <timestamp>2006-06-30T13:43:40Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added explanation of console and error output. Still need to describe the complexities of keyboard input.</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!\n&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds a new line character to the text of the argument). A useful additional method call is System.out.println() which prints a new line character.

'''Rest of this section is Work in Progress'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6581</id>
      <timestamp>2006-06-30T13:44:18Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Standard input/output */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!\n&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds a new line character to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints a new line character.

'''Rest of this section is Work in Progress'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6582</id>
      <timestamp>2006-06-30T13:49:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added a bit more explanation of println() versus print(&quot;\n&quot;)</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

'''Rest of this section is Work in Progress'''
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6585</id>
      <timestamp>2006-07-01T10:20:53Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Documentation for console IO finished</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [Wikipedia|Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all, text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));&lt;/codeblock&gt;
&lt;codeblock language=&quot;java&quot;&gt;
Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6589</id>
      <timestamp>2006-07-01T10:34:04Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>minor edit to correct documentation</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

Before reading from or writing to a file, ''fopen()'' is used to open it. There are lots of functions able to read from and writing to files. We choose ''fgets()'' and ''fputs()''. This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
/* Correct me: This won't work in Java
if((fp=fopen(&quot;input.txt&quot;, &quot;r&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot read \&quot;input.txt\&quot;\n&quot;);
    return;
}

line[79]='\0';
fgets(line, 80, fp);

fclose(fp);

if((fp=fopen(&quot;output.txt&quot;, &quot;w&quot;))==NULL) {
    fprintf(stderr, &quot;Cannot write \&quot;output.txt\&quot;\n&quot;);
    return;
}

fputs(line, fp);

fclose(fp);
*/
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  /* Rewrite this C code for Java
  FILE *fp;
  char line[80];
  int ch;
  */

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6590</id>
      <timestamp>2006-07-01T11:00:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>File IO in progress</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

'''TODO''' rewrite for Java

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6591</id>
      <timestamp>2006-07-01T11:04:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Checkpoint: file IO edit in progress...</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;




== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6592</id>
      <timestamp>2006-07-01T11:06:59Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* File reading writing */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

Edit in progress:

* Read line
* Close input file
* Open output file
* Write line
* Close output file

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6593</id>
      <timestamp>2006-07-01T11:24:18Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* File reading writing */</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
..read line, error if null
&lt;/codeblock&gt;


* Close input file
Edit in progress:

* Open output file
* Write line
* Close output file

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6594</id>
      <timestamp>2006-07-01T13:45:07Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>File input complete</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
String line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = in.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
in.close();
&lt;/codeblock&gt;

Edit in progress:

* Open output file
* Write line
* Close output file

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6595</id>
      <timestamp>2006-07-01T13:46:40Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Removed declaration of line from example (it's declared earlier)</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;
To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = in.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
in.close();
&lt;/codeblock&gt;

Edit in progress:

* Open output file
* Write line
* Close output file

Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6596</id>
      <timestamp>2006-07-01T14:01:06Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>File IO Complete: Ready for testing</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;);
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6597</id>
      <timestamp>2006-07-01T14:02:38Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Missing closing quote!</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;);
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6598</id>
      <timestamp>2006-07-01T14:03:13Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Another missing quote!</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;);
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;);
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6599</id>
      <timestamp>2006-07-01T14:08:46Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Fixed a couple of compiler errors. Code should now work!</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6600</id>
      <timestamp>2006-07-01T14:11:52Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added a reference to Eckel (used for details of file IO)</comment>
      <text xml:space="preserve">{{develop}}
'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6601</id>
      <timestamp>2006-07-01T14:12:41Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Removed {{{develop}}} tag. Ready for review.</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6602</id>
      <timestamp>2006-07-01T14:14:18Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Tidying up punctiation</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has an exception handler built-in to the system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled. Here we print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6603</id>
      <timestamp>2006-07-01T14:17:25Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Handling IO Exceptions */</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]

[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6604</id>
      <timestamp>2006-07-01T14:18:41Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added &quot;Basic constructs (C)&quot; to See Also section</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6802</id>
      <timestamp>2006-07-11T12:46:58Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Basic constructs (Java)]] moved to [[Basic constructs (Java) on Wheels]]</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6966</id>
      <timestamp>2006-07-11T14:28:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Basic constructs (Java) on Wheels]] moved to [[Basic constructs (Java)]]: revert</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. [http://java.sun.com/docs/books/tutorial/ That Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>7410</id>
      <timestamp>2006-08-18T11:54:38Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Minor correction of introduction</comment>
      <text xml:space="preserve">'''At the moment just a straight copy of [[Basic constructs (C)]].'''

This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. The [http://java.sun.com/docs/books/tutorial/ Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>7411</id>
      <timestamp>2006-08-18T11:57:03Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Removed &quot;this is a copy of Basic Constructs (C), because with extended treatment of Java IO, it isn't any more!</comment>
      <text xml:space="preserve">This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. The [http://java.sun.com/docs/books/tutorial/ Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data around (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. The make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>7412</id>
      <timestamp>2006-08-18T11:59:38Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Corrections to the commentary</comment>
      <text xml:space="preserve">This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. The [http://java.sun.com/docs/books/tutorial/ Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. To make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the execption handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>13238</id>
      <timestamp>2008-04-28T00:31:37Z</timestamp>
      <contributor>
        <ip>140.141.216.118</ip>
      </contributor>
      <comment>/* Handling IO Exceptions */</comment>
      <text xml:space="preserve">This article describes some basic constructs in the [http://en.wikipedia.org/wiki/Java_programming_language Java programming language]. This is not a tutorial, just a collection of example code. The [http://java.sun.com/docs/books/tutorial/ Java Tutorial] is the standard place to go for a tutorial introduction to the Java language.

== Loops ==

There are 3 standard ways to create a loop in Java.

The for-loop is the most commonly used.

The following example will print the numbers from ''0'' to ''9'' on separate lines.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;for loop&gt;&gt;=
System.out.println(&quot;For loop&quot;);
for(int i = 0; i &lt; 10; i++) {
    System.out.println(i);
}
System.out.println();
&lt;/codeblock&gt;

Here is an example of a while-loop. The output is exactly the same as in the for-loop example.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;while loop&gt;&gt;=
System.out.println(&quot;While loop&quot;);
int j = 0;
while(j &lt; 10) {
    System.out.println(j);
    j++;
}
System.out.println();
&lt;/codeblock&gt;

The do-while-loop works like the while-loop, except the test expression is evaluated after the code block.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;do-while loop&gt;&gt;=
System.out.println(&quot;Do-while loop&quot;);
int k = 0;
do {
    System.out.println(k);
    k++;
} while (k &lt; 10);
System.out.println();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;loops&gt;&gt;=
public void loops()
{
    &lt;&lt;for loop&gt;&gt;

    &lt;&lt;while loop&gt;&gt;

    &lt;&lt;do-while loop&gt;&gt;
}
&lt;/codeblock&gt;

Note:
Sometimes infinite (never ending) loops might be useful. You can write them as &lt;code&gt;for(;;)&lt;/code&gt;, &lt;code&gt;while(true)&lt;/code&gt;.

== Simple I/O ==

Unfortunately, compared with similar languages like C, Java's I/O is rather more challenging than it should be. Most programs dealing with input/output require the ''java.io'' package.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;import java.io&gt;&gt;=
import java.io.*;
&lt;/codeblock&gt;

Java has a very rich IO system. Here we illustrate the two most commonly required IO methods: standard input and output (input from keyboard, output to console) and text-file IO.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;input and output&gt;&gt;=
void io() throws IOException
{
  String line = null;

  &lt;&lt;standard input and output&gt;&gt;

  &lt;&lt;file input and output&gt;&gt;
}
&lt;/codeblock&gt;

=== Standard input/output ===
Output to the console (stdout) and the error stream (stderr) is relatively simple in Java and is handled by the methods &lt;code&gt;println(String)&lt;/code&gt; and &lt;code&gt;print(String)&lt;/code&gt; of the &lt;code&gt;java.io.PrintStream&lt;/code&gt; methods of the system objects &lt;code&gt;java.lang.System.out&lt;/code&gt; and &lt;code&gt;java.lang.System.err&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
System.out.print(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;/code&gt; and 
&lt;codeblock language=&quot;java&quot;&gt;
System.out.println(&quot;Hello World!&quot;);
&lt;/codeblock&gt;
prints &lt;code&gt;Hello World!&lt;NEWLINE&gt;&lt;/code&gt; (that is &lt;code&gt;println&lt;/code&gt; adds the system-specific new-line character sequence to the text of the argument). A useful additional method call is &lt;code&gt;System.out.println()&lt;/code&gt; which prints only the new line character. For portability it is safer to use &lt;code&gt;println&lt;/code&gt; than to use the C-like convention &lt;code&gt;System.out.print(&quot;Hello World!\n&quot;);&lt;/code&gt;

In Java, intput from the keyboard (stdin) is more of a challenge! For reasons of flexibility, the Java IO system is designed so that different sources and sinks of data can easily be combined. For this purpose it makes use of the [http://en.wikipedia.org/wiki/Decorator_pattern Decorator pattern] which makes it relatively simple to wrap a suitable IO processor around any source of data (for example a file, keyboard or network connection). Unfortunately, the designers of the language failed to provide a simple-to-use object for the simplest form of IO of all: text from the keyboard. The object &lt;code&gt;java.lang.System.in&lt;/code&gt;, which represents the keyboard, is a &lt;code&gt;java.io.InputStream&lt;/code&gt;, an object which cannot be used directly to input lines of text. To make it useful as a source of strings, &lt;em&gt;System.in&lt;/em&gt; has to be decorated by an &lt;code&gt;InputStreamReader&lt;/code&gt; which itself has to be decorated by a &lt;code&gt;BufferedStreamReader&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;create source of input&gt;&gt;=
BufferedReader in = new BufferedReader(
    new InputStreamReader(System.in));
&lt;/codeblock&gt;

Once we have done this, we can read a line from the keyboard using the method &lt;code&gt;in.readLine()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;standard input and output&gt;&gt;=
System.out.println(&quot;Standard I/O&quot;);
&lt;&lt;create source of input&gt;&gt;
System.out.print(&quot;Type a line of text (enter with Return): &quot;);
line = in.readLine();
System.out.println(&quot;You entered: &quot; + line);
System.out.println();
&lt;/codeblock&gt;

=== File reading writing ===

This code will read the first line of the file ''input.txt'' and write the same line to ''output.txt''.

=== Create a File to Read and Write ===

Let's create a file for testing purposes.
&lt;codeblock&gt;
&lt;&lt;input.txt&gt;&gt;=
Now is the Winter of our Discontent
Made glorious Summer by this son of Yorke;
&lt;/codeblock&gt;

=== Reading from a Text File ===

To read a text file it has to be opened. In Java this is achieved decorating a &lt;code&gt;FileReader&lt;/code&gt; with a &lt;code&gt;BufferedReader&lt;/code&gt;. The filename is passed to the &lt;code&gt;FileReader&lt;/code&gt; as a constructor argument.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open input file&gt;&gt;=
BufferedReader fin = new BufferedReader(
    new FileReader(&quot;input.txt&quot;));
&lt;/codeblock&gt;

To read a line from the file, we simply call &lt;code&gt;readLine()&lt;/code&gt; on the &lt;code&gt;BufferedReader&lt;/code&gt;. If we have reached the end of the line, &lt;code&gt;readLine&lt;/code&gt; returns &lt;code&gt;null&lt;/code&gt;:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;read first line from input file&gt;&gt;=
line = fin.readLine();
if (line == null) 
    throw new EOFException(&quot;Unexpected End of File encountered while reading \&quot;input.txt\&quot;&quot;);
&lt;/codeblock&gt;


Closing an input file is a simple as calling the &lt;code&gt;close()&lt;/code&gt; method on the &lt;code&gt;BufferedReader&lt;/code&gt;. This will also close the &lt;code&gt;FileReader&lt;/code&gt; and hence the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close input file&gt;&gt;=
fin.close();
&lt;/codeblock&gt;

=== Writing a Text File ===

Opening a file for writing is similar to the procedure for opening a file for reading. This time we decorate a &lt;code&gt;FileWriter&lt;/code&gt; with a &lt;code&gt;BufferedWriter&lt;/code&gt;, and decorate the &lt;code&gt;BufferedWriter&lt;/code&gt; in turn with a &lt;code&gt;PrintWriter&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;open output file&gt;&gt;=
PrintWriter fout = new PrintWriter(
    new BufferedWriter(
        new FileWriter(&quot;output.txt&quot;)));
&lt;/codeblock&gt;

We can use &lt;code&gt;fout.println&lt;/code&gt; to print the line to this new file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;write line to output file&gt;&gt;=
fout.println(line);
&lt;/codeblock&gt;

Now close the &lt;code&gt;PrintWriter&lt;/code&gt; which closes the file.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;close output file&gt;&gt;=
fout.close();
&lt;/codeblock&gt;

=== Handling IO Exceptions ===
Java has support for exceptions built-into the language, and an exception handler built-in to the runtime system. IO operations should make use of ''try-catch'' blocks to ensure that any IO errors are handled by the exception handler. As we can't actually do anything useful if this progam fails (which will most likely be due to file permissions), we simply print an error message and ''rethrow'' the exception which will cause the program to close and print a stack trace.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;file input and output&gt;&gt;=
try {
    &lt;&lt;open input file&gt;&gt;
    &lt;&lt;read first line from input file&gt;&gt;
    &lt;&lt;close input file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot read \&quot;input.txt\&quot;&quot;);
    throw e;
}

try {
    &lt;&lt;open output file&gt;&gt;
    &lt;&lt;write line to output file&gt;&gt;
    &lt;&lt;close output file&gt;&gt;
}
catch (IOException e) {
    System.err.println(&quot;ERROR: Cannot write to \&quot;output.txt\&quot;&quot;);
    throw e;
}
&lt;/codeblock&gt;

== Command line arguments ==

Java is always executed by starting the virtual machine and passing it the class that contains the ''main'' method:
  java AClass [command line arguments]

The optional command line arguments are passed to the body of the main method via an array of strings which is conventionally named &lt;code&gt;args&lt;/code&gt;. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args) throws Exception
{
    BasicConstructs bc = new BasicConstructs();

    &lt;&lt;validate command-line arguments&gt;&gt;

    &lt;&lt;process command-line arguments&gt;&gt;
 
    System.exit(0);
}
&lt;/codeblock&gt;
Array access is used to access the arguments. The number of arguments to process will be accessible via the field &lt;code&gt;args.length&lt;/code&gt;. Unlike C, this number does not include the command itself (which will always be ''java classname''). 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process command-line arguments&gt;&gt;=
for (int i = 0; i &lt; args.length; i++) {
    if ( &quot;loops&quot;.equals(args[i]) ) bc.loops();
    else if ( &quot;io&quot;.equals(args[i]) ) bc.io();
    else {
       &lt;&lt;unexpected command-line argument&gt;&gt;
    }
}
&lt;/codeblock&gt;

When the wrong number of arguments are passed to the program: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;validate command-line arguments&gt;&gt;=
if (args.length &lt; 1) {
    System.err.println(&quot;ERROR: Wrong number of arguments&quot;);
    bc.usage();
}
&lt;/codeblock&gt;
or incorrect or unexpected arguments are encountered while processing the command-line arguments:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected command-line argument&gt;&gt;=
System.err.println(&quot;ERROR: Unexpected command line argument: &quot; + args[i]);
bc.usage();
&lt;/codeblock&gt;
programs normally display an error mesage, along with a usage message showing the allowed arguments.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;display usage message&gt;&gt;=
private void usage()
{
    System.err.println(&quot;Usage java BasicConstructs loops|io&quot;);
    System.exit(1);
}
&lt;/codeblock&gt;

== The Program ==

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BasicConstructs.java&gt;&gt;=
&lt;&lt;import java.io&gt;&gt;

public class BasicConstructs {

    &lt;&lt;loops&gt;&gt;

    &lt;&lt;input and output&gt;&gt;

    &lt;&lt;display usage message&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

== Reference ==

Bruce Eckel, ''Thinking in Java'', 4th Ed., Prentice Hall, 2006.

== See also ==

* [[Hello World (Java)]]
* [[Basic constructs (C)]]
[[Category:Basic constructs]]
[[Category:Programming language:Java]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (OCaml)</title>
    <id>2935</id>
    <revision>
      <id>8682</id>
      <timestamp>2007-01-25T22:09:59Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <comment>Initial entry</comment>
      <text xml:space="preserve">This article describes some basic constructs in  [http://caml.inria.fr OCaml]. This is not a tutorial, just a collection of example code. The [http://www.ocaml-tutorial.org/ Objective CAML Tutorial] is a fine tutorial introduction to OCaml.

==Functions==

As OCaml is a functional programming language, it seems appropriate to cover function definition first.  In OCaml there are a few different ways to declare a function, but the most common is the standard &lt;code&gt;let&lt;/code&gt; definition.  Here, the general structure of the definition is &lt;code&gt;let funname param1 ... paramN = body of function&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let add a b = a + b;;
&lt;/codeblock&gt;

Note the two semicolons at the end of the definition.  This bit of punctuation is used in OCaml to signify the end of an expression.  However, it is usually an optional bit of punctuation.  When writing code that will be compiled or run through the interpreter one doesn't need to include the semicolons.  The only time they are needed is when working with the [http://caml.inria.fr/pub/docs/manual-ocaml/manual023.html interactive toploop], then the semicolons are needed to signal to the interpreter that the expression (or set of expressions) you've just typed in are to be evaluated.

Also note that the parameters are separate elements following the function name, not a parenthesized list like in many common languages.  This doesn't mean that you can't use that style of function definition, it just means something slightly different.  Unlike the definition above, which takes two parameters adds them and returns the result, the definition

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function2&gt;&gt;=
let add' (a, b) = a + b;;
&lt;/codeblock&gt;

creates a function that takes a single parameter which is a two-tuple, deconstructs the tuple, adds the constituent elements and returns the result.  These functions are applied as one might expect:

&lt;codeblock language=ocaml&gt;
# add 10 15;;
- : int = 25
# add' (30, 40);;
- : int = 70
&lt;/codeblock&gt;

===Anonymous functions===

Another way to define a function is with the &lt;code&gt;fun&lt;/code&gt; keyword:

&lt;codeblock language=ocaml&gt;
fun a b -&gt; a + b;;
&lt;/codeblock&gt;

This creates a function without a name (an anonymous function) that adds two values together.  This may seem like an odd concept to some, but in functional languages, a function is just a value, like strings or ints, and no one finds the use of unnamed strings and ints odd.  As we will see in a bit, this is actually quite useful.

Anonymous functions can be applied in a fairly straight-forward manner:

&lt;codeblock language=ocaml&gt;
#   (fun a b -&gt; (a * 10) + b) 5 7;;
- : int = 57
&lt;/codeblock&gt;

And as they are simply values, we can use &lt;code&gt;let&lt;/code&gt; to bind them to a name:

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_anon&gt;&gt;=
let add_anon = fun a b -&gt; a + b;;
&lt;/codeblock&gt;

&lt;codeblock&gt;
#   add_anon 10 3;;
- : int = 13
&lt;/codeblock&gt;

This isn't immediately useful, but there are places where it comes in handy.  Note also that this is equivalent to &lt;code&gt;let&lt;/code&gt; construction shown first -- indeed, the &lt;code&gt;let&lt;/code&gt; construction is just sugar for this form.

===Pattern matching functions===

Functions can also be defined using the &lt;code&gt;function&lt;/code&gt; keyword and pattern matching.  Here, &lt;code&gt;function&lt;/code&gt; accepts a single value and tries to match it to one of several patterns.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let silly = function
| 0 -&gt; &quot;zero&quot;
| 1 -&gt; &quot;one&quot;
| x when x &lt; 2 -&gt; &quot;negative number&quot;
| _ -&gt; &quot;some other number&quot;
&lt;/codeblock&gt;

Here, the patterns are separated with the &lt;code&gt;|&lt;/code&gt; character (the initial one is optional), and they are constructed by specifying the pattern to be matched, followed by a &lt;code&gt;-&gt;&lt;/code&gt;, followed by the code to perform if that case matches.  The  patterns are checked in order, and only the first match is used, so in the example above, passing a 0 into &lt;code&gt;silly&lt;/code&gt; will result in &quot;zero&quot; being returned, and not &quot;negative number&quot;, even though it matches the pattern &lt;code&gt;x when x &amp;lt; 2&gt;&lt;/code&gt; as well.  The final pattern &lt;code&gt;_&lt;/code&gt; is a pattern that matches all values, and here would be matched by all numbers greater than 1.  Another variant of this would use a pattern like &lt;code&gt;| x -&gt; &quot;something&quot;&lt;/code&gt;.  Here, the &lt;code&gt;x&lt;/code&gt; matches anything, but instead of throwing away the value that was matched, it is bound to the name &lt;code&gt;x&lt;/code&gt;, and can be used in the code for that case, e.g. &lt;code&gt;| x -&gt; sprintf &quot;You passed in: %d&quot; x&lt;/code&gt;.

Note that these constructs can be combined:

&lt;codeblock language=ocaml&gt;
&lt;&lt;combo_function&gt;&gt;=
let sillier a = fun b -&gt; function
| 0 -&gt; a
| 1 -&gt; b
| x when x &lt; 2 -&gt; a + b
| _ -&gt; a * b
&lt;/codeblock&gt;

Here, &lt;code&gt;sillier&lt;/code&gt; is a function that takes three values, integers &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt;, and a third integer that selects the operations we perform on a and b.

&lt;codeblock language=ocaml&gt;
# sillier 10 20 0;;
- : int = 10
# sillier 10 20 1;;
- : int = 20
# sillier 10 20 (-1);;
- : int = 30
# sillier 10 20 100;;
- : int = 200
&lt;/codeblock&gt;

===Recursive functions===

If one wishes to define a recursive function, they must use the &lt;code&gt;let rec&lt;/code&gt; construct to inform the compiler/interpreter, that the specified name is to be used recursively.

&lt;codeblock language=ocaml&gt;
&lt;&lt;factorial&gt;&gt;=
let rec factorial n = if n &lt;= 1 then 1 else factorial (n-1) * n
&lt;/codeblock&gt;

This can also be used with the &lt;code&gt;function&lt;/code&gt; keyword in a useful way.  Here we compute the length of a list using pattern matching.  First we check if the list is empty, if it is, then the length is 0.  If not, we match it against some unused element and the tail of the list, and we then recursively call &lt;code&gt;length&lt;/code&gt; on the tail of the list and add 1 to the result.

&lt;codeblock language=ocaml&gt;
&lt;&lt;length&gt;&gt;=
let rec length = function
| [] -&gt; 0
| _::t -&gt; length t + 1
&lt;/codeblock&gt;

===Higher order functions===

As we have seen, functions are values in OCaml, just like ints, floats, and strings, and so we can pass them into functions as arguments, as well as create and return them from functions.  Functions that accept other functions as parameters are referred to as higher order functions (HOFs).  An example of this is a function that searches a list for the first element that matches some predicate.

&lt;codeblock language=ocaml&gt;
&lt;&lt;find&gt;&gt;=
let rec find test = function
| [] -&gt; raise Not_found
| h::t -&gt; if test h then h else find test t
&lt;/codeblock&gt;

Here we pass an anonymous function into find in order to find the first value greater than 10 and then to find the first negative value.  The last example looks for the first multiple of 11, and not finding any raises the built-in exception &lt;code&gt;Not_found&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
let l = [1; 1; 2; 3; 5; 8; 13; 21; -7; 600];;

find (fun x -&gt; x &gt; 10) l;;
find (fun x -&gt; x &lt; 0) l;;
find (fun x -&gt; x mod 11 = 0) l;;
&lt;/codeblock&gt;

===Currying===

Currying is (in essence) a way looking at functions of multiple arguments as a series of functions of one argument that return functions that work with the other arguments.  In OCaml, this makes sense, as functions are values, and can be created and returned by other functions trivially.  As an example of what this means, consider the first function example on this page, &lt;code&gt;let add a b = a + b&lt;/code&gt;.  We generally think of this as a function that accepts two arguments and returns a value.  Really, it's not that at all.

OCaml converts that function definition under the covers to the equivalent:

&lt;codeblock language=ocaml&gt;
&lt;&lt;curry&gt;&gt;=
let add = fun a -&gt; fun b -&gt; a + b
&lt;/codeblock&gt;

What this form means is that &lt;code&gt;add&lt;/code&gt; is a function that takes a single argument, binds its value to the name a and returns an anonymous function that takes a single argument, binds its value to the name b, and then computes the value a+b according to the bindings from the function applications and returns the result.  Why this is important is that it allows us to use partial application to specialize the functions we have.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;partial&gt;&gt;=
let add1 = add 1;;
let add10 = add 10;;
&lt;/codeblock&gt;

Here, we have used Currying to our advantage to create two new functions, &lt;code&gt;add1&lt;/code&gt; and &lt;code&gt;add10&lt;/code&gt; that each take a single argument and add 1 and 10 to that argument, respectively.

&lt;codeblock&gt;
# add1 10;;
- : int = 11
# add10 10;;
- : int = 20
&lt;/codeblock&gt;

==Conditionals==

There are two forms of conditionals in OCaml, if/then expressions and pattern matching.

===If/Then===

The if then construct is fairly straight-forward, and similar to similar constructs in other languages.  The basic form of the if/then is &lt;code&gt;if test then e1 else e2&lt;/code&gt;, where &lt;code&gt;test&lt;/code&gt; is an expression that evaluates to a boolean value, and &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; are expressions that are evaluated in the true and false branches of the test respectively.  The primary catch with if/then in OCaml is that both &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; must have the same type, so expressions like &lt;code&gt;if test then 1 else &quot;two&quot;&lt;/code&gt; are not allowed.  Additionally if the type of the true branch is &lt;code&gt;unit&lt;/code&gt;, then the else branch is not required, e.g. &lt;code&gt;if test then print_string &quot;true!&quot;&lt;/code&gt; is equivalent to &lt;code&gt;if test then print_string &quot;true!&quot; else ()&lt;/code&gt;.  Note, however, that this con lead to mistakes where multiple unit valued expressions are to be executed in a given branch.  For example:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;;
  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

This is parsed as

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;;
)

  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which results in a syntax error.  More troublesome is something like the following:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which is parsed as:

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
);  
print_endline &quot;what?&quot;
&lt;/codeblock&gt;

So the &lt;code&gt;print_endline &quot;what?&quot;&lt;/code&gt; expression is always evaluated.  To be safe, wrap multi-statement blocks in parens or &lt;code&gt;begin/end&lt;/code&gt; pairs

&lt;codeblock language=ocaml&gt;
if test then
  (
    print_endline &quot;hi&quot;;
    print_string &quot;baby&quot;
  )
else
  begin
    print_string &quot;bye&quot;;
    print_endline &quot;what?&quot;
  end
&lt;/codeblock&gt;

===Pattern Matching===

Pattern matching is a powerful construct of OCaml that allows for conditional branching based on the structure and content of a value.  Pattern matching is initiated in OCaml in one of two ways: the first is the &lt;code&gt;function&lt;/code&gt; keyword, described above, and the second is the &lt;code&gt;match ... with&lt;/code&gt; construct.  The general form of the &lt;code&gt;match ... with&lt;/code&gt; construct is as follows:

&lt;codeblock language=ocaml&gt;
match exp with
| patt_1 -&gt; ex_1
...
| patt_n -&gt; ex_n
&lt;/codeblock&gt;

That is, the keyword &lt;code&gt;match&lt;/code&gt; followed by an expression that evaluates to a value, followed by the &lt;code&gt;with&lt;/code&gt; keyword, then a series of pattern/expression pairs, separated by &lt;code&gt;|&lt;/code&gt; characters (the first one is optional).  The value that &lt;code&gt;exn&lt;/code&gt; evaluates to is checked against the patterns, in order of definition, and if one matches (say &lt;code&gt;patt_i&lt;/code&gt;), then the entire match expression reduces to the corresponding expression (&lt;code&gt;ex_i&lt;/code&gt;).

A pattern can be any of the following recursive constructs:
* A constant value : one of { integer-literal, float-literal; char-literal, string-literal, constant variant value, &lt;code&gt;false&lt;/code&gt;, &lt;code&gt;true&lt;/code&gt;, &lt;code&gt;[]&lt;/code&gt;, &lt;code&gt;()&lt;/code&gt;, constant polymorphic variant }
* &lt;code&gt;_&lt;/code&gt; : matches any pattern and throws away the value
* variable-name  : matches any pattern and binds the value to the variable name for use in the corresponding expression
* ''pattern'' as variable-name : the value that matches ''pattern'' is bound to variable-name for use in the corresponding expression
* ( ''pattern'' )
* ( ''pattern'' : type-annotation )
* ''pattern'' | ''pattern'' : multiple patterns may correspond to the same expression
* constr ''pattern'' : Here, constr is one of OCaml's variant type values, and ''pattern'' is its associated data
* `tag-name ''pattern'' : Here, tag-name is one of OCaml's polymorphic variants, and ''pattern'' is its associated data
* # typeconstr-name : used to match some set of polymorphic variants
* ''pattern'', ''pattern'', ..., ''pattern'' : these are tuples of patterns
* { field-name_1 = ''pattern''; ... ; field-name_n = ''pattern''} : matching against records
* [ ''pattern'' ; ... ; ''pattern''] : matching against a list
* ''pattern'' :: ''pattern'' : matching against consed values
* [| ''pattern'' ; ... ; ''pattern'' |] : matching against arrays

Some example patterns are

* &lt;code&gt;[]&lt;/code&gt; : the empty list
* &lt;code&gt;h::t&lt;/code&gt; : a non empty list, binding the head and tail to the variables &lt;code&gt;h&lt;/code&gt; and &lt;code&gt;t&lt;/code&gt;, respectively
* &lt;code&gt;h::_&lt;/code&gt; : a non empty list, binding the head to &lt;code&gt;h&lt;/code&gt; and throwing away the tail
* &lt;code&gt;(_,_,x)&lt;/code&gt; : a three-tuple where the first two values are thrown away and the third is bound to &lt;code&gt;x&lt;/code&gt;
* h::(h2::_ as t) : a list with at least two elements in it, where the head is bound to &lt;code&gt;h&lt;/code&gt;, the second element is bound to &lt;code&gt;h2&lt;/code&gt;, and the list minus its first value is bound to &lt;code&gt;t&lt;/code&gt;
* &lt;code&gt;Some ((h1,(h2 : float),_,1)::next::_)&lt;/code&gt; : a &lt;code&gt;Some&lt;/code&gt; constructer with associated data that is a list of four-tuples, at least two elements in length, where the first value in the tuple at the head is bound to &lt;code&gt;h1&lt;/code&gt;, the second is bound to &lt;code&gt;h2&lt;/code&gt; and is restricted to being a floating point value, the third is thrown away, and the fourth is a 1.  The second element is bound to &lt;code&gt;next&lt;/code&gt;, and the rest of the list is thrown away.

This kind of feature is very powerful, and lets us write very succinct code that operates on the structure of data.  For example, a function that throws away every other element of a list can be written simply:

&lt;codeblock language=ocaml&gt;
&lt;&lt;odds&gt;&gt;=
let rec odds = function
| ([] | [_]) as l -&gt; l
| h::_::t -&gt; h::(odds t);;
&lt;/codeblock&gt;

Here the first pattern matches lists with zero or one elements and returns that list, while the second pattern matches all lists with at least two elements, throws away the second, saves the first, and conses it onto the list created by throwing away every other element of the remaining list.

==Looping==

While looping is often handled via recursive functions in OCaml, e.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;loop_rec&gt;&gt;=
let rec loop times f =
match times with
| 0 -&gt; ()
| _ -&gt; f (); loop (times-1) f;;
&lt;/codeblock&gt;

there are other built-in options, the &lt;code&gt;for&lt;/code&gt; and &lt;code&gt;while loops&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
for counter = start to stop do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
while test do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

The for loop loops over the range provided (both endpoints inclusive), performing whatever code lies within the &lt;code&gt;do&lt;/code&gt; and &lt;code&gt;done&lt;/code&gt; keywords, rebinding the counter variable to the current value each time.  For loops can also count backwards, using &lt;code&gt;downto&lt;/code&gt; rather than &lt;code&gt;to&lt;/code&gt;.  The endpoints of the loop don't have to be constants, they can be any expression that evaluates to an int, and the entire for loop evaluates to &lt;code&gt;()&lt;/code&gt;.  Note that there is no &quot;step&quot; option as in languages such as C.

While loops are similar to those found in other languages.  So long as the conditional evaluates to &lt;code&gt;true&lt;/code&gt;, the loop body is evaluated.  Like the for loop, the entire while loop evaluates to &lt;code&gt;()&lt;/code&gt;.

==I/O==

===Simple I/O===
I/O is performed using stdin, stdout, and stderr using the various read, print, and prerr functions respectively.

; &lt;code&gt;read_line&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Returns the resulting string, minus the newline.
; &lt;code&gt;read_int&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to an int, raising an exception if it cannot.
; &lt;code&gt;read_float&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to a float, raising an exception if it cannot.
; &lt;code&gt;print_char&lt;/code&gt; : prints a character to stdout
; &lt;code&gt;print_newline&lt;/code&gt; : prints a newline character to stdout
; &lt;code&gt;print_string&lt;/code&gt; : prints a string to stdout
; &lt;code&gt;print_endline&lt;/code&gt; : prints a string to stdout followed by a newline character
; &lt;code&gt;print_int&lt;/code&gt; : prints an int to stdout
; &lt;code&gt;print_float&lt;/code&gt; : prints a float to stdout
; &lt;code&gt;prerr_char&lt;/code&gt; : prints a character to stderr
; &lt;code&gt;prerr_newline&lt;/code&gt; : prints a newline character to stderr
; &lt;code&gt;prerr_string&lt;/code&gt; : prints a string to stderr
; &lt;code&gt;prerr_endline&lt;/code&gt; : prints a string to stderr followed by a newline character
; &lt;code&gt;prerr_int&lt;/code&gt; : prints an int to stderr
; &lt;code&gt;prerr_float&lt;/code&gt; : prints a float to stderr

Formatted printing can be done via the &lt;code&gt;Printf&lt;/code&gt; module which contain (among other things) functions &lt;code&gt;printf&lt;/code&gt; and &lt;code&gt;sprintf&lt;/code&gt; that use format strings similar to those of C.  E.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;printf&gt;&gt;=
Printf.printf &quot;0x%0X\n&quot; 500;;
let s = Printf.sprintf &quot;%d: %s --\t%08.3f&quot; 7 &quot;whoopie&quot; 1.4432578;;
&lt;/codeblock&gt;

will print &lt;code&gt;0x1F4&lt;/code&gt; followed by a newline to stdout, and bind the string &lt;code&gt;&quot;7: whoopie --	0001.443&quot;&lt;/code&gt; to &lt;code&gt;s&lt;/code&gt;.

===File I/O===

Files are usually worked with via input and output channels.  To open the file data.in for reading and the file data.out for writing, one would do the following:

&lt;codeblock language=ocaml&gt;
&lt;&lt;channels&gt;&gt;=
let in_channel = open_in &quot;data.in&quot;
let out_channel = open_out &quot;data.out&quot;
&lt;/codeblock&gt;

The channels can now be read from and written to using the various input and output functions.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;io&gt;&gt;=
let line = input_line in_channel
output_string out_channel line; output_char out_channel '\n';;
&lt;/codeblock&gt;

Will read the next line from in_channel (connected to data.in), and copy that line followed by a newline character into out_channel (connected to data.out).  Doing this repeatedly would copy data.in to data.out.

In addition to the simple I/O functions, formatted data can also be written using the &lt;code&gt;Printf&lt;/code&gt; module's &lt;code&gt;fprintf&lt;/code&gt; function.  Here, &lt;code&gt;Printf.fprintf channel format arg1 ... argN&lt;/code&gt; will print arguments 1 through N to output channel &lt;code&gt;channel&lt;/code&gt; according to the format string &lt;code&gt;format&lt;/code&gt;.

==Command line arguments==

Command line arguments are available as a string array named &lt;code&gt;Sys.argv&lt;/code&gt;.  &lt;code&gt;Sys.argv.(0)&lt;/code&gt; contains the name of the program that was executed, and subsequent entries in the array contain the additional arguments, if any, un the order they were presented on the command line.  So, to print the name of the program followed by the arguments, each on a new line, one can do:

&lt;codeblock language=ocaml&gt;
&lt;&lt;arguments&gt;&gt;=
print_endline Sys.argv.(0);
for i = 1 to Array.length Sys.argv - 1 do
  print_endline Sys.argv.(i)
done;;
&lt;/codeblock&gt;

==The Program==
&lt;codeblock&gt;
&lt;&lt;basic_constructs.ml&gt;&gt;=
&lt;&lt;let_function&gt;&gt;

&lt;&lt;let_function2&gt;&gt;

&lt;&lt;let_anon&gt;&gt;

&lt;&lt;let_function&gt;&gt;

&lt;&lt;combo_function&gt;&gt;

&lt;&lt;factorial&gt;&gt;

&lt;&lt;length&gt;&gt;

&lt;&lt;find&gt;&gt;

&lt;&lt;curry&gt;&gt;

&lt;&lt;partial&gt;&gt;

&lt;&lt;odds&gt;&gt;

&lt;&lt;loop_rec&gt;&gt;

&lt;&lt;printf&gt;&gt;

&lt;&lt;channels&gt;&gt;
  
&lt;&lt;io&gt;&gt;
&lt;/codeblock&gt;

== See also ==

* [[Hello World (OCaml)]]
* [[Basic constructs (C)]]
* [[Basic constructs (Java)]]
[[Category:Basic constructs]]
[[Category:Programming language:OCaml]]</text>
    </revision>
    <revision>
      <id>8683</id>
      <timestamp>2007-01-25T22:11:47Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <minor/>
      <comment>Fixed hello world link at end</comment>
      <text xml:space="preserve">This article describes some basic constructs in  [http://caml.inria.fr OCaml]. This is not a tutorial, just a collection of example code. The [http://www.ocaml-tutorial.org/ Objective CAML Tutorial] is a fine tutorial introduction to OCaml.

==Functions==

As OCaml is a functional programming language, it seems appropriate to cover function definition first.  In OCaml there are a few different ways to declare a function, but the most common is the standard &lt;code&gt;let&lt;/code&gt; definition.  Here, the general structure of the definition is &lt;code&gt;let funname param1 ... paramN = body of function&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let add a b = a + b;;
&lt;/codeblock&gt;

Note the two semicolons at the end of the definition.  This bit of punctuation is used in OCaml to signify the end of an expression.  However, it is usually an optional bit of punctuation.  When writing code that will be compiled or run through the interpreter one doesn't need to include the semicolons.  The only time they are needed is when working with the [http://caml.inria.fr/pub/docs/manual-ocaml/manual023.html interactive toploop], then the semicolons are needed to signal to the interpreter that the expression (or set of expressions) you've just typed in are to be evaluated.

Also note that the parameters are separate elements following the function name, not a parenthesized list like in many common languages.  This doesn't mean that you can't use that style of function definition, it just means something slightly different.  Unlike the definition above, which takes two parameters adds them and returns the result, the definition

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function2&gt;&gt;=
let add' (a, b) = a + b;;
&lt;/codeblock&gt;

creates a function that takes a single parameter which is a two-tuple, deconstructs the tuple, adds the constituent elements and returns the result.  These functions are applied as one might expect:

&lt;codeblock language=ocaml&gt;
# add 10 15;;
- : int = 25
# add' (30, 40);;
- : int = 70
&lt;/codeblock&gt;

===Anonymous functions===

Another way to define a function is with the &lt;code&gt;fun&lt;/code&gt; keyword:

&lt;codeblock language=ocaml&gt;
fun a b -&gt; a + b;;
&lt;/codeblock&gt;

This creates a function without a name (an anonymous function) that adds two values together.  This may seem like an odd concept to some, but in functional languages, a function is just a value, like strings or ints, and no one finds the use of unnamed strings and ints odd.  As we will see in a bit, this is actually quite useful.

Anonymous functions can be applied in a fairly straight-forward manner:

&lt;codeblock language=ocaml&gt;
#   (fun a b -&gt; (a * 10) + b) 5 7;;
- : int = 57
&lt;/codeblock&gt;

And as they are simply values, we can use &lt;code&gt;let&lt;/code&gt; to bind them to a name:

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_anon&gt;&gt;=
let add_anon = fun a b -&gt; a + b;;
&lt;/codeblock&gt;

&lt;codeblock&gt;
#   add_anon 10 3;;
- : int = 13
&lt;/codeblock&gt;

This isn't immediately useful, but there are places where it comes in handy.  Note also that this is equivalent to &lt;code&gt;let&lt;/code&gt; construction shown first -- indeed, the &lt;code&gt;let&lt;/code&gt; construction is just sugar for this form.

===Pattern matching functions===

Functions can also be defined using the &lt;code&gt;function&lt;/code&gt; keyword and pattern matching.  Here, &lt;code&gt;function&lt;/code&gt; accepts a single value and tries to match it to one of several patterns.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let silly = function
| 0 -&gt; &quot;zero&quot;
| 1 -&gt; &quot;one&quot;
| x when x &lt; 2 -&gt; &quot;negative number&quot;
| _ -&gt; &quot;some other number&quot;
&lt;/codeblock&gt;

Here, the patterns are separated with the &lt;code&gt;|&lt;/code&gt; character (the initial one is optional), and they are constructed by specifying the pattern to be matched, followed by a &lt;code&gt;-&gt;&lt;/code&gt;, followed by the code to perform if that case matches.  The  patterns are checked in order, and only the first match is used, so in the example above, passing a 0 into &lt;code&gt;silly&lt;/code&gt; will result in &quot;zero&quot; being returned, and not &quot;negative number&quot;, even though it matches the pattern &lt;code&gt;x when x &amp;lt; 2&gt;&lt;/code&gt; as well.  The final pattern &lt;code&gt;_&lt;/code&gt; is a pattern that matches all values, and here would be matched by all numbers greater than 1.  Another variant of this would use a pattern like &lt;code&gt;| x -&gt; &quot;something&quot;&lt;/code&gt;.  Here, the &lt;code&gt;x&lt;/code&gt; matches anything, but instead of throwing away the value that was matched, it is bound to the name &lt;code&gt;x&lt;/code&gt;, and can be used in the code for that case, e.g. &lt;code&gt;| x -&gt; sprintf &quot;You passed in: %d&quot; x&lt;/code&gt;.

Note that these constructs can be combined:

&lt;codeblock language=ocaml&gt;
&lt;&lt;combo_function&gt;&gt;=
let sillier a = fun b -&gt; function
| 0 -&gt; a
| 1 -&gt; b
| x when x &lt; 2 -&gt; a + b
| _ -&gt; a * b
&lt;/codeblock&gt;

Here, &lt;code&gt;sillier&lt;/code&gt; is a function that takes three values, integers &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt;, and a third integer that selects the operations we perform on a and b.

&lt;codeblock language=ocaml&gt;
# sillier 10 20 0;;
- : int = 10
# sillier 10 20 1;;
- : int = 20
# sillier 10 20 (-1);;
- : int = 30
# sillier 10 20 100;;
- : int = 200
&lt;/codeblock&gt;

===Recursive functions===

If one wishes to define a recursive function, they must use the &lt;code&gt;let rec&lt;/code&gt; construct to inform the compiler/interpreter, that the specified name is to be used recursively.

&lt;codeblock language=ocaml&gt;
&lt;&lt;factorial&gt;&gt;=
let rec factorial n = if n &lt;= 1 then 1 else factorial (n-1) * n
&lt;/codeblock&gt;

This can also be used with the &lt;code&gt;function&lt;/code&gt; keyword in a useful way.  Here we compute the length of a list using pattern matching.  First we check if the list is empty, if it is, then the length is 0.  If not, we match it against some unused element and the tail of the list, and we then recursively call &lt;code&gt;length&lt;/code&gt; on the tail of the list and add 1 to the result.

&lt;codeblock language=ocaml&gt;
&lt;&lt;length&gt;&gt;=
let rec length = function
| [] -&gt; 0
| _::t -&gt; length t + 1
&lt;/codeblock&gt;

===Higher order functions===

As we have seen, functions are values in OCaml, just like ints, floats, and strings, and so we can pass them into functions as arguments, as well as create and return them from functions.  Functions that accept other functions as parameters are referred to as higher order functions (HOFs).  An example of this is a function that searches a list for the first element that matches some predicate.

&lt;codeblock language=ocaml&gt;
&lt;&lt;find&gt;&gt;=
let rec find test = function
| [] -&gt; raise Not_found
| h::t -&gt; if test h then h else find test t
&lt;/codeblock&gt;

Here we pass an anonymous function into find in order to find the first value greater than 10 and then to find the first negative value.  The last example looks for the first multiple of 11, and not finding any raises the built-in exception &lt;code&gt;Not_found&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
let l = [1; 1; 2; 3; 5; 8; 13; 21; -7; 600];;

find (fun x -&gt; x &gt; 10) l;;
find (fun x -&gt; x &lt; 0) l;;
find (fun x -&gt; x mod 11 = 0) l;;
&lt;/codeblock&gt;

===Currying===

Currying is (in essence) a way looking at functions of multiple arguments as a series of functions of one argument that return functions that work with the other arguments.  In OCaml, this makes sense, as functions are values, and can be created and returned by other functions trivially.  As an example of what this means, consider the first function example on this page, &lt;code&gt;let add a b = a + b&lt;/code&gt;.  We generally think of this as a function that accepts two arguments and returns a value.  Really, it's not that at all.

OCaml converts that function definition under the covers to the equivalent:

&lt;codeblock language=ocaml&gt;
&lt;&lt;curry&gt;&gt;=
let add = fun a -&gt; fun b -&gt; a + b
&lt;/codeblock&gt;

What this form means is that &lt;code&gt;add&lt;/code&gt; is a function that takes a single argument, binds its value to the name a and returns an anonymous function that takes a single argument, binds its value to the name b, and then computes the value a+b according to the bindings from the function applications and returns the result.  Why this is important is that it allows us to use partial application to specialize the functions we have.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;partial&gt;&gt;=
let add1 = add 1;;
let add10 = add 10;;
&lt;/codeblock&gt;

Here, we have used Currying to our advantage to create two new functions, &lt;code&gt;add1&lt;/code&gt; and &lt;code&gt;add10&lt;/code&gt; that each take a single argument and add 1 and 10 to that argument, respectively.

&lt;codeblock&gt;
# add1 10;;
- : int = 11
# add10 10;;
- : int = 20
&lt;/codeblock&gt;

==Conditionals==

There are two forms of conditionals in OCaml, if/then expressions and pattern matching.

===If/Then===

The if then construct is fairly straight-forward, and similar to similar constructs in other languages.  The basic form of the if/then is &lt;code&gt;if test then e1 else e2&lt;/code&gt;, where &lt;code&gt;test&lt;/code&gt; is an expression that evaluates to a boolean value, and &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; are expressions that are evaluated in the true and false branches of the test respectively.  The primary catch with if/then in OCaml is that both &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; must have the same type, so expressions like &lt;code&gt;if test then 1 else &quot;two&quot;&lt;/code&gt; are not allowed.  Additionally if the type of the true branch is &lt;code&gt;unit&lt;/code&gt;, then the else branch is not required, e.g. &lt;code&gt;if test then print_string &quot;true!&quot;&lt;/code&gt; is equivalent to &lt;code&gt;if test then print_string &quot;true!&quot; else ()&lt;/code&gt;.  Note, however, that this con lead to mistakes where multiple unit valued expressions are to be executed in a given branch.  For example:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;;
  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

This is parsed as

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;;
)

  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which results in a syntax error.  More troublesome is something like the following:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which is parsed as:

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
);  
print_endline &quot;what?&quot;
&lt;/codeblock&gt;

So the &lt;code&gt;print_endline &quot;what?&quot;&lt;/code&gt; expression is always evaluated.  To be safe, wrap multi-statement blocks in parens or &lt;code&gt;begin/end&lt;/code&gt; pairs

&lt;codeblock language=ocaml&gt;
if test then
  (
    print_endline &quot;hi&quot;;
    print_string &quot;baby&quot;
  )
else
  begin
    print_string &quot;bye&quot;;
    print_endline &quot;what?&quot;
  end
&lt;/codeblock&gt;

===Pattern Matching===

Pattern matching is a powerful construct of OCaml that allows for conditional branching based on the structure and content of a value.  Pattern matching is initiated in OCaml in one of two ways: the first is the &lt;code&gt;function&lt;/code&gt; keyword, described above, and the second is the &lt;code&gt;match ... with&lt;/code&gt; construct.  The general form of the &lt;code&gt;match ... with&lt;/code&gt; construct is as follows:

&lt;codeblock language=ocaml&gt;
match exp with
| patt_1 -&gt; ex_1
...
| patt_n -&gt; ex_n
&lt;/codeblock&gt;

That is, the keyword &lt;code&gt;match&lt;/code&gt; followed by an expression that evaluates to a value, followed by the &lt;code&gt;with&lt;/code&gt; keyword, then a series of pattern/expression pairs, separated by &lt;code&gt;|&lt;/code&gt; characters (the first one is optional).  The value that &lt;code&gt;exn&lt;/code&gt; evaluates to is checked against the patterns, in order of definition, and if one matches (say &lt;code&gt;patt_i&lt;/code&gt;), then the entire match expression reduces to the corresponding expression (&lt;code&gt;ex_i&lt;/code&gt;).

A pattern can be any of the following recursive constructs:
* A constant value : one of { integer-literal, float-literal; char-literal, string-literal, constant variant value, &lt;code&gt;false&lt;/code&gt;, &lt;code&gt;true&lt;/code&gt;, &lt;code&gt;[]&lt;/code&gt;, &lt;code&gt;()&lt;/code&gt;, constant polymorphic variant }
* &lt;code&gt;_&lt;/code&gt; : matches any pattern and throws away the value
* variable-name  : matches any pattern and binds the value to the variable name for use in the corresponding expression
* ''pattern'' as variable-name : the value that matches ''pattern'' is bound to variable-name for use in the corresponding expression
* ( ''pattern'' )
* ( ''pattern'' : type-annotation )
* ''pattern'' | ''pattern'' : multiple patterns may correspond to the same expression
* constr ''pattern'' : Here, constr is one of OCaml's variant type values, and ''pattern'' is its associated data
* `tag-name ''pattern'' : Here, tag-name is one of OCaml's polymorphic variants, and ''pattern'' is its associated data
* # typeconstr-name : used to match some set of polymorphic variants
* ''pattern'', ''pattern'', ..., ''pattern'' : these are tuples of patterns
* { field-name_1 = ''pattern''; ... ; field-name_n = ''pattern''} : matching against records
* [ ''pattern'' ; ... ; ''pattern''] : matching against a list
* ''pattern'' :: ''pattern'' : matching against consed values
* [| ''pattern'' ; ... ; ''pattern'' |] : matching against arrays

Some example patterns are

* &lt;code&gt;[]&lt;/code&gt; : the empty list
* &lt;code&gt;h::t&lt;/code&gt; : a non empty list, binding the head and tail to the variables &lt;code&gt;h&lt;/code&gt; and &lt;code&gt;t&lt;/code&gt;, respectively
* &lt;code&gt;h::_&lt;/code&gt; : a non empty list, binding the head to &lt;code&gt;h&lt;/code&gt; and throwing away the tail
* &lt;code&gt;(_,_,x)&lt;/code&gt; : a three-tuple where the first two values are thrown away and the third is bound to &lt;code&gt;x&lt;/code&gt;
* h::(h2::_ as t) : a list with at least two elements in it, where the head is bound to &lt;code&gt;h&lt;/code&gt;, the second element is bound to &lt;code&gt;h2&lt;/code&gt;, and the list minus its first value is bound to &lt;code&gt;t&lt;/code&gt;
* &lt;code&gt;Some ((h1,(h2 : float),_,1)::next::_)&lt;/code&gt; : a &lt;code&gt;Some&lt;/code&gt; constructer with associated data that is a list of four-tuples, at least two elements in length, where the first value in the tuple at the head is bound to &lt;code&gt;h1&lt;/code&gt;, the second is bound to &lt;code&gt;h2&lt;/code&gt; and is restricted to being a floating point value, the third is thrown away, and the fourth is a 1.  The second element is bound to &lt;code&gt;next&lt;/code&gt;, and the rest of the list is thrown away.

This kind of feature is very powerful, and lets us write very succinct code that operates on the structure of data.  For example, a function that throws away every other element of a list can be written simply:

&lt;codeblock language=ocaml&gt;
&lt;&lt;odds&gt;&gt;=
let rec odds = function
| ([] | [_]) as l -&gt; l
| h::_::t -&gt; h::(odds t);;
&lt;/codeblock&gt;

Here the first pattern matches lists with zero or one elements and returns that list, while the second pattern matches all lists with at least two elements, throws away the second, saves the first, and conses it onto the list created by throwing away every other element of the remaining list.

==Looping==

While looping is often handled via recursive functions in OCaml, e.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;loop_rec&gt;&gt;=
let rec loop times f =
match times with
| 0 -&gt; ()
| _ -&gt; f (); loop (times-1) f;;
&lt;/codeblock&gt;

there are other built-in options, the &lt;code&gt;for&lt;/code&gt; and &lt;code&gt;while loops&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
for counter = start to stop do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
while test do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

The for loop loops over the range provided (both endpoints inclusive), performing whatever code lies within the &lt;code&gt;do&lt;/code&gt; and &lt;code&gt;done&lt;/code&gt; keywords, rebinding the counter variable to the current value each time.  For loops can also count backwards, using &lt;code&gt;downto&lt;/code&gt; rather than &lt;code&gt;to&lt;/code&gt;.  The endpoints of the loop don't have to be constants, they can be any expression that evaluates to an int, and the entire for loop evaluates to &lt;code&gt;()&lt;/code&gt;.  Note that there is no &quot;step&quot; option as in languages such as C.

While loops are similar to those found in other languages.  So long as the conditional evaluates to &lt;code&gt;true&lt;/code&gt;, the loop body is evaluated.  Like the for loop, the entire while loop evaluates to &lt;code&gt;()&lt;/code&gt;.

==I/O==

===Simple I/O===
I/O is performed using stdin, stdout, and stderr using the various read, print, and prerr functions respectively.

; &lt;code&gt;read_line&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Returns the resulting string, minus the newline.
; &lt;code&gt;read_int&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to an int, raising an exception if it cannot.
; &lt;code&gt;read_float&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to a float, raising an exception if it cannot.
; &lt;code&gt;print_char&lt;/code&gt; : prints a character to stdout
; &lt;code&gt;print_newline&lt;/code&gt; : prints a newline character to stdout
; &lt;code&gt;print_string&lt;/code&gt; : prints a string to stdout
; &lt;code&gt;print_endline&lt;/code&gt; : prints a string to stdout followed by a newline character
; &lt;code&gt;print_int&lt;/code&gt; : prints an int to stdout
; &lt;code&gt;print_float&lt;/code&gt; : prints a float to stdout
; &lt;code&gt;prerr_char&lt;/code&gt; : prints a character to stderr
; &lt;code&gt;prerr_newline&lt;/code&gt; : prints a newline character to stderr
; &lt;code&gt;prerr_string&lt;/code&gt; : prints a string to stderr
; &lt;code&gt;prerr_endline&lt;/code&gt; : prints a string to stderr followed by a newline character
; &lt;code&gt;prerr_int&lt;/code&gt; : prints an int to stderr
; &lt;code&gt;prerr_float&lt;/code&gt; : prints a float to stderr

Formatted printing can be done via the &lt;code&gt;Printf&lt;/code&gt; module which contain (among other things) functions &lt;code&gt;printf&lt;/code&gt; and &lt;code&gt;sprintf&lt;/code&gt; that use format strings similar to those of C.  E.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;printf&gt;&gt;=
Printf.printf &quot;0x%0X\n&quot; 500;;
let s = Printf.sprintf &quot;%d: %s --\t%08.3f&quot; 7 &quot;whoopie&quot; 1.4432578;;
&lt;/codeblock&gt;

will print &lt;code&gt;0x1F4&lt;/code&gt; followed by a newline to stdout, and bind the string &lt;code&gt;&quot;7: whoopie --	0001.443&quot;&lt;/code&gt; to &lt;code&gt;s&lt;/code&gt;.

===File I/O===

Files are usually worked with via input and output channels.  To open the file data.in for reading and the file data.out for writing, one would do the following:

&lt;codeblock language=ocaml&gt;
&lt;&lt;channels&gt;&gt;=
let in_channel = open_in &quot;data.in&quot;
let out_channel = open_out &quot;data.out&quot;
&lt;/codeblock&gt;

The channels can now be read from and written to using the various input and output functions.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;io&gt;&gt;=
let line = input_line in_channel
output_string out_channel line; output_char out_channel '\n';;
&lt;/codeblock&gt;

Will read the next line from in_channel (connected to data.in), and copy that line followed by a newline character into out_channel (connected to data.out).  Doing this repeatedly would copy data.in to data.out.

In addition to the simple I/O functions, formatted data can also be written using the &lt;code&gt;Printf&lt;/code&gt; module's &lt;code&gt;fprintf&lt;/code&gt; function.  Here, &lt;code&gt;Printf.fprintf channel format arg1 ... argN&lt;/code&gt; will print arguments 1 through N to output channel &lt;code&gt;channel&lt;/code&gt; according to the format string &lt;code&gt;format&lt;/code&gt;.

==Command line arguments==

Command line arguments are available as a string array named &lt;code&gt;Sys.argv&lt;/code&gt;.  &lt;code&gt;Sys.argv.(0)&lt;/code&gt; contains the name of the program that was executed, and subsequent entries in the array contain the additional arguments, if any, un the order they were presented on the command line.  So, to print the name of the program followed by the arguments, each on a new line, one can do:

&lt;codeblock language=ocaml&gt;
&lt;&lt;arguments&gt;&gt;=
print_endline Sys.argv.(0);
for i = 1 to Array.length Sys.argv - 1 do
  print_endline Sys.argv.(i)
done;;
&lt;/codeblock&gt;

==The Program==
&lt;codeblock&gt;
&lt;&lt;basic_constructs.ml&gt;&gt;=
&lt;&lt;let_function&gt;&gt;

&lt;&lt;let_function2&gt;&gt;

&lt;&lt;let_anon&gt;&gt;

&lt;&lt;let_function&gt;&gt;

&lt;&lt;combo_function&gt;&gt;

&lt;&lt;factorial&gt;&gt;

&lt;&lt;length&gt;&gt;

&lt;&lt;find&gt;&gt;

&lt;&lt;curry&gt;&gt;

&lt;&lt;partial&gt;&gt;

&lt;&lt;odds&gt;&gt;

&lt;&lt;loop_rec&gt;&gt;

&lt;&lt;printf&gt;&gt;

&lt;&lt;channels&gt;&gt;
  
&lt;&lt;io&gt;&gt;
&lt;/codeblock&gt;

== See also ==

* [[Hello World (OCaml/F_Sharp)]]
* [[Basic constructs (C)]]
* [[Basic constructs (Java)]]
[[Category:Basic constructs]]
[[Category:Programming language:OCaml]]</text>
    </revision>
    <revision>
      <id>16456</id>
      <timestamp>2009-06-08T00:30:15Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This article describes some basic constructs in  [http://caml.inria.fr OCaml]. This is not a tutorial, just a collection of example code. The [http://www.ocaml-tutorial.org/ Objective CAML Tutorial] is a fine tutorial introduction to OCaml.

==Functions==

As OCaml is a functional programming language, it seems appropriate to cover function definition first.  In OCaml there are a few different ways to declare a function, but the most common is the standard &lt;code&gt;let&lt;/code&gt; definition.  Here, the general structure of the definition is &lt;code&gt;let funname param1 ... paramN = body of function&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let add a b = a + b;;
&lt;/codeblock&gt;

Note the two semicolons at the end of the definition.  This bit of punctuation is used in OCaml to signify the end of an expression.  However, it is usually an optional bit of punctuation.  When writing code that will be compiled or run through the interpreter one doesn't need to include the semicolons.  The only time they are needed is when working with the [http://caml.inria.fr/pub/docs/manual-ocaml/manual023.html interactive toploop], then the semicolons are needed to signal to the interpreter that the expression (or set of expressions) you've just typed in are to be evaluated.

Also note that the parameters are separate elements following the function name, not a parenthesized list like in many common languages.  This doesn't mean that you can't use that style of function definition, it just means something slightly different.  Unlike the definition above, which takes two parameters adds them and returns the result, the definition

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function2&gt;&gt;=
let add' (a, b) = a + b;;
&lt;/codeblock&gt;

creates a function that takes a single parameter which is a two-tuple, deconstructs the tuple, adds the constituent elements and returns the result.  These functions are applied as one might expect:

&lt;codeblock language=ocaml&gt;
# add 10 15;;
- : int = 25
# add' (30, 40);;
- : int = 70
&lt;/codeblock&gt;

===Anonymous functions===

Another way to define a function is with the &lt;code&gt;fun&lt;/code&gt; keyword:

&lt;codeblock language=ocaml&gt;
fun a b -&gt; a + b;;
&lt;/codeblock&gt;

This creates a function without a name (an anonymous function) that adds two values together.  This may seem like an odd concept to some, but in functional languages, a function is just a value, like strings or ints, and no one finds the use of unnamed strings and ints odd.  As we will see in a bit, this is actually quite useful.

Anonymous functions can be applied in a fairly straight-forward manner:

&lt;codeblock language=ocaml&gt;
#   (fun a b -&gt; (a * 10) + b) 5 7;;
- : int = 57
&lt;/codeblock&gt;

And as they are simply values, we can use &lt;code&gt;let&lt;/code&gt; to bind them to a name:

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_anon&gt;&gt;=
let add_anon = fun a b -&gt; a + b;;
&lt;/codeblock&gt;

&lt;codeblock&gt;
#   add_anon 10 3;;
- : int = 13
&lt;/codeblock&gt;

This isn't immediately useful, but there are places where it comes in handy.  Note also that this is equivalent to &lt;code&gt;let&lt;/code&gt; construction shown first -- indeed, the &lt;code&gt;let&lt;/code&gt; construction is just sugar for this form.

===Pattern matching functions===

Functions can also be defined using the &lt;code&gt;function&lt;/code&gt; keyword and pattern matching.  Here, &lt;code&gt;function&lt;/code&gt; accepts a single value and tries to match it to one of several patterns.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let silly = function
| 0 -&gt; &quot;zero&quot;
| 1 -&gt; &quot;one&quot;
| x when x &lt; 2 -&gt; &quot;negative number&quot;
| _ -&gt; &quot;some other number&quot;
&lt;/codeblock&gt;

Here, the patterns are separated with the &lt;code&gt;|&lt;/code&gt; character (the initial one is optional), and they are constructed by specifying the pattern to be matched, followed by a &lt;code&gt;-&gt;&lt;/code&gt;, followed by the code to perform if that case matches.  The  patterns are checked in order, and only the first match is used, so in the example above, passing a 0 into &lt;code&gt;silly&lt;/code&gt; will result in &quot;zero&quot; being returned, and not &quot;negative number&quot;, even though it matches the pattern &lt;code&gt;x when x &amp;lt; 2&gt;&lt;/code&gt; as well.  The final pattern &lt;code&gt;_&lt;/code&gt; is a pattern that matches all values, and here would be matched by all numbers greater than 1.  Another variant of this would use a pattern like &lt;code&gt;| x -&gt; &quot;something&quot;&lt;/code&gt;.  Here, the &lt;code&gt;x&lt;/code&gt; matches anything, but instead of throwing away the value that was matched, it is bound to the name &lt;code&gt;x&lt;/code&gt;, and can be used in the code for that case, e.g. &lt;code&gt;| x -&gt; sprintf &quot;You passed in: %d&quot; x&lt;/code&gt;.

Note that these constructs can be combined:

&lt;codeblock language=ocaml&gt;
&lt;&lt;combo_function&gt;&gt;=
let sillier a = fun b -&gt; function
| 0 -&gt; a
| 1 -&gt; b
| x when x &lt; 2 -&gt; a + b
| _ -&gt; a * b
&lt;/codeblock&gt;

Here, &lt;code&gt;sillier&lt;/code&gt; is a function that takes three values, integers &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt;, and a third integer that selects the operations we perform on a and b.

&lt;codeblock language=ocaml&gt;
# sillier 10 20 0;;
- : int = 10
# sillier 10 20 1;;
- : int = 20
# sillier 10 20 (-1);;
- : int = 30
# sillier 10 20 100;;
- : int = 200
&lt;/codeblock&gt;

===Recursive functions===

If one wishes to define a recursive function, they must use the &lt;code&gt;let rec&lt;/code&gt; construct to inform the compiler/interpreter, that the specified name is to be used recursively.

&lt;codeblock language=ocaml&gt;
&lt;&lt;factorial&gt;&gt;=
let rec factorial n = if n &lt;= 1 then 1 else factorial (n-1) * n
&lt;/codeblock&gt;

This can also be used with the &lt;code&gt;function&lt;/code&gt; keyword in a useful way.  Here we compute the length of a list using pattern matching.  First we check if the list is empty, if it is, then the length is 0.  If not, we match it against some unused element and the tail of the list, and we then recursively call &lt;code&gt;length&lt;/code&gt; on the tail of the list and add 1 to the result.

&lt;codeblock language=ocaml&gt;
&lt;&lt;length&gt;&gt;=
let rec length = function
| [] -&gt; 0
| _::t -&gt; length t + 1
&lt;/codeblock&gt;

===Higher order functions===

As we have seen, functions are values in OCaml, just like ints, floats, and strings, and so we can pass them into functions as arguments, as well as create and return them from functions.  Functions that accept other functions as parameters are referred to as higher order functions (HOFs).  An example of this is a function that searches a list for the first element that matches some predicate.

&lt;codeblock language=ocaml&gt;
&lt;&lt;find&gt;&gt;=
let rec find test = function
| [] -&gt; raise Not_found
| h::t -&gt; if test h then h else find test t
&lt;/codeblock&gt;

Here we pass an anonymous function into find in order to find the first value greater than 10 and then to find the first negative value.  The last example looks for the first multiple of 11, and not finding any raises the built-in exception &lt;code&gt;Not_found&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
let l = [1; 1; 2; 3; 5; 8; 13; 21; -7; 600];;

find (fun x -&gt; x &gt; 10) l;;
find (fun x -&gt; x &lt; 0) l;;
find (fun x -&gt; x mod 11 = 0) l;;
&lt;/codeblock&gt;

===Currying===

Currying is (in essence) a way looking at functions of multiple arguments as a series of functions of one argument that return functions that work with the other arguments.  In OCaml, this makes sense, as functions are values, and can be created and returned by other functions trivially.  As an example of what this means, consider the first function example on this page, &lt;code&gt;let add a b = a + b&lt;/code&gt;.  We generally think of this as a function that accepts two arguments and returns a value.  Really, it's not that at all.

OCaml converts that function definition under the covers to the equivalent:

&lt;codeblock language=ocaml&gt;
&lt;&lt;curry&gt;&gt;=
let add = fun a -&gt; fun b -&gt; a + b
&lt;/codeblock&gt;

What this form means is that &lt;code&gt;add&lt;/code&gt; is a function that takes a single argument, binds its value to the name a and returns an anonymous function that takes a single argument, binds its value to the name b, and then computes the value a+b according to the bindings from the function applications and returns the result.  Why this is important is that it allows us to use partial application to specialize the functions we have.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;partial&gt;&gt;=
let add1 = add 1;;
let add10 = add 10;;
&lt;/codeblock&gt;

Here, we have used Currying to our advantage to create two new functions, &lt;code&gt;add1&lt;/code&gt; and &lt;code&gt;add10&lt;/code&gt; that each take a single argument and add 1 and 10 to that argument, respectively.

&lt;codeblock&gt;
# add1 10;;
- : int = 11
# add10 10;;
- : int = 20
&lt;/codeblock&gt;

==Conditionals==

There are two forms of conditionals in OCaml, if/then expressions and pattern matching.

===If/Then===

The if then construct is fairly straight-forward, and similar to similar constructs in other languages.  The basic form of the if/then is &lt;code&gt;if test then e1 else e2&lt;/code&gt;, where &lt;code&gt;test&lt;/code&gt; is an expression that evaluates to a boolean value, and &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; are expressions that are evaluated in the true and false branches of the test respectively.  The primary catch with if/then in OCaml is that both &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; must have the same type, so expressions like &lt;code&gt;if test then 1 else &quot;two&quot;&lt;/code&gt; are not allowed.  Additionally if the type of the true branch is &lt;code&gt;unit&lt;/code&gt;, then the else branch is not required, e.g. &lt;code&gt;if test then print_string &quot;true!&quot;&lt;/code&gt; is equivalent to &lt;code&gt;if test then print_string &quot;true!&quot; else ()&lt;/code&gt;.  Note, however, that this con lead to mistakes where multiple unit valued expressions are to be executed in a given branch.  For example:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;;
  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

This is parsed as

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
);

  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which results in a syntax error.  More troublesome is something like the following:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which is parsed as:

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
);  
print_endline &quot;what?&quot;
&lt;/codeblock&gt;

So the &lt;code&gt;print_endline &quot;what?&quot;&lt;/code&gt; expression is always evaluated.  The reason for this is that the semicolon has lower precedence than the if/then expression.  To fix this, wrap multi-statement blocks in parens or &lt;code&gt;begin/end&lt;/code&gt; pairs

&lt;codeblock language=ocaml&gt;
if test then
  (
    print_endline &quot;hi&quot;;
    print_string &quot;baby&quot;
  )
else
  begin
    print_string &quot;bye&quot;;
    print_endline &quot;what?&quot;
  end
&lt;/codeblock&gt;

===Pattern Matching===

Pattern matching is a powerful construct of OCaml that allows for conditional branching based on the structure and content of a value.  Pattern matching is initiated in OCaml in one of two ways: the first is the &lt;code&gt;function&lt;/code&gt; keyword, described above, and the second is the &lt;code&gt;match ... with&lt;/code&gt; construct.  The general form of the &lt;code&gt;match ... with&lt;/code&gt; construct is as follows:

&lt;codeblock language=ocaml&gt;
match exp with
| patt_1 -&gt; ex_1
...
| patt_n -&gt; ex_n
&lt;/codeblock&gt;

That is, the keyword &lt;code&gt;match&lt;/code&gt; followed by an expression that evaluates to a value, followed by the &lt;code&gt;with&lt;/code&gt; keyword, then a series of pattern/expression pairs, separated by &lt;code&gt;|&lt;/code&gt; characters (the first one is optional).  The value that &lt;code&gt;exn&lt;/code&gt; evaluates to is checked against the patterns, in order of definition, and if one matches (say &lt;code&gt;patt_i&lt;/code&gt;), then the entire match expression reduces to the corresponding expression (&lt;code&gt;ex_i&lt;/code&gt;).

A pattern can be any of the following recursive constructs:
* A constant value : one of { integer-literal, float-literal; char-literal, string-literal, constant variant value, &lt;code&gt;false&lt;/code&gt;, &lt;code&gt;true&lt;/code&gt;, &lt;code&gt;[]&lt;/code&gt;, &lt;code&gt;()&lt;/code&gt;, constant polymorphic variant }
* &lt;code&gt;_&lt;/code&gt; : matches any pattern and throws away the value
* variable-name  : matches any pattern and binds the value to the variable name for use in the corresponding expression
* ''pattern'' as variable-name : the value that matches ''pattern'' is bound to variable-name for use in the corresponding expression
* ( ''pattern'' )
* ( ''pattern'' : type-annotation )
* ''pattern'' | ''pattern'' : multiple patterns may correspond to the same expression
* constr ''pattern'' : Here, constr is one of OCaml's variant type values, and ''pattern'' is its associated data
* `tag-name ''pattern'' : Here, tag-name is one of OCaml's polymorphic variants, and ''pattern'' is its associated data
* # typeconstr-name : used to match some set of polymorphic variants
* ''pattern'', ''pattern'', ..., ''pattern'' : these are tuples of patterns
* { field-name_1 = ''pattern''; ... ; field-name_n = ''pattern''} : matching against records
* [ ''pattern'' ; ... ; ''pattern''] : matching against a list
* ''pattern'' :: ''pattern'' : matching against consed values
* [| ''pattern'' ; ... ; ''pattern'' |] : matching against arrays

Some example patterns are

* &lt;code&gt;[]&lt;/code&gt; : the empty list
* &lt;code&gt;h::t&lt;/code&gt; : a non empty list, binding the head and tail to the variables &lt;code&gt;h&lt;/code&gt; and &lt;code&gt;t&lt;/code&gt;, respectively
* &lt;code&gt;h::_&lt;/code&gt; : a non empty list, binding the head to &lt;code&gt;h&lt;/code&gt; and throwing away the tail
* &lt;code&gt;(_,_,x)&lt;/code&gt; : a three-tuple where the first two values are thrown away and the third is bound to &lt;code&gt;x&lt;/code&gt;
* h::(h2::_ as t) : a list with at least two elements in it, where the head is bound to &lt;code&gt;h&lt;/code&gt;, the second element is bound to &lt;code&gt;h2&lt;/code&gt;, and the list minus its first value is bound to &lt;code&gt;t&lt;/code&gt;
* &lt;code&gt;Some ((h1,(h2 : float),_,1)::next::_)&lt;/code&gt; : a &lt;code&gt;Some&lt;/code&gt; constructer with associated data that is a list of four-tuples, at least two elements in length, where the first value in the tuple at the head is bound to &lt;code&gt;h1&lt;/code&gt;, the second is bound to &lt;code&gt;h2&lt;/code&gt; and is restricted to being a floating point value, the third is thrown away, and the fourth is a 1.  The second element is bound to &lt;code&gt;next&lt;/code&gt;, and the rest of the list is thrown away.

This kind of feature is very powerful, and lets us write very succinct code that operates on the structure of data.  For example, a function that throws away every other element of a list can be written simply:

&lt;codeblock language=ocaml&gt;
&lt;&lt;odds&gt;&gt;=
let rec odds = function
| ([] | [_]) as l -&gt; l
| h::_::t -&gt; h::(odds t);;
&lt;/codeblock&gt;

Here the first pattern matches lists with zero or one elements and returns that list, while the second pattern matches all lists with at least two elements, throws away the second, saves the first, and conses it onto the list created by throwing away every other element of the remaining list.

==Looping==

While looping is often handled via recursive functions in OCaml, e.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;loop_rec&gt;&gt;=
let rec loop times f =
match times with
| 0 -&gt; ()
| _ -&gt; f (); loop (times-1) f;;
&lt;/codeblock&gt;

there are other built-in options, the &lt;code&gt;for&lt;/code&gt; and &lt;code&gt;while loops&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
for counter = start to stop do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
while test do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

The for loop loops over the range provided (both endpoints inclusive), performing whatever code lies within the &lt;code&gt;do&lt;/code&gt; and &lt;code&gt;done&lt;/code&gt; keywords, rebinding the counter variable to the current value each time.  For loops can also count backwards, using &lt;code&gt;downto&lt;/code&gt; rather than &lt;code&gt;to&lt;/code&gt;.  The endpoints of the loop don't have to be constants, they can be any expression that evaluates to an int, and the entire for loop evaluates to &lt;code&gt;()&lt;/code&gt;.  Note that there is no &quot;step&quot; option as in languages such as C.

While loops are similar to those found in other languages.  So long as the conditional evaluates to &lt;code&gt;true&lt;/code&gt;, the loop body is evaluated.  Like the for loop, the entire while loop evaluates to &lt;code&gt;()&lt;/code&gt;.

==I/O==

===Simple I/O===
I/O is performed using stdin, stdout, and stderr using the various read, print, and prerr functions respectively.

; &lt;code&gt;read_line&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Returns the resulting string, minus the newline.
; &lt;code&gt;read_int&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to an int, raising an exception if it cannot.
; &lt;code&gt;read_float&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to a float, raising an exception if it cannot.
; &lt;code&gt;print_char&lt;/code&gt; : prints a character to stdout
; &lt;code&gt;print_newline&lt;/code&gt; : prints a newline character to stdout
; &lt;code&gt;print_string&lt;/code&gt; : prints a string to stdout
; &lt;code&gt;print_endline&lt;/code&gt; : prints a string to stdout followed by a newline character
; &lt;code&gt;print_int&lt;/code&gt; : prints an int to stdout
; &lt;code&gt;print_float&lt;/code&gt; : prints a float to stdout
; &lt;code&gt;prerr_char&lt;/code&gt; : prints a character to stderr
; &lt;code&gt;prerr_newline&lt;/code&gt; : prints a newline character to stderr
; &lt;code&gt;prerr_string&lt;/code&gt; : prints a string to stderr
; &lt;code&gt;prerr_endline&lt;/code&gt; : prints a string to stderr followed by a newline character
; &lt;code&gt;prerr_int&lt;/code&gt; : prints an int to stderr
; &lt;code&gt;prerr_float&lt;/code&gt; : prints a float to stderr

Formatted printing can be done via the &lt;code&gt;Printf&lt;/code&gt; module which contain (among other things) functions &lt;code&gt;printf&lt;/code&gt; and &lt;code&gt;sprintf&lt;/code&gt; that use format strings similar to those of C.  E.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;printf&gt;&gt;=
Printf.printf &quot;0x%0X\n&quot; 500;;
let s = Printf.sprintf &quot;%d: %s --\t%08.3f&quot; 7 &quot;whoopie&quot; 1.4432578;;
&lt;/codeblock&gt;

will print &lt;code&gt;0x1F4&lt;/code&gt; followed by a newline to stdout, and bind the string &lt;code&gt;&quot;7: whoopie --	0001.443&quot;&lt;/code&gt; to &lt;code&gt;s&lt;/code&gt;.

===File I/O===

Files are usually worked with via input and output channels.  To open the file data.in for reading and the file data.out for writing, one would do the following:

&lt;codeblock language=ocaml&gt;
&lt;&lt;channels&gt;&gt;=
let in_channel = open_in &quot;data.in&quot;;;
let out_channel = open_out &quot;data.out&quot;;;
&lt;/codeblock&gt;

The channels can now be read from and written to using the various input and output functions.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;io&gt;&gt;=
let line = input_line in_channel;;
output_string out_channel line; output_char out_channel '\n';;
&lt;/codeblock&gt;

Will read the next line from in_channel (connected to data.in), and copy that line followed by a newline character into out_channel (connected to data.out).  Doing this repeatedly would copy data.in to data.out.

In addition to the simple I/O functions, formatted data can also be written using the &lt;code&gt;Printf&lt;/code&gt; module's &lt;code&gt;fprintf&lt;/code&gt; function.  Here, &lt;code&gt;Printf.fprintf channel format arg1 ... argN&lt;/code&gt; will print arguments 1 through N to output channel &lt;code&gt;channel&lt;/code&gt; according to the format string &lt;code&gt;format&lt;/code&gt;.

==Command line arguments==

Command line arguments are available as a string array named &lt;code&gt;Sys.argv&lt;/code&gt;.  &lt;code&gt;Sys.argv.(0)&lt;/code&gt; contains the name of the program that was executed, and subsequent entries in the array contain the additional arguments, if any, un the order they were presented on the command line.  So, to print the name of the program followed by the arguments, each on a new line, one can do:

&lt;codeblock language=ocaml&gt;
&lt;&lt;arguments&gt;&gt;=
print_endline Sys.argv.(0);
for i = 1 to Array.length Sys.argv - 1 do
  print_endline Sys.argv.(i)
done;;
&lt;/codeblock&gt;

==The Program==
&lt;codeblock&gt;
&lt;&lt;basic_constructs.ml&gt;&gt;=
&lt;&lt;let_function&gt;&gt;

&lt;&lt;let_function2&gt;&gt;

&lt;&lt;let_anon&gt;&gt;

&lt;&lt;let_function&gt;&gt;

&lt;&lt;combo_function&gt;&gt;

&lt;&lt;factorial&gt;&gt;

&lt;&lt;length&gt;&gt;

&lt;&lt;find&gt;&gt;

&lt;&lt;curry&gt;&gt;

&lt;&lt;partial&gt;&gt;

&lt;&lt;odds&gt;&gt;

&lt;&lt;loop_rec&gt;&gt;

&lt;&lt;printf&gt;&gt;

&lt;&lt;channels&gt;&gt;
  
&lt;&lt;io&gt;&gt;
&lt;/codeblock&gt;

== See also ==

* [[Hello World (OCaml/F_Sharp)]]
* [[Basic constructs (C)]]
* [[Basic constructs (Java)]]
[[Category:Basic constructs]]
[[Category:Programming language:OCaml]]</text>
    </revision>
    <revision>
      <id>16869</id>
      <timestamp>2010-09-23T13:18:05Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">I bet Mr. Moderator is pissed of with me now &gt;.&gt;</text>
    </revision>
    <revision>
      <id>16901</id>
      <timestamp>2010-09-23T15:49:11Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Spoon!|Spoon!]]</comment>
      <text xml:space="preserve">This article describes some basic constructs in  [http://caml.inria.fr OCaml]. This is not a tutorial, just a collection of example code. The [http://www.ocaml-tutorial.org/ Objective CAML Tutorial] is a fine tutorial introduction to OCaml.

==Functions==

As OCaml is a functional programming language, it seems appropriate to cover function definition first.  In OCaml there are a few different ways to declare a function, but the most common is the standard &lt;code&gt;let&lt;/code&gt; definition.  Here, the general structure of the definition is &lt;code&gt;let funname param1 ... paramN = body of function&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let add a b = a + b;;
&lt;/codeblock&gt;

Note the two semicolons at the end of the definition.  This bit of punctuation is used in OCaml to signify the end of an expression.  However, it is usually an optional bit of punctuation.  When writing code that will be compiled or run through the interpreter one doesn't need to include the semicolons.  The only time they are needed is when working with the [http://caml.inria.fr/pub/docs/manual-ocaml/manual023.html interactive toploop], then the semicolons are needed to signal to the interpreter that the expression (or set of expressions) you've just typed in are to be evaluated.

Also note that the parameters are separate elements following the function name, not a parenthesized list like in many common languages.  This doesn't mean that you can't use that style of function definition, it just means something slightly different.  Unlike the definition above, which takes two parameters adds them and returns the result, the definition

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function2&gt;&gt;=
let add' (a, b) = a + b;;
&lt;/codeblock&gt;

creates a function that takes a single parameter which is a two-tuple, deconstructs the tuple, adds the constituent elements and returns the result.  These functions are applied as one might expect:

&lt;codeblock language=ocaml&gt;
# add 10 15;;
- : int = 25
# add' (30, 40);;
- : int = 70
&lt;/codeblock&gt;

===Anonymous functions===

Another way to define a function is with the &lt;code&gt;fun&lt;/code&gt; keyword:

&lt;codeblock language=ocaml&gt;
fun a b -&gt; a + b;;
&lt;/codeblock&gt;

This creates a function without a name (an anonymous function) that adds two values together.  This may seem like an odd concept to some, but in functional languages, a function is just a value, like strings or ints, and no one finds the use of unnamed strings and ints odd.  As we will see in a bit, this is actually quite useful.

Anonymous functions can be applied in a fairly straight-forward manner:

&lt;codeblock language=ocaml&gt;
#   (fun a b -&gt; (a * 10) + b) 5 7;;
- : int = 57
&lt;/codeblock&gt;

And as they are simply values, we can use &lt;code&gt;let&lt;/code&gt; to bind them to a name:

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_anon&gt;&gt;=
let add_anon = fun a b -&gt; a + b;;
&lt;/codeblock&gt;

&lt;codeblock&gt;
#   add_anon 10 3;;
- : int = 13
&lt;/codeblock&gt;

This isn't immediately useful, but there are places where it comes in handy.  Note also that this is equivalent to &lt;code&gt;let&lt;/code&gt; construction shown first -- indeed, the &lt;code&gt;let&lt;/code&gt; construction is just sugar for this form.

===Pattern matching functions===

Functions can also be defined using the &lt;code&gt;function&lt;/code&gt; keyword and pattern matching.  Here, &lt;code&gt;function&lt;/code&gt; accepts a single value and tries to match it to one of several patterns.

&lt;codeblock language=ocaml&gt;
&lt;&lt;let_function&gt;&gt;=
let silly = function
| 0 -&gt; &quot;zero&quot;
| 1 -&gt; &quot;one&quot;
| x when x &lt; 2 -&gt; &quot;negative number&quot;
| _ -&gt; &quot;some other number&quot;
&lt;/codeblock&gt;

Here, the patterns are separated with the &lt;code&gt;|&lt;/code&gt; character (the initial one is optional), and they are constructed by specifying the pattern to be matched, followed by a &lt;code&gt;-&gt;&lt;/code&gt;, followed by the code to perform if that case matches.  The  patterns are checked in order, and only the first match is used, so in the example above, passing a 0 into &lt;code&gt;silly&lt;/code&gt; will result in &quot;zero&quot; being returned, and not &quot;negative number&quot;, even though it matches the pattern &lt;code&gt;x when x &amp;lt; 2&gt;&lt;/code&gt; as well.  The final pattern &lt;code&gt;_&lt;/code&gt; is a pattern that matches all values, and here would be matched by all numbers greater than 1.  Another variant of this would use a pattern like &lt;code&gt;| x -&gt; &quot;something&quot;&lt;/code&gt;.  Here, the &lt;code&gt;x&lt;/code&gt; matches anything, but instead of throwing away the value that was matched, it is bound to the name &lt;code&gt;x&lt;/code&gt;, and can be used in the code for that case, e.g. &lt;code&gt;| x -&gt; sprintf &quot;You passed in: %d&quot; x&lt;/code&gt;.

Note that these constructs can be combined:

&lt;codeblock language=ocaml&gt;
&lt;&lt;combo_function&gt;&gt;=
let sillier a = fun b -&gt; function
| 0 -&gt; a
| 1 -&gt; b
| x when x &lt; 2 -&gt; a + b
| _ -&gt; a * b
&lt;/codeblock&gt;

Here, &lt;code&gt;sillier&lt;/code&gt; is a function that takes three values, integers &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt;, and a third integer that selects the operations we perform on a and b.

&lt;codeblock language=ocaml&gt;
# sillier 10 20 0;;
- : int = 10
# sillier 10 20 1;;
- : int = 20
# sillier 10 20 (-1);;
- : int = 30
# sillier 10 20 100;;
- : int = 200
&lt;/codeblock&gt;

===Recursive functions===

If one wishes to define a recursive function, they must use the &lt;code&gt;let rec&lt;/code&gt; construct to inform the compiler/interpreter, that the specified name is to be used recursively.

&lt;codeblock language=ocaml&gt;
&lt;&lt;factorial&gt;&gt;=
let rec factorial n = if n &lt;= 1 then 1 else factorial (n-1) * n
&lt;/codeblock&gt;

This can also be used with the &lt;code&gt;function&lt;/code&gt; keyword in a useful way.  Here we compute the length of a list using pattern matching.  First we check if the list is empty, if it is, then the length is 0.  If not, we match it against some unused element and the tail of the list, and we then recursively call &lt;code&gt;length&lt;/code&gt; on the tail of the list and add 1 to the result.

&lt;codeblock language=ocaml&gt;
&lt;&lt;length&gt;&gt;=
let rec length = function
| [] -&gt; 0
| _::t -&gt; length t + 1
&lt;/codeblock&gt;

===Higher order functions===

As we have seen, functions are values in OCaml, just like ints, floats, and strings, and so we can pass them into functions as arguments, as well as create and return them from functions.  Functions that accept other functions as parameters are referred to as higher order functions (HOFs).  An example of this is a function that searches a list for the first element that matches some predicate.

&lt;codeblock language=ocaml&gt;
&lt;&lt;find&gt;&gt;=
let rec find test = function
| [] -&gt; raise Not_found
| h::t -&gt; if test h then h else find test t
&lt;/codeblock&gt;

Here we pass an anonymous function into find in order to find the first value greater than 10 and then to find the first negative value.  The last example looks for the first multiple of 11, and not finding any raises the built-in exception &lt;code&gt;Not_found&lt;/code&gt;.

&lt;codeblock language=ocaml&gt;
let l = [1; 1; 2; 3; 5; 8; 13; 21; -7; 600];;

find (fun x -&gt; x &gt; 10) l;;
find (fun x -&gt; x &lt; 0) l;;
find (fun x -&gt; x mod 11 = 0) l;;
&lt;/codeblock&gt;

===Currying===

Currying is (in essence) a way looking at functions of multiple arguments as a series of functions of one argument that return functions that work with the other arguments.  In OCaml, this makes sense, as functions are values, and can be created and returned by other functions trivially.  As an example of what this means, consider the first function example on this page, &lt;code&gt;let add a b = a + b&lt;/code&gt;.  We generally think of this as a function that accepts two arguments and returns a value.  Really, it's not that at all.

OCaml converts that function definition under the covers to the equivalent:

&lt;codeblock language=ocaml&gt;
&lt;&lt;curry&gt;&gt;=
let add = fun a -&gt; fun b -&gt; a + b
&lt;/codeblock&gt;

What this form means is that &lt;code&gt;add&lt;/code&gt; is a function that takes a single argument, binds its value to the name a and returns an anonymous function that takes a single argument, binds its value to the name b, and then computes the value a+b according to the bindings from the function applications and returns the result.  Why this is important is that it allows us to use partial application to specialize the functions we have.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;partial&gt;&gt;=
let add1 = add 1;;
let add10 = add 10;;
&lt;/codeblock&gt;

Here, we have used Currying to our advantage to create two new functions, &lt;code&gt;add1&lt;/code&gt; and &lt;code&gt;add10&lt;/code&gt; that each take a single argument and add 1 and 10 to that argument, respectively.

&lt;codeblock&gt;
# add1 10;;
- : int = 11
# add10 10;;
- : int = 20
&lt;/codeblock&gt;

==Conditionals==

There are two forms of conditionals in OCaml, if/then expressions and pattern matching.

===If/Then===

The if then construct is fairly straight-forward, and similar to similar constructs in other languages.  The basic form of the if/then is &lt;code&gt;if test then e1 else e2&lt;/code&gt;, where &lt;code&gt;test&lt;/code&gt; is an expression that evaluates to a boolean value, and &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; are expressions that are evaluated in the true and false branches of the test respectively.  The primary catch with if/then in OCaml is that both &lt;code&gt;e1&lt;/code&gt; and &lt;code&gt;e2&lt;/code&gt; must have the same type, so expressions like &lt;code&gt;if test then 1 else &quot;two&quot;&lt;/code&gt; are not allowed.  Additionally if the type of the true branch is &lt;code&gt;unit&lt;/code&gt;, then the else branch is not required, e.g. &lt;code&gt;if test then print_string &quot;true!&quot;&lt;/code&gt; is equivalent to &lt;code&gt;if test then print_string &quot;true!&quot; else ()&lt;/code&gt;.  Note, however, that this con lead to mistakes where multiple unit valued expressions are to be executed in a given branch.  For example:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;;
  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

This is parsed as

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
);

  print_string &quot;bye&quot;
else
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which results in a syntax error.  More troublesome is something like the following:

&lt;codeblock language=ocaml&gt;
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
  print_endline &quot;what?&quot;
&lt;/codeblock&gt;

Which is parsed as:

&lt;codeblock language=ocaml&gt;
(
if test then
  print_endline &quot;hi&quot;
else
  print_string &quot;bye&quot;;
);  
print_endline &quot;what?&quot;
&lt;/codeblock&gt;

So the &lt;code&gt;print_endline &quot;what?&quot;&lt;/code&gt; expression is always evaluated.  The reason for this is that the semicolon has lower precedence than the if/then expression.  To fix this, wrap multi-statement blocks in parens or &lt;code&gt;begin/end&lt;/code&gt; pairs

&lt;codeblock language=ocaml&gt;
if test then
  (
    print_endline &quot;hi&quot;;
    print_string &quot;baby&quot;
  )
else
  begin
    print_string &quot;bye&quot;;
    print_endline &quot;what?&quot;
  end
&lt;/codeblock&gt;

===Pattern Matching===

Pattern matching is a powerful construct of OCaml that allows for conditional branching based on the structure and content of a value.  Pattern matching is initiated in OCaml in one of two ways: the first is the &lt;code&gt;function&lt;/code&gt; keyword, described above, and the second is the &lt;code&gt;match ... with&lt;/code&gt; construct.  The general form of the &lt;code&gt;match ... with&lt;/code&gt; construct is as follows:

&lt;codeblock language=ocaml&gt;
match exp with
| patt_1 -&gt; ex_1
...
| patt_n -&gt; ex_n
&lt;/codeblock&gt;

That is, the keyword &lt;code&gt;match&lt;/code&gt; followed by an expression that evaluates to a value, followed by the &lt;code&gt;with&lt;/code&gt; keyword, then a series of pattern/expression pairs, separated by &lt;code&gt;|&lt;/code&gt; characters (the first one is optional).  The value that &lt;code&gt;exn&lt;/code&gt; evaluates to is checked against the patterns, in order of definition, and if one matches (say &lt;code&gt;patt_i&lt;/code&gt;), then the entire match expression reduces to the corresponding expression (&lt;code&gt;ex_i&lt;/code&gt;).

A pattern can be any of the following recursive constructs:
* A constant value : one of { integer-literal, float-literal; char-literal, string-literal, constant variant value, &lt;code&gt;false&lt;/code&gt;, &lt;code&gt;true&lt;/code&gt;, &lt;code&gt;[]&lt;/code&gt;, &lt;code&gt;()&lt;/code&gt;, constant polymorphic variant }
* &lt;code&gt;_&lt;/code&gt; : matches any pattern and throws away the value
* variable-name  : matches any pattern and binds the value to the variable name for use in the corresponding expression
* ''pattern'' as variable-name : the value that matches ''pattern'' is bound to variable-name for use in the corresponding expression
* ( ''pattern'' )
* ( ''pattern'' : type-annotation )
* ''pattern'' | ''pattern'' : multiple patterns may correspond to the same expression
* constr ''pattern'' : Here, constr is one of OCaml's variant type values, and ''pattern'' is its associated data
* `tag-name ''pattern'' : Here, tag-name is one of OCaml's polymorphic variants, and ''pattern'' is its associated data
* # typeconstr-name : used to match some set of polymorphic variants
* ''pattern'', ''pattern'', ..., ''pattern'' : these are tuples of patterns
* { field-name_1 = ''pattern''; ... ; field-name_n = ''pattern''} : matching against records
* [ ''pattern'' ; ... ; ''pattern''] : matching against a list
* ''pattern'' :: ''pattern'' : matching against consed values
* [| ''pattern'' ; ... ; ''pattern'' |] : matching against arrays

Some example patterns are

* &lt;code&gt;[]&lt;/code&gt; : the empty list
* &lt;code&gt;h::t&lt;/code&gt; : a non empty list, binding the head and tail to the variables &lt;code&gt;h&lt;/code&gt; and &lt;code&gt;t&lt;/code&gt;, respectively
* &lt;code&gt;h::_&lt;/code&gt; : a non empty list, binding the head to &lt;code&gt;h&lt;/code&gt; and throwing away the tail
* &lt;code&gt;(_,_,x)&lt;/code&gt; : a three-tuple where the first two values are thrown away and the third is bound to &lt;code&gt;x&lt;/code&gt;
* h::(h2::_ as t) : a list with at least two elements in it, where the head is bound to &lt;code&gt;h&lt;/code&gt;, the second element is bound to &lt;code&gt;h2&lt;/code&gt;, and the list minus its first value is bound to &lt;code&gt;t&lt;/code&gt;
* &lt;code&gt;Some ((h1,(h2 : float),_,1)::next::_)&lt;/code&gt; : a &lt;code&gt;Some&lt;/code&gt; constructer with associated data that is a list of four-tuples, at least two elements in length, where the first value in the tuple at the head is bound to &lt;code&gt;h1&lt;/code&gt;, the second is bound to &lt;code&gt;h2&lt;/code&gt; and is restricted to being a floating point value, the third is thrown away, and the fourth is a 1.  The second element is bound to &lt;code&gt;next&lt;/code&gt;, and the rest of the list is thrown away.

This kind of feature is very powerful, and lets us write very succinct code that operates on the structure of data.  For example, a function that throws away every other element of a list can be written simply:

&lt;codeblock language=ocaml&gt;
&lt;&lt;odds&gt;&gt;=
let rec odds = function
| ([] | [_]) as l -&gt; l
| h::_::t -&gt; h::(odds t);;
&lt;/codeblock&gt;

Here the first pattern matches lists with zero or one elements and returns that list, while the second pattern matches all lists with at least two elements, throws away the second, saves the first, and conses it onto the list created by throwing away every other element of the remaining list.

==Looping==

While looping is often handled via recursive functions in OCaml, e.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;loop_rec&gt;&gt;=
let rec loop times f =
match times with
| 0 -&gt; ()
| _ -&gt; f (); loop (times-1) f;;
&lt;/codeblock&gt;

there are other built-in options, the &lt;code&gt;for&lt;/code&gt; and &lt;code&gt;while loops&lt;/code&gt;:

&lt;codeblock language=ocaml&gt;
for counter = start to stop do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
while test do
  (* some expression that evaluates to unit *)
done
&lt;/codeblock&gt;

The for loop loops over the range provided (both endpoints inclusive), performing whatever code lies within the &lt;code&gt;do&lt;/code&gt; and &lt;code&gt;done&lt;/code&gt; keywords, rebinding the counter variable to the current value each time.  For loops can also count backwards, using &lt;code&gt;downto&lt;/code&gt; rather than &lt;code&gt;to&lt;/code&gt;.  The endpoints of the loop don't have to be constants, they can be any expression that evaluates to an int, and the entire for loop evaluates to &lt;code&gt;()&lt;/code&gt;.  Note that there is no &quot;step&quot; option as in languages such as C.

While loops are similar to those found in other languages.  So long as the conditional evaluates to &lt;code&gt;true&lt;/code&gt;, the loop body is evaluated.  Like the for loop, the entire while loop evaluates to &lt;code&gt;()&lt;/code&gt;.

==I/O==

===Simple I/O===
I/O is performed using stdin, stdout, and stderr using the various read, print, and prerr functions respectively.

; &lt;code&gt;read_line&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Returns the resulting string, minus the newline.
; &lt;code&gt;read_int&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to an int, raising an exception if it cannot.
; &lt;code&gt;read_float&lt;/code&gt; : Flushes stdout then reads from stdin until a newline character is seen.  Attempts to convert the resulting string to a float, raising an exception if it cannot.
; &lt;code&gt;print_char&lt;/code&gt; : prints a character to stdout
; &lt;code&gt;print_newline&lt;/code&gt; : prints a newline character to stdout
; &lt;code&gt;print_string&lt;/code&gt; : prints a string to stdout
; &lt;code&gt;print_endline&lt;/code&gt; : prints a string to stdout followed by a newline character
; &lt;code&gt;print_int&lt;/code&gt; : prints an int to stdout
; &lt;code&gt;print_float&lt;/code&gt; : prints a float to stdout
; &lt;code&gt;prerr_char&lt;/code&gt; : prints a character to stderr
; &lt;code&gt;prerr_newline&lt;/code&gt; : prints a newline character to stderr
; &lt;code&gt;prerr_string&lt;/code&gt; : prints a string to stderr
; &lt;code&gt;prerr_endline&lt;/code&gt; : prints a string to stderr followed by a newline character
; &lt;code&gt;prerr_int&lt;/code&gt; : prints an int to stderr
; &lt;code&gt;prerr_float&lt;/code&gt; : prints a float to stderr

Formatted printing can be done via the &lt;code&gt;Printf&lt;/code&gt; module which contain (among other things) functions &lt;code&gt;printf&lt;/code&gt; and &lt;code&gt;sprintf&lt;/code&gt; that use format strings similar to those of C.  E.g.

&lt;codeblock language=ocaml&gt;
&lt;&lt;printf&gt;&gt;=
Printf.printf &quot;0x%0X\n&quot; 500;;
let s = Printf.sprintf &quot;%d: %s --\t%08.3f&quot; 7 &quot;whoopie&quot; 1.4432578;;
&lt;/codeblock&gt;

will print &lt;code&gt;0x1F4&lt;/code&gt; followed by a newline to stdout, and bind the string &lt;code&gt;&quot;7: whoopie --	0001.443&quot;&lt;/code&gt; to &lt;code&gt;s&lt;/code&gt;.

===File I/O===

Files are usually worked with via input and output channels.  To open the file data.in for reading and the file data.out for writing, one would do the following:

&lt;codeblock language=ocaml&gt;
&lt;&lt;channels&gt;&gt;=
let in_channel = open_in &quot;data.in&quot;;;
let out_channel = open_out &quot;data.out&quot;;;
&lt;/codeblock&gt;

The channels can now be read from and written to using the various input and output functions.  For example:

&lt;codeblock language=ocaml&gt;
&lt;&lt;io&gt;&gt;=
let line = input_line in_channel;;
output_string out_channel line; output_char out_channel '\n';;
&lt;/codeblock&gt;

Will read the next line from in_channel (connected to data.in), and copy that line followed by a newline character into out_channel (connected to data.out).  Doing this repeatedly would copy data.in to data.out.

In addition to the simple I/O functions, formatted data can also be written using the &lt;code&gt;Printf&lt;/code&gt; module's &lt;code&gt;fprintf&lt;/code&gt; function.  Here, &lt;code&gt;Printf.fprintf channel format arg1 ... argN&lt;/code&gt; will print arguments 1 through N to output channel &lt;code&gt;channel&lt;/code&gt; according to the format string &lt;code&gt;format&lt;/code&gt;.

==Command line arguments==

Command line arguments are available as a string array named &lt;code&gt;Sys.argv&lt;/code&gt;.  &lt;code&gt;Sys.argv.(0)&lt;/code&gt; contains the name of the program that was executed, and subsequent entries in the array contain the additional arguments, if any, un the order they were presented on the command line.  So, to print the name of the program followed by the arguments, each on a new line, one can do:

&lt;codeblock language=ocaml&gt;
&lt;&lt;arguments&gt;&gt;=
print_endline Sys.argv.(0);
for i = 1 to Array.length Sys.argv - 1 do
  print_endline Sys.argv.(i)
done;;
&lt;/codeblock&gt;

==The Program==
&lt;codeblock&gt;
&lt;&lt;basic_constructs.ml&gt;&gt;=
&lt;&lt;let_function&gt;&gt;

&lt;&lt;let_function2&gt;&gt;

&lt;&lt;let_anon&gt;&gt;

&lt;&lt;let_function&gt;&gt;

&lt;&lt;combo_function&gt;&gt;

&lt;&lt;factorial&gt;&gt;

&lt;&lt;length&gt;&gt;

&lt;&lt;find&gt;&gt;

&lt;&lt;curry&gt;&gt;

&lt;&lt;partial&gt;&gt;

&lt;&lt;odds&gt;&gt;

&lt;&lt;loop_rec&gt;&gt;

&lt;&lt;printf&gt;&gt;

&lt;&lt;channels&gt;&gt;
  
&lt;&lt;io&gt;&gt;
&lt;/codeblock&gt;

== See also ==

* [[Hello World (OCaml/F_Sharp)]]
* [[Basic constructs (C)]]
* [[Basic constructs (Java)]]
[[Category:Basic constructs]]
[[Category:Programming language:OCaml]]</text>
    </revision>
  </page>
  <page>
    <title>Basic constructs (Unlambda)</title>
    <id>3955</id>
    <revision>
      <id>16786</id>
      <timestamp>2010-07-31T18:29:06Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>A start</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow).

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;.

[[Category:Basic constructs]]</text>
    </revision>
    <revision>
      <id>16787</id>
      <timestamp>2010-08-01T13:22:58Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>Some more</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow).

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Flow control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16788</id>
      <timestamp>2010-08-01T14:12:52Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Built-in functions */ added I/O functions</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Flow control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16789</id>
      <timestamp>2010-08-02T10:25:32Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Evaluation control */ renamed section</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16791</id>
      <timestamp>2010-08-07T09:48:21Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>More stuff</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

== Boolean values and operations ==
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is &lt;code&gt;v&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt; is &lt;code&gt;i&lt;/code&gt;. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``ki``''BC''v&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`ki``ssv
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16792</id>
      <timestamp>2010-08-07T09:49:41Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Boolean values and operations */ wrong level</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is &lt;code&gt;v&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt; is &lt;code&gt;i&lt;/code&gt;. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``ki``''BC''v&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`ki``ssv
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16793</id>
      <timestamp>2010-08-07T10:04:38Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* The delay function &lt;code&gt;d&lt;/code&gt; */ actually it's syntactic sugar for avoiding abstraction elimination</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`Fx&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;x``.a.bx&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is &lt;code&gt;v&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt; is &lt;code&gt;i&lt;/code&gt;. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``ki``''BC''v&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`ki``ssv
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16794</id>
      <timestamp>2010-08-07T10:06:01Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* The delay function &lt;code&gt;d&lt;/code&gt; */ typography</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is &lt;code&gt;v&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt; is &lt;code&gt;i&lt;/code&gt;. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``ki``''BC''v&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`ki``ssv
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16795</id>
      <timestamp>2010-08-08T07:56:30Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ extended a bit</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''G''.&amp;lambda;''F''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16796</id>
      <timestamp>2010-08-08T08:01:20Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Boolean values and operations */</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16797</id>
      <timestamp>2010-08-08T08:11:09Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ test programs</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16798</id>
      <timestamp>2010-08-08T08:34:21Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ fixed bug (abstraction eliminated version of not missed a `k`k, and that bug was copied to ifthenelse</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16799</id>
      <timestamp>2010-08-08T08:38:15Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ The test for not was missing the call to not :-)</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16800</id>
      <timestamp>2010-08-08T09:11:49Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ added or function ant test programs for and and or</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
   `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
`k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
   `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16801</id>
      <timestamp>2010-08-08T09:16:32Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ fixed test programs: k needs two backticks</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16802</id>
      <timestamp>2010-08-08T09:18:15Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ the or test program should, of course, get a different name</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16803</id>
      <timestamp>2010-08-08T09:20:40Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ ... and should use or, of course :-)</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16804</id>
      <timestamp>2010-08-08T09:33:42Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Boolean values and operations */ Added a note that this triggers a bug in the perl unlambda implementation</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16805</id>
      <timestamp>2010-08-09T19:41:17Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Basic data types and control structures */ started section on tuples and lists</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

== Tuples and lists ==
The simplest compound data structure is the pair. A pair holds two data items, i.e. in Unlambda two functions. A pair can be implemented by a function which takes another function as argument and applies that function to the two elements of the pair. The pair constructor takes the two arguments and returns that function, i.e.
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''f''.``fxy&lt;code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;pair&gt;&gt;=
``s``s`ks``s`kk``s`ks``s`k`sik`kk
&lt;/codeblock&gt;
Of course one needs also functions to get the members of the pair back. To get the first member, the standard way is to pass a function to the pair which takes two arguments and returns the first. The resulting function can be seen on the Unlambda homepage (or here on the page [[Turing machine imulator (Unlambda)]]. However there's another, shorter way to get the first element.

Consider what happens if you call a pair (which, after all, is just a function) on a continuation. Well, the pair applies that continuation on its two members. More exactly, due to currying, it first applies it to the first member &amp;hellip; and at that point the continuation replaces the current evaluation, effectively making the corresponding call/cc return with the first member of the pair. Now the &lt;code&gt;c&lt;/code&gt; builtin function just calls its argument on the current continuation, therefore if we call it on a pair, we get its first member back. Or in short, the «first» function can be written simply as
&lt;codeblock&gt;
&lt;&lt;first&gt;&gt;=
c
&lt;/codeblock&gt;
Now, can we do an equally clever trick with «cdr», which gets the second member of the pair? Well, in principle yes, except that this time it gets more complicated than the standard way. However, as we will see in a moment, it still has some advantage over the standard way. The complication comes from the fact that to get the second member, we have to pass &lt;code&gt;`k«cont»&lt;/code&gt; to the pair (so the first argument gets ignored, and the second thrown on the continuation). Therefore the «second» function reads
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock&gt;
&lt;&lt;second&gt;&gt;=
``s`kc``s``s`ksk`kk
&lt;/codeblock&gt;

Now an obvious extension of the concept of a pair is the concept of a triple, which contains three elements. Such a triple can be defined along the lines of the tuple as
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''z''.&amp;lambda;''f''.```''fxyz''
or after abstraction elimination
&lt;codeblock&gt;
&lt;&lt;triple&gt;&gt;=
``s``s`ks``s`k`s`ks``s`k`s`kk``s`k`s`ks``s``s`ks``s`kk``s`ks``s`k`sik`kk`k`kk
&lt;/codeblock&gt;
Now what about out access functions? Well, due to the use of continuations, the access functions stop evaluation as soon as the corresponding member is thrown at them. Therefore «first» doesn't care that the triple would call it on three arguments instead of two, since after the first one the function returns anyway. Similarly, the function «second» doesn't care that the triple would pass a third argument. This would not work with the standard definitions; on those, one would need to have separate definitions for the accessors.

Of course for our triple, we need an access function for the third member. The definition is straightforward:
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;C.`''F''`k`k''C''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;third&gt;&gt;=
``s`kc``s``s`ksk`k``s`kkk
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16806</id>
      <timestamp>2010-08-09T19:44:43Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Tuples and lists */ fixed markup and typography</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

== Tuples and lists ==
The simplest compound data structure is the pair. A pair holds two data items, i.e. in Unlambda two functions. A pair can be implemented by a function which takes another function as argument and applies that function to the two elements of the pair. The pair constructor takes the two arguments and returns that function, i.e.
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''f''.``fxy&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;pair&gt;&gt;=
``s``s`ks``s`kk``s`ks``s`k`sik`kk
&lt;/codeblock&gt;
Of course one needs also functions to get the members of the pair back. To get the first member, the standard way is to pass a function to the pair which takes two arguments and returns the first. The resulting function can be seen on the Unlambda homepage (or here on the page [[Turing machine imulator (Unlambda)]]. However there's another, shorter way to get the first element.

Consider what happens if you call a pair (which, after all, is just a function) on a continuation. Well, the pair applies that continuation on its two members. More exactly, due to currying, it first applies it to the first member &amp;hellip; and at that point the continuation replaces the current evaluation, effectively making the corresponding call/cc return with the first member of the pair. Now the &lt;code&gt;c&lt;/code&gt; builtin function just calls its argument on the current continuation, therefore if we call it on a pair, we get its first member back. Or in short, the «first» function can be written simply as
&lt;codeblock&gt;
&lt;&lt;first&gt;&gt;=
c
&lt;/codeblock&gt;
Now, can we do an equally clever trick with «cdr», which gets the second member of the pair? Well, in principle yes, except that this time it gets more complicated than the standard way. However, as we will see in a moment, it still has some advantage over the standard way. The complication comes from the fact that to get the second member, we have to pass &lt;code&gt;`k«cont»&lt;/code&gt; to the pair (so the first argument gets ignored, and the second thrown on the continuation). Therefore the «second» function reads
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock&gt;
&lt;&lt;second&gt;&gt;=
``s`kc``s``s`ksk`kk
&lt;/codeblock&gt;

Now an obvious extension of the concept of a pair is the concept of a triple, which contains three elements. Such a triple can be defined along the lines of the tuple as
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''z''.&amp;lambda;''f''.```''fxyz''&lt;/code&gt;
or after abstraction elimination
&lt;codeblock&gt;
&lt;&lt;triple&gt;&gt;=
``s``s`ks``s`k`s`ks``s`k`s`kk``s`k`s`ks``s``s`ks``s`kk``s`ks``s`k`sik`kk`k`kk
&lt;/codeblock&gt;
Now what about out access functions? Well, due to the use of continuations, the access functions stop evaluation as soon as the corresponding member is thrown at them. Therefore «first» doesn't care that the triple would call it on three arguments instead of two, since after the first one the function returns anyway. Similarly, the function «second» doesn't care that the triple would pass a third argument. This would not work with the standard definitions; on those, one would need to have separate definitions for the accessors.

Of course for our triple, we need an access function for the third member. The definition is straightforward:
: &lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k`k''C''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;third&gt;&gt;=
``s`kc``s``s`ksk`k``s`kkk
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16807</id>
      <timestamp>2010-08-09T21:10:22Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Tuples and lists */ fixed wrong heading level</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

=== Tuples and lists ===
The simplest compound data structure is the pair. A pair holds two data items, i.e. in Unlambda two functions. A pair can be implemented by a function which takes another function as argument and applies that function to the two elements of the pair. The pair constructor takes the two arguments and returns that function, i.e.
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''f''.``fxy&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;pair&gt;&gt;=
``s``s`ks``s`kk``s`ks``s`k`sik`kk
&lt;/codeblock&gt;
Of course one needs also functions to get the members of the pair back. To get the first member, the standard way is to pass a function to the pair which takes two arguments and returns the first. The resulting function can be seen on the Unlambda homepage (or here on the page [[Turing machine imulator (Unlambda)]]. However there's another, shorter way to get the first element.

Consider what happens if you call a pair (which, after all, is just a function) on a continuation. Well, the pair applies that continuation on its two members. More exactly, due to currying, it first applies it to the first member &amp;hellip; and at that point the continuation replaces the current evaluation, effectively making the corresponding call/cc return with the first member of the pair. Now the &lt;code&gt;c&lt;/code&gt; builtin function just calls its argument on the current continuation, therefore if we call it on a pair, we get its first member back. Or in short, the «first» function can be written simply as
&lt;codeblock&gt;
&lt;&lt;first&gt;&gt;=
c
&lt;/codeblock&gt;
Now, can we do an equally clever trick with «cdr», which gets the second member of the pair? Well, in principle yes, except that this time it gets more complicated than the standard way. However, as we will see in a moment, it still has some advantage over the standard way. The complication comes from the fact that to get the second member, we have to pass &lt;code&gt;`k«cont»&lt;/code&gt; to the pair (so the first argument gets ignored, and the second thrown on the continuation). Therefore the «second» function reads
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock&gt;
&lt;&lt;second&gt;&gt;=
``s`kc``s``s`ksk`kk
&lt;/codeblock&gt;

Now an obvious extension of the concept of a pair is the concept of a triple, which contains three elements. Such a triple can be defined along the lines of the tuple as
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''z''.&amp;lambda;''f''.```''fxyz''&lt;/code&gt;
or after abstraction elimination
&lt;codeblock&gt;
&lt;&lt;triple&gt;&gt;=
``s``s`ks``s`k`s`ks``s`k`s`kk``s`k`s`ks``s``s`ks``s`kk``s`ks``s`k`sik`kk`k`kk
&lt;/codeblock&gt;
Now what about out access functions? Well, due to the use of continuations, the access functions stop evaluation as soon as the corresponding member is thrown at them. Therefore «first» doesn't care that the triple would call it on three arguments instead of two, since after the first one the function returns anyway. Similarly, the function «second» doesn't care that the triple would pass a third argument. This would not work with the standard definitions; on those, one would need to have separate definitions for the accessors.

Of course for our triple, we need an access function for the third member. The definition is straightforward:
: &lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k`k''C''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;third&gt;&gt;=
``s`kc``s``s`ksk`k``s`kkk
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16808</id>
      <timestamp>2010-08-10T19:56:52Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Tuples and lists */ some more</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

=== Tuples and lists ===
The simplest compound data structure is the pair. A pair holds two data items, i.e. in Unlambda two functions. A pair can be implemented by a function which takes another function as argument and applies that function to the two elements of the pair. The pair constructor takes the two arguments and returns that function, i.e.
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''f''.``fxy&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;pair&gt;&gt;=
``s``s`ks``s`kk``s`ks``s`k`sik`kk
&lt;/codeblock&gt;
Of course one needs also functions to get the members of the pair back. To get the first member, the standard way is to pass a function to the pair which takes two arguments and returns the first. The resulting function can be seen on the Unlambda homepage (or here on the page [[Turing machine imulator (Unlambda)]]. However there's another, shorter way to get the first element (this function will be called «tfirst», for &quot;tuple first&quot;, because there will be another first function for lists, «lfirst»).

Consider what happens if you call a pair (which, after all, is just a function) on a continuation. Well, the pair applies that continuation on its two members. More exactly, due to currying, it first applies it to the first member &amp;hellip; and at that point the continuation replaces the current evaluation, effectively making the corresponding call/cc return with the first member of the pair. Now the &lt;code&gt;c&lt;/code&gt; builtin function just calls its argument on the current continuation, therefore if we call it on a pair, we get its first member back. Or in short, the «tfirst» function can be written simply as
&lt;codeblock&gt;
&lt;&lt;tfirst&gt;&gt;=
c
&lt;/codeblock&gt;
Now, can we do an equally clever trick to get the second member of the pair? Well, in principle yes, except that this time it gets more complicated than the standard way. However, as we will see in a moment, it still has some advantage over the standard way. The complication comes from the fact that to get the second member, we have to pass &lt;code&gt;`k«cont»&lt;/code&gt; to the pair (so the first argument gets ignored, and the second thrown on the continuation). Therefore the «tsecond» function reads
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock&gt;
&lt;&lt;tsecond&gt;&gt;=
``s`kc``s``s`ksk`kk
&lt;/codeblock&gt;

Now an obvious extension of the concept of a pair is the concept of a triple, which contains three elements. Such a triple can be defined along the lines of the tuple as
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''z''.&amp;lambda;''f''.```''fxyz''&lt;/code&gt;
or after abstraction elimination
&lt;codeblock&gt;
&lt;&lt;triple&gt;&gt;=
``s``s`ks``s`k`s`ks``s`k`s`kk``s`k`s`ks``s``s`ks``s`kk``s`ks``s`k`sik`kk`k`kk
&lt;/codeblock&gt;
Now what about out access functions? Well, due to the use of continuations, the access functions stop evaluation as soon as the corresponding member is thrown at them. Therefore «first» doesn't care that the triple would call it on three arguments instead of two, since after the first one the function returns anyway. Similarly, the function «second» doesn't care that the triple would pass a third argument. This would not work with the standard definitions; on those, one would need to have separate definitions for the accessors.

Of course for our triple, we need an access function for the third member. The definition is straightforward:
: &lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k`k''C''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;tthird&gt;&gt;=
``s`kc``s``s`ksk`k``s`kkk
&lt;/codeblock&gt;

Now there are in principle infinitely many tuples, therefore it doesn't make sense to define a separate constructor for each tuple type. Instead, we define a &quot;tuple extender&quot;, which takes an ''n''-tuple and a value and returns an (''n''+1)-tuple of which the first ''n'' values are the same as from the ''n''-tuple, and the last one is the one newly provided. An (''n''+1)-tuple applies its arguments to ''n''+1 arguments; thanks to currying this means first applying it to ''n'' arguments, and then applying the result to the additional argument. Applying the function to the first ''n'' arguments is done by passing the function to the original ''n''-tuple. Therefore the tuple extender is
:&lt;code&gt;&amp;lambda;''T''.&amp;lambda;''x''.&amp;lambda;''f''.``''Tfx''&lt;/code&gt;
where &lt;code&gt;''T''&lt;code&gt; is the tuple to be extended and ''x'' is the new value. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;tupleext&gt;&gt;=
``s``s`ks``s`kks`kk
&lt;/codeblock&gt;
By noting that a &quot;0-tuple&quot; doesn't apply its function at all, i.e. is the identity function &lt;code&gt;i&lt;/code&gt;, all tuples can be recursively built using «tupleext». For example, an alternative to &lt;code&gt;``«triple».a.b.c&lt;/code&gt; would be &lt;code&gt;``«tupleext»``«tupleext»``«tupleext»i.a.b.c&lt;/code&gt;.

While tuples contain a fixed number of values, often the number of items to be stored isn't known from the beginning. In that case, the data can be stored in a list. A list is just a pair where the first item contains the first item of the list, and the second item contains the list of the other elements. There's one exception, however, which is the empty list, «nil». This will be defined as &lt;code&gt;v&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;nil&gt;&gt;=
v
&lt;/codeblock&gt;

We of course need a function to distinguish the empty list and a non-empty list, i.e. an empty list and a pair. Now a pair can only be detected by applying it to a function, which means that the function is applied to the two arguments. However, we are not interested in the two arguments, therefore we use a function which ignores its two arguments. Since applying &lt;code&gt;v&lt;/code&gt; to anything returns &lt;code&gt;v&lt;/code&gt; again (which is &lt;code&gt;«false»&lt;/code&gt;), we will return &lt;code&gt;«true»&lt;/code&gt;, i.e. &lt;code&gt;i&lt;/code&gt; for nonempty lists, i.e. pairs. Therefore our function will be called «nonempty». The definition is simple:
:&lt;code&gt;^''f''`''f''`k`ki&lt;/code&gt;
or after abstraction elimination
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;nonempty&gt;&gt;=
``si`k`k`ki
&lt;/codeblock&gt;
The first element of the list is the first element of the pair:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;lfirst&gt;&gt;=
&lt;&lt;tfirst&gt;&gt;
&lt;/codeblock&gt;
Note that for «nil» this gives «nil» again.

The rest of the list is the second argument of the list. However since this time we don't have to care about higher tuples, we use the standard form which is shorter for the second element:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;lrest&gt;&gt;=
``si`k`ki
&lt;/codeblock&gt;
Note that again, this maps «nil» to «nil».

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
    <revision>
      <id>16827</id>
      <timestamp>2010-08-19T18:53:52Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Basic data types and control structures */ added Church integers, some other small corrections and extensions</comment>
      <text xml:space="preserve">{{develop}}
This page describes some basic constructs of Unlambda.

== Function calls ==
From a language point of view, there's only one basic construct in Unlambda: Function application. Function application looks like this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;function application&gt;&gt;=
`&lt;&lt;applied function&gt;&gt; &lt;&lt;argument&gt;&gt;
&lt;/codeblock&gt;
where first the applied function and after that the argument (which itself is a function) is evaluated, and then the function is called in the argument. For example, as applied function we can use a built-in function which, when called, prints an &quot;a&quot; and returns its argument unchanged.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;applied function&gt;&gt;=
.a
&lt;/codeblock&gt;
Likewise, the argument is a built-in function which just prints &quot;b&quot; when called, and returns its argument unchanged:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;argument&gt;&gt;=
.b
&lt;/codeblock&gt;
Now the following program, which contains just the above function call, just prints &quot;a&quot;, because the only function called is &lt;code&gt;.a&lt;/code&gt;. The argument is evaluated, but not called (in this case, the argument doesn't contain a function call at all, therefore evaluation just gives the named function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall.unl&gt;&gt;=
&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;

The following program shows that the function argument is evaluated by using the above function evaluation as argument for another function call, where the argument is &lt;code&gt;.c&lt;/code&gt;.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall2.unl&gt;&gt;=
`&lt;&lt;function application&gt;&gt; .c
&lt;/codeblock&gt;
This program prints &quot;ab&quot;: First, the applied function of the outer function call is evaluated. This is just the function application above, which prints a and returns &lt;code&gt;.b&lt;/code&gt;. The argument doesn't contain a function call. Now the result of the first function application, i.e. &lt;code&gt;.b&lt;/code&gt;, is applied to the argument &lt;code&gt;.c&lt;/code&gt;. This call prints &quot;b&quot; and returns the argument &lt;code&gt;.c&lt;/code&gt;.

The following shows evaluation of the argument:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;funcall3.unl&gt;&gt;=
`.c&lt;&lt;function application&gt;&gt;
&lt;/codeblock&gt;
In this case, the function application above is the argument of the function &lt;code&gt;.c&lt;/code&gt;. Evaluation of that function prints &quot;a&quot; and returns &lt;code&gt;.b&lt;/code&gt;, the latter being used as argument to &lt;code&gt;.c&lt;/code&gt; which prints &quot;c&quot; and again returns its argument. Therefore this program prints &quot;ac&quot;.

Note that Unlambda functions only take a single argument. However multi-argument functions can be defined indirectly by currying. Say you want to implement a function &lt;math&gt;(x,y)\mapsto f(x,y)&lt;/math&gt;. Then you actually implement &lt;math&gt;x\mapsto(y\mapsto f(x,y))&lt;/math&gt;. That is, your function takes only the first argument, but doesn't calculate f, but returns a second function which expects the second argument and then calculates f on both arguments.

== Built-in functions ==
Unlambda has several built-in functions. Those functions are used as the building block to create other functions.

=== Pure functions ===
Pure functions are functions which do not have any side effects (like I/O or changing the program flow) and do not depend on global state.

==== The constant function creator &lt;code&gt;k&lt;/code&gt; ====
The function &lt;code&gt;k&lt;/code&gt; takes one function as argument and returns a constant function with that value, i.e. a function which ignores its argument and simply always returns the same value. For example, the following constructs the constant function which always returns &lt;code&gt;.a&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;constant .a&gt;&gt;=
`k.a
&lt;/codeblock&gt;
Applying that function to anything returns &lt;code&gt;.a&lt;/code&gt;, for example:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;get .a from constant function&gt;&gt;=
`&lt;&lt;constant .a&gt;&gt; .b
&lt;/codeblock&gt;
The following program proves this by applying the result to yet another function, which causes .a to be printed, thus showing that &lt;code&gt;.a&lt;/code&gt; was indeed called:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;consta.unl&gt;&gt;=
`&lt;&lt;get .a from constant function&gt;&gt; .c
&lt;/codeblock&gt;
Note that &lt;code&gt;.b&lt;/code&gt; could have been replaced by an arbitrary unlambda expression, except that any side effects from evaluating it will of course be seen.

Another way to describe this function is that it is a curried function which takes two arguments and returns the first.

==== The substitution function &lt;code&gt;s&lt;/code&gt; ====
The substitution function is a curried function that takes three arguments, applies both the first and the second separately to the third, and then applies the result of the first application to the result of the second. In other words, &lt;code&gt;```sABC&lt;/code&gt; is equivalent to &lt;code&gt;``AC`BC&lt;/code&gt; (except for the order of evaluation of A, B and C). The following program demonstrates this:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;substabc.unl&gt;&gt;=
```s.a.b.c
&lt;/codeblock&gt;
This prints &quot;abc&quot; as can be seen as follows: By the rule above, the program is equivalent to &lt;code&gt;``.a.c`.b.c&lt;/code&gt;. Now &lt;code&gt;`.a.c&lt;/code&gt; prints &quot;a&quot; and returns &lt;code&gt;.c&lt;/code&gt; and &lt;code&gt;`.b.c&lt;/code&gt; prints &quot;b&quot; and returns &quot;c&quot;. Finally, &lt;code&gt;`.c.c&lt;/code&gt; prints &quot;c&quot; and returns &lt;code&gt;.c&lt;/code&gt;.

Note that s and k are already sufficient to make the language Turing complete.

==== The identity function &lt;code&gt;i&lt;/code&gt; ====
The identity function is quite simple: It just returns its argument unchanged. Actually, it could be considered syntactic sugar, because it's equivalent to &lt;code&gt;``skk&lt;/code&gt;. The following code demonstrates the identity function by applying it to &lt;code&gt;.a&lt;/code&gt; and then applying the result to another function (&lt;code&gt;.b&lt;/code), which has the same effect as directly applying &lt;code&gt;.a&lt;/code&gt; to &lt;code&gt;.b&lt;/code&gt;, which prints &quot;a&quot; (and returns &lt;code&gt;.b&lt;/code&gt;).
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;identity.unl&gt;&gt;=
``i.a.b
&lt;/codeblock&gt;

==== The self-returning function &lt;code&gt;v&lt;/code&gt; ====
The function &lt;code&gt;v&lt;/code&gt; is a special case of a constant function: It always returns itself. Like &lt;code&gt;i&lt;/code&gt;, it can be considered syntactic sugar, because it can be written as &lt;code&gt;```s``s`kskk``s``s`kskk&lt;/code&gt;.

=== Evaluation control ===
The functions in this section are used to change the order of evaluation.

==== The delay function &lt;code&gt;d&lt;/code&gt; ====
Application of the delay function causes its argument ''not'' to be evaluated. Since it modifies the normal evaluation algorithm, it's strictly speaking not a function, but a special form. It returns a function which, when called, evaluates the argument of &lt;code&gt;d&lt;/code&gt; and then applies that to the argument of the call. The following example demonstrates how &lt;code&gt;d&lt;/code&gt; prevents immediate evaluation:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function&gt;&gt;=
`d`.a.b
&lt;&lt;delay1.unl&gt;&gt;=
&lt;&lt;delayed function&gt;&gt;
&lt;/codeblock&gt;
Normally, evaluating the argument &lt;code&gt;`.a.b&lt;/code&gt; would cause &quot;a&quot; to be printed (and the argument to &lt;code&gt;d&lt;/code&gt; to be &lt;code&gt;.b&lt;/code&gt;. However, due to the special properties of &lt;code&gt;d&lt;/code&gt; the argument remains unevaluated, and the program doesn't print anything.

The following example demonstrates the delayed evaluation of the argument when the resulting function is called. Here, it is applied to the identity function, which causes first the argument to &lt;code&gt;d&lt;/code&gt; (&lt;code&gt;`.a.b&lt;/code&gt;) to be evaluated (printing &quot;a&quot; and returning &lt;code&gt;.b&lt;/code&gt;), and then the result of that evaluation to be applied to the argument (here, &lt;code&gt;i&lt;/code&gt;), which in this case causes &quot;b&quot; to be printed. Therefore the result is exactly the same as if the code had been &lt;code&gt;``.a.bi&lt;/code&gt;
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function&gt;&gt; i
&lt;/codeblock&gt;

In some sense, this function can also be considered syntactic sugar, because the same effect can be achieved by replacing &lt;code&gt;`dF&lt;/code&gt; with &lt;code&gt;&amp;lambda;''x''.`F''x''&lt;/code&gt; (or actually, the result of doing abstraction elimination on it). To demonstrate that, we note that &lt;code&gt;&amp;lambda;''x''``.a.b''x''&lt;/code&gt; is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delayed function without d&gt;&gt;=
``s``s`k.a`k.bi
&lt;codeblock&gt;
Just as with using &lt;code&gt;d&lt;/code&gt;, this doesn't print anything when used directly:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay1a.unl&gt;&gt;=
&lt;&lt;delayed function without d&gt;&gt;
&lt;/codeblock&gt;
But if called, it does print &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;delay2.unl&gt;&gt;=
`&lt;&lt;delayed function without d&gt;&gt; i
&lt;/codeblock&gt;

==== The call with current continuation function &lt;code&gt;c&lt;/code&gt; ====
The function &quot;call with current continuation&quot; (call/cc for short) is the functional language equivalent to goto. What it does is to capture the current program state in a so-called continuation, and pass that to the function passed as argument. The continuation is a special function which replaces the current program state with the restored one, except that it places its argument at the point where the original call/cc was.

Since this description is quite abstract (and the call/cc isn't exactly an easy concept to grasp), here an example program which prints &quot;ab&quot;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;callcc.unl&gt;&gt;=
``c.a.b
&lt;/codeblock&gt;
This program runs as follows:
First, the call/cc function &lt;code&gt;c&lt;/code&gt; is called on &lt;code&gt;.a&lt;/code&gt;. This generates a continuation, which could be denoted by the pseudo-Unlambda code &lt;code&gt;&amp;lt;`$.b&amp;gt;&lt;/code&gt;. In between the angle brackets is the captured state, with the $ noting the place where the call to call/cc had been. This continuation is now passed as argument to the argument of &lt;code&gt;c&lt;/code&gt;, i.e. &lt;code&gt;.a&lt;/code&gt;. Therefore after the call to &lt;code&gt;c&lt;/code&gt;, the code looks like this:
:&lt;code&gt;``.a&lt;`$.b&gt;.b&lt;/code&gt;
What happens next is obvious: The function &lt;code&gt;.a&lt;/code&gt; is applied to the continuation. This prints &quot;a&quot; and returns the argument, i.e. the continuation, unchanged. Therefore now we have
:&lt;code&gt;`&lt;`$.b&gt;.b&lt;/code&gt;
At this place, we have a call of the continuation. This means to replace the dollar sign in the continuation by the argument (the &lt;code&gt;.b&lt;/code&gt; following the continuation, this gives &lt;code&gt;&amp;lt;`.b.b&amp;gt;&lt;/code&gt;), and then &lt;em&gt;replacing the complete expression to evaluate&lt;/em&gt; with the content of the continuation, so we now only have to evaluate
:&lt;code&gt;`.b.b&lt;/code&gt;
that is a simple application of &lt;code&gt;.b&lt;/code&gt; which prints &quot;b&quot; and returns its argument (which happens to be &lt;code&gt;.b&lt;/code&gt; as well). Therefore the complete output of the program is &quot;ab&quot;.

==== The exit function &lt;code&gt;e&lt;/code&gt; ====
The exit function, introduced in Unlambda 2.0, just terminates the program, returning its argument (which most Unlambda implementations ignore anyway). It can be considered syntactic sugar because the same effect can be achieved by rewriting the program to a function taking an exit function as argument, and then using a top-level call/cc (&lt;code&gt;c&lt;/code&gt;) to supply a continuation to it. The continuation of a top-level call/cc is of course just &lt;code&gt;&amp;lt;$&amp;gt;&lt;/code&gt;, and therefore any call to it just replaces the current expression to evaluate with the argument of the call, which in effect is exactly what &lt;code&gt;e&lt;/code&gt; does.

The following program demonstrates the use of &lt;code&gt;e&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;exit.unl&gt;&gt;=
`.a`e`.bi
&lt;/codeblock&gt;
This prints &quot;b&quot; and then exits. The function &lt;code&gt;.a&lt;/code&gt; is never executed since the exit function is executed first (on evaluating the argument of &lt;code&gt;.a&lt;/code&gt;).

&lt;small&gt;Note: The perl implementation in the Unlambda-2.0.0 distribution only does this correctly when single-stepping; when just running, it incorrectly prints &quot;a&quot; as well.&lt;/small&gt;

=== Input/Output functions ===
The functions in this category are for reading characters from standard input and writing them to standard output. All of them either have side effects or depend on global state, therefore none of them is pure.

==== The character output functions &lt;code&gt;.''x''&lt;/code&gt; ====
For each character ''x'', there's a function named &lt;code&gt;.''x''&lt;/code&gt; which acts like the identity function, except that it has the side effect of printing the character ''x'' to standard output. For example, applying &lt;code&gt;.a&lt;/code&gt; to a function outputs &quot;a&quot; and returns its argument unchanged. Actually these functions have already been used in all examples above. The following is a simple program which simply prints &quot;a&quot; (and returns the identity function):
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printa.unl&gt;&gt;=
`.ai
&lt;/codeblock&gt;

==== The newline function &lt;code&gt;r&lt;/code&gt; ====
The function &lt;code&gt;r&lt;/code&gt; starts a new line. It is equivalent to &lt;code&gt;.''newline''&lt;/code&gt;. The following program prints an empty line:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;println.unl&gt;&gt;=
`ri
&lt;/codeblock&gt;

==== The character read function &lt;code&gt;@&lt;/code&gt; ====
Since Unlambda 2.0, also standard input is supported. For this, the concept of the ''current character'' is introduced.

The current character is read from standard input with &lt;code&gt;@&lt;/code&gt;. This takes as argument one function, which is called either with &lt;code&gt;i&lt;/code&gt; if a character could be read, or with &lt;code&gt;v&lt;/code&gt; if no character could be read (EOF or read error). This function has the side effect of consuming one character from standard input.

==== The character test functions &lt;code&gt;?''x''&lt;/code&gt; ====
This function compares the current character to the character ''x'' and applies its argument to &lt;code&gt;i&lt;/code&gt; if they are equal, and &lt;code&gt;v&lt;/code&gt; otherwise. If there's no current character (&lt;code&gt;@&lt;/code&gt; was not yet called, or the latest call failed), the characters are considered not equal.

This function has no side effects, but depends on global state.

==== The character reprint function &lt;code&gt;|&lt;/code&gt; ====
If there is a current character (''x''), this calls its argument on the corresponding output function &lt;code&gt;.''x''&lt;/code&gt;. Otherwise it calls its argument on &lt;code&gt;v&lt;/code&gt;.

== Basic data types and control structures ==
Since Unlambda doesn't provide any data types except functions, all data has to be created using functions. In this section, definitions of some basic data types and control structures are defined. Those can be used as a sort of standard library for Unlambda programs.

=== Pseudofunctions ===
This section will not only define functions, but also what I'll call pseudofunctions. Pseudofunctions are not really a genuine Unlambda concept, however they are an useful concept when writing Unlambda programs.

To explain what I mean with pseudofunctions, let's take an example. As described above, the function &lt;code&gt;`k''F''&lt;/code&gt; (where &lt;code&gt;''F''&lt;/code&gt; is an arbitrary function) is a constant function which ignores its argument and returns &lt;code&gt;''F''&lt;/code&gt;. Now, how would one write a function which takes ''two'' arguments (in curried form), ignores them, and returns &lt;code&gt;''F''&lt;/code&gt;? Well, this obviously can be achieved with &lt;code&gt;`k`k''F''&lt;/code&gt;: Applying to the first argument ignores that and returns &lt;code&gt;`k''F''&lt;/code&gt;, which then applied on the second argument ignores that, too, and returns &lt;code&gt;''F''&lt;/code&gt;.

Now if you look at the function &lt;code&gt;`k`k''F''&lt;/code&gt;, on a superficial view it looks like a function application: It has the typical form &lt;code&gt;`«something»''F''&lt;/code&gt;. However, that &lt;code&gt;«something»&lt;/code&gt; is &lt;code&gt;k`k&lt;/code&gt; which clearly isn't an Unlambda function. This is what I call a pseudofunction: If in a function call you put it lexically between an application operator and an argument, it gives a valid Unlambda expression which acts just as if you had a function there, except that it isn't a function (and isn't evaluated as single block). Note, however, that pseudofunctions cannot be used as arguments; there you need true functions.

Now of course you could also make a true function which has the same effect, so why bother with pseudofunctions at all? Let's look at the example above: The Unlambda function corresponding to the pseudofunction above is, of course, &lt;code&gt;&amp;lambda''F''.`k`k''F''&lt;/code&gt;, which after abstraction elimination gives &lt;code&gt;``s`kkk&lt;/code&gt;. That is, the function above could also be written as &lt;code&gt;```s`kkk''F''&lt;/code&gt;, where now the text between the initial &lt;code&gt;`&lt;/code&gt; and the final &lt;code&gt;''F''&lt;/code&gt; is a true Unlambda function. However, this function expression is more complicated (in this case, the extra complication is minor, because the pseudofunction is short, and in additions some shortcuts in abstraction elimination could be applied; however, this isn't true in general; e.g. the pseudofunction &lt;code&gt;.o`.l`.l`.e`.H&lt;/code&gt; gets expanded to the true function &lt;code&gt;``s`k.o``s`k.l``s`k.l``s`k.e``s`k.Hi&lt;/code&gt;), and will also take more time to evaluate (because the evaluation forst basically will re-derive the expression &lt;code&gt;`k`k''F'&lt;/code&gt; and then evaluate that).

The general form of a pseudofunction is a list of Unlambda functions separated by &lt;code&gt;`&lt;/code&gt;, i.e. &lt;code&gt;''F''&lt;sub&gt;1&lt;/sub&gt;`''F''&lt;sub&gt;2&lt;/sub&gt;`&amp;hellip;`''F&lt;sub&gt;n&lt;/sub&gt;''&lt;/code&gt;. In the following, pseudofunctions will be named by prepending a star to the name of the function.

The concept can be generalized to more arguments: A two-argument pseudofunction only gives a valid Unlambda expression (and thus a function) if &quot;applied&quot; to two functions, and the same for more arguments. An ''n''-argument pseudofunction will be denoted by starting with ''n'' stars. As a general rule, an ''n''-star chunk has to be immediately preceded by ''n'' evaluation operators (&lt;code&gt;`&lt;/code&gt;) to get a valid Unlambda expression.

=== Boolean values and operations ===
Since Unlambda 2.0, there's an &quot;official&quot; boolean representation, which is fixed by the fact that the input functions use it:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;true&gt;&gt;=
i
&lt;&lt;false&gt;&gt;=
v
&lt;/codeblock&gt;
With this choice, the ''and'' function is quite easy: Just apply the first boolean to the second. If the first ine is ''true'', i.e. &lt;code&gt;i&lt;/code&gt;, the second argument will be returned, while ''false'', i.e. &lt;code&gt;v&lt;/code&gt;, will just return itself. The ''and'' function therefore is &lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.`''xy''&lt;/code&gt;, i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;and&gt;&gt;=
i
&lt;/codeblock&gt;
On the other hand, the ''not'' function is quite complicated: Since there's no comparison function for functions, the only way to distinguish between &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;v&lt;/code&gt; is to call it. However, &lt;code&gt;v&lt;/code&gt; just returns itself, therefore to determine if the called function was &lt;code&gt;v&lt;/code&gt; or &lt;code&gt;i&lt;/code&gt;, you have to determine whether the return value was &lt;code&gt;v&lt;/code&gt; or the argument. This would, of course, again be done by calling the function. But calling &lt;code&gt;v&lt;/code&gt; always returns &lt;/code&gt;v&lt;/code&gt;, but we want a function which returns &lt;code&gt;i&lt;/code&gt; when given &lt;code&gt;v&lt;/code&gt;. So it seems we are stuck, and if we could only use the pure functions, we would be. However, there is a way out: Continuations: If a continuation is called, the current state of evaluation is ''replaced'' by the state stored in the continuation. That way we can distinguish between a continuation and a pure function without looking at the return value. So &lt;code&gt;``i&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will call the continuation with ''F'' (and therefore make the ''call/cc'' return with &lt;code&gt;''F''&lt;/code&gt;) while &lt;code&gt;``v&amp;lt;continuation&amp;gt;''F''&lt;/code&gt; will just consume the continuation, and subsequently &lt;code&gt;''F''&lt;/code&gt;. So if we ignore that value and just return &lt;code&gt;''G''&lt;/code&gt; (i.e. apply the constant function &lt;code&gt;`k''G''&lt;/code&gt;), that will only be evaluated if the applied function was ''not'' &lt;code&gt;v&lt;/code&gt;. For the ''not'' function, of course &lt;code&gt;''F''&lt;code&gt; is ''false'' and &lt;code&gt;''G''&lt;/code&gt; is ''true''. The continuation is, of course, supplied as an argument by &lt;code&gt;c&lt;/code&gt;, so the ''not'' function is given by
:&lt;code&gt;&amp;lambda;''B''.`c&amp;lambda;''C''.``k«true»``''BC''«false»&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;not&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;true&gt;&gt;``ss`k`k&lt;&lt;false&gt;&gt;
&lt;/codeblock&gt;
From the above explanation, one sees immediately one way how to write an ifthenelse function: Instead of using &lt;code&gt;v&lt;/code for &lt;code&gt;''F''&lt;code&gt; and &lt;code&gt;i&lt;/code&gt; for &lt;code&gt;''G''&lt;/code&gt;, one could simply pass them as function arguments, i.e. use
:&lt;code&gt;&amp;lambda;''B''.&amp;lambda;''F''.&amp;lambda;''G''.`c&amp;lambda;''C''.``k''G''``''BCF''&lt;/code&gt;
which would give a huge expression after abstraction elimination. However, it turns out that there's a better (i.e. shorter and more efficient) way to implement it:

Consider what happens if you supply ''true'' as first argument: Then you get a function which takes two arguments and returns the first. Also, if you supply ''false'', you get a function which takes two arguments and returns the second. Therefore we can avoid the extra overhead of abstraction elimination by simply using those two functions for &lt;code&gt;''F''&lt;/code&gt; and &lt;code&gt;''G''&lt;/code&gt;. The functions are, of course:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;return first of two arguments&gt;&gt;=
k
&lt;&lt;return second of two arguments&gt;&gt;=
`ki
&lt;/codeblock&gt;
Therefore the ifthenelse function reads:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ifthenelse&gt;&gt;=
``s`kc``s`k`s`k`k&lt;&lt;return second of two arguments&gt;&gt;``ss`k`k&lt;&lt;return first of two arguments&gt;&gt;
&lt;/codeblock&gt;

With the above explanation, it's also now obvious how to write the ''or'' function: If the first argument of ''or'' is ''false'', the result equals the second argument; &lt;code&gt;''G''&lt;/code&gt; therefore is the identity function. If however the first argument is ''true'', the result is ''true'', independent of the second argument, therefore &lt;code&gt;''F''&lt;/code&gt; is &lt;code&gt;`k«true»&lt;/code&gt;. Therefore the or function reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;or&gt;&gt;=
``s`kc``s`k`s`k`ki``ss`k`k`k&lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;

Let's test the functions above. If everything is correct, the first of the following programs should print a line containing &quot;T&quot;, while the second one should write &quot;F&quot; in a line:
&lt;codeblock&gt;
&lt;&lt;testiftrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testiffalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

Testing the not function is equally easy:
&lt;codeblock&gt;
&lt;&lt;testifnottrue.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;true&gt;&gt; .T .F i
&lt;&lt;testifnotfalse.unl&gt;&gt;=
`r` ```&lt;&lt;ifthenelse&gt;&gt; `&lt;&lt;not&gt;&gt; &lt;&lt;false&gt;&gt; .T .F i
&lt;/codeblock&gt;

For the further tests, we first define a function which prints out a boolean. It's simply:
:&lt;code&gt;&amp;lambda;''b'' ````«ifthenelse» b .T .F ''b''&lt;/code&gt;
where the &lt;code&gt;''b''&lt;/code&gt; at the end means that apart of the side effect of printing the value, it acts as an identity function. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;printbool&gt;&gt;=
``s``s``s``s`k&lt;&lt;ifthenelse&gt;&gt;i`k.T`k.Fi
&lt;/codeblock&gt;
Using &lt;code&gt;k&lt;/code&gt; to chain the different invocations together (we don't actually care about the results after printing them), the test program for ''and'' reads
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testand.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;and&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
and should print &quot;FFFT&quot;.

Testing ''or'' works the same way:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;testor.unl&gt;&gt;=
`r
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;false&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;false&gt;&gt; &lt;&lt;true&gt;&gt;
``k `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;false&gt;&gt;
    `&lt;&lt;printbool&gt;&gt; ``&lt;&lt;or&gt;&gt; &lt;&lt;true&gt;&gt; &lt;&lt;true&gt;&gt;
&lt;/codeblock&gt;
This time we should get &quot;FTTT&quot;

&lt;small&gt;Note: This seems to trigger a bug in the Perl implementation of unlambda-2.0.0, but the Java version executes it without problems, and with the correct output.&lt;/small&gt;

=== Tuples ===
The simplest compound data structure is the pair. A pair holds two data items, i.e. in Unlambda two functions. A pair can be implemented by a function which takes another function as argument and applies that function to the two elements of the pair. The pair constructor takes the two arguments and returns that function, i.e.
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''f''.``fxy&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;pair&gt;&gt;=
``s``s`ks``s`kk``s`ks``s`k`sik`kk
&lt;/codeblock&gt;
Of course one needs also functions to get the members of the pair back. To get the first member, the standard way is to pass a function to the pair which takes two arguments and returns the first. The resulting function can be seen on the Unlambda homepage (or here on the page [[Turing machine imulator (Unlambda)]]. However there's another, shorter way to get the first element (this function will be called «tfirst», for &quot;tuple first&quot;, because there will be another first function for lists, «lfirst»).

Consider what happens if you call a pair (which, after all, is just a function) on a continuation. Well, the pair applies that continuation on its two members. More exactly, due to currying, it first applies it to the first member &amp;hellip; and at that point the continuation replaces the current evaluation, effectively making the corresponding call/cc return with the first member of the pair. Now the &lt;code&gt;c&lt;/code&gt; builtin function just calls its argument on the current continuation, therefore if we call it on a pair, we get its first member back. Or in short, the «tfirst» function can be written simply as
&lt;codeblock&gt;
&lt;&lt;tfirst&gt;&gt;=
c
&lt;/codeblock&gt;
Now, can we do a similar trick to get the second member of the pair? Well, in principle yes, except that this time it gets more complicated than the standard way. However, as we will see in a moment, it still has some advantage over the standard way. The complication comes from the fact that to get the second member, we have to pass &lt;code&gt;`k«cont»&lt;/code&gt; to the pair (so the first argument gets ignored, and the second thrown on the continuation). Therefore the «tsecond» function reads
:&lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock&gt;
&lt;&lt;tsecond&gt;&gt;=
``s`kc``s``s`ksk`kk
&lt;/codeblock&gt;

Now an obvious extension of the concept of a pair is the concept of a triple, which contains three elements. Such a triple can be defined along the lines of the tuple as
:&lt;code&gt;&amp;lambda;''x''.&amp;lambda;''y''.&amp;lambda;''z''.&amp;lambda;''f''.```''fxyz''&lt;/code&gt;
or after abstraction elimination
&lt;codeblock&gt;
&lt;&lt;triple&gt;&gt;=
``s``s`ks``s`k`s`ks``s`k`s`kk``s`k`s`ks``s``s`ks``s`kk``s`ks``s`k`sik`kk`k`kk
&lt;/codeblock&gt;
Now what about out access functions? Well, due to the use of continuations, the access functions stop evaluation as soon as the corresponding member is thrown at them. Therefore «first» doesn't care that the triple would call it on three arguments instead of two, since after the first one the function returns anyway. Similarly, the function «second» doesn't care that the triple would pass a third argument. This would not work with the standard definitions; on those, one would need to have separate definitions for the accessors.

Of course for our triple, we need an access function for the third member. The definition is straightforward:
: &lt;code&gt;&amp;lambda;''F''.`c&amp;lambda;''C''.`''F''`k`k''C''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;tthird&gt;&gt;=
``s`kc``s``s`ksk`k``s`kkk
&lt;/codeblock&gt;

Now there are in principle infinitely many tuples, therefore it doesn't make sense to define a separate constructor for each tuple type. Instead, we define a &quot;tuple extender&quot;, which takes an ''n''-tuple and a value and returns an (''n''+1)-tuple of which the first ''n'' values are the same as from the ''n''-tuple, and the last one is the one newly provided. An (''n''+1)-tuple applies its arguments to ''n''+1 arguments; thanks to currying this means first applying it to ''n'' arguments, and then applying the result to the additional argument. Applying the function to the first ''n'' arguments is done by passing the function to the original ''n''-tuple. Therefore the tuple extender is
:&lt;code&gt;&amp;lambda;''T''.&amp;lambda;''x''.&amp;lambda;''f''.``''Tfx''&lt;/code&gt;
where &lt;code&gt;''T''&lt;/code&gt; is the tuple to be extended and ''x'' is the new value. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;tupleext&gt;&gt;=
``s``s`ks``s`kks`kk
&lt;/codeblock&gt;
By noting that a &quot;0-tuple&quot; doesn't apply its function at all, i.e. is the identity function &lt;code&gt;i&lt;/code&gt;, all tuples can be recursively built using «tupleext». For example, an alternative to &lt;code&gt;``«triple».a.b.c&lt;/code&gt; would be &lt;code&gt;``«tupleext»``«tupleext»``«tupleext»i.a.b.c&lt;/code&gt;.

=== Church integers ===
One data type which is needed quite often are integers. A quite standard way to express integers as functions are church integers: The church integer representation of the number ''n'' is a function with two arguments, which applies its first argument to the second argument ''n'' times. That is, the number 0 is represented by
:&lt;code&gt;&amp;lambda;''f''.&amp;lambda;''x''.''x''&lt;/code&gt;
that is
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ci0&gt;&gt;=
`ki
&lt;/codeblock&gt;
the number 1 by
:&lt;code&gt;&amp;lambda;''f''.&amp;lambda;''x''.`''fx''&lt;/code&gt;
i.e.
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ci1&gt;&gt;=
i
&lt;/codeblock&gt;
the number 2 by
:&lt;code&gt;&amp;lambda;''f''.&amp;lambda;''x''.`''f''`''fx''&lt;/code&gt;
or
&lt;&lt;ci2&gt;&gt;=
``s``s`kski
&lt;/codeblock&gt;
and so on. The number ''n''+1 can be generated from the number ''n'' by the successor function, which generates a function which applies its first argument one extra time, that is
:&lt;code&gt;&amp;lamda;''n''.&amp;lambda;''f''.&amp;lambda;''x''`''f''`''nfx''&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;cisucc&gt;&gt;=
`s``s`ksk
&lt;/codeblock&gt;
Addition ''m''+''n'' can be done by calculating the ''n''-th successor of ''m'', i.e.
:&lt;code&gt;&amp;lambda;''m''.&amp;lambda;''n''.``''m''«cisucc»''n''&lt;/code&gt;
Since we know by definition that ''m'' is a pure function, we can simplify that to
:&lt;code&gt;&amp;lambda;''m''.`m«cisucc»
which differs from the previous expression only by the fact that m is immediately applied. Abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;ciplus&gt;&gt;=
``si`k&lt;&lt;cisucc&gt;&gt;
&lt;/codeblock&gt;
The product of ''m'' and ''n'' is formed by applying ''n'' ''m'' times, i.e.
:&lt;code&gt;&amp;lambda;''m''.&amp;lambda;''n''.&amp;lambda;''f''.&amp;lambda;''x''.``m`nfx&lt;/code&gt;
or
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;citimes&gt;&gt;=
``s`ksk
&lt;/codeblock&gt;

One use of Church integers is to define an accessor function for the ''n''-th member of a tuple (note that the first member has the index 0). The basic observation is that you have to quote the continuation ''n'' times in the accessor, i.e. &lt;code&gt;`''n''k«cont»&lt;/code&gt;. Therefore we can get the ''n''-th function by adding another lambda-dependency of ''n'' and replacing k with `''n''k in «tsecond»:
:&lt;code&gt;λ''n''.λ''F''.`cλ''C''.`''F''``''n''k''C''&lt;/code&gt;
which after abstraction elimination gives
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;tci n-th&gt;&gt;=
``s`k`s`kc``s`k`s``s`ksk``s``s`ksk`k`kk
&lt;/codeblock&gt;

=== Lists ===
While tuples contain a fixed number of values, often the number of items to be stored isn't known from the beginning. In that case, the data can be stored in a list. A list is just a pair where the first item contains the first item of the list, and the second item contains the list of the other elements. There's one exception, however, which is the empty list, «nil». This will be defined as &lt;code&gt;v&lt;/code&gt;:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;nil&gt;&gt;=
v
&lt;/codeblock&gt;

We of course need a function to distinguish the empty list and a non-empty list, i.e. an empty list and a pair. Now a pair can only be detected by applying it to a function, which means that the function is applied to the two arguments. However, we are not interested in the two arguments, therefore we use a function which ignores its two arguments. Since applying &lt;code&gt;v&lt;/code&gt; to anything returns &lt;code&gt;v&lt;/code&gt; again (which is &lt;code&gt;«false»&lt;/code&gt;), we will return &lt;code&gt;«true»&lt;/code&gt;, i.e. &lt;code&gt;i&lt;/code&gt; for nonempty lists, i.e. pairs. Therefore our function will be called «nonempty». The definition is simple:
:&lt;code&gt;^''f''`''f''`k`ki&lt;/code&gt;
or after abstraction elimination
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;nonempty&gt;&gt;=
``si`k`k`ki
&lt;/codeblock&gt;
The first element of the list is the first element of the pair:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;lfirst&gt;&gt;=
&lt;&lt;tfirst&gt;&gt;
&lt;/codeblock&gt;
Note that for «nil» this gives «nil» again.

The rest of the list is the second argument of the list. However since this time we don't have to care about higher tuples, we use the standard form which is shorter for the second element:
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;lrest&gt;&gt;=
``si`k`ki
&lt;/codeblock&gt;
Note that again, this maps «nil» to «nil».
Of course, we can also define functions for the second and third element of a list. The second element is just the first element of the rest of the list. This can be encoded in the pseudofunction
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;*lsecond&gt;&gt;=
`&lt;&lt;lfirst&gt;&gt;`&lt;&lt;lrest&gt;&gt;
&lt;/codeblock&gt;
or the function
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;lsecond&gt;&gt;=
``s`k&lt;&lt;lfirst&gt;&gt;``s`k&lt;&lt;lrest&gt;&gt;i
&lt;/codeblock&gt;
In the same way, the third element can be accessed with
&lt;codeblock language=&quot;unlambda&quot;&gt;
&lt;&lt;*lthird&gt;&gt;=
`&lt;&lt;lfirst&gt;&gt;`&lt;&lt;lrest&gt;&gt;`&lt;&lt;lrest&gt;&gt;
&lt;&lt;lthird&gt;&gt;=
``s`k&lt;&lt;lfirst&gt;&gt;``s`k&lt;&lt;lrest&gt;&gt;``s`k&lt;&lt;lrest&gt;&gt;i
&lt;/codeblock&gt;

[[Category:Basic constructs]]
[[Category:Programming language:Unlambda]]</text>
    </revision>
  </page>
  <page>
    <title>Befunge interpreter (C)</title>
    <id>3248</id>
    <revision>
      <id>11587</id>
      <timestamp>2007-11-17T17:27:15Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created initial codedump</comment>
      <text xml:space="preserve">{{codedump}}

This is an interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language.

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;

void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	srand(time(NULL));

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
			case '!': push(!pop()); break;
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11588</id>
      <timestamp>2007-11-17T17:47:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>introduction</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;

void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	srand(time(NULL));

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
			case '!': push(!pop()); break;
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11589</id>
      <timestamp>2007-11-17T18:12:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Implementation */ rearranged code, more text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Executing the code ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

&lt;codeblock language=c&gt;

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
			case '!': push(!pop()); break;
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11590</id>
      <timestamp>2007-11-17T18:13:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Reading the program code */ text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Executing the code ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

&lt;codeblock language=c&gt;

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
			case '!': push(!pop()); break;
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11591</id>
      <timestamp>2007-11-17T18:14:03Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Executing the code */ added missing tag</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Executing the code ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
			case '!': push(!pop()); break;
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11592</id>
      <timestamp>2007-11-17T18:23:36Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Executing the code */ more text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Executing the code ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the befunge command for entering text mode. In this mode, the ASCII-value of all characters encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

As Befunge is a stack-based language, most commands involve stack-manipulation. The basic basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
			case '?': dir=(rand()/7)&amp;3; break;
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11593</id>
      <timestamp>2007-11-17T18:45:16Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Executing the code */ more text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This aritcle describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to chage it's own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple. 

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the befunge command for entering text mode. In this mode, the ASCII-value of all characters encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The push ''push'' operation is implicit for any numbers.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge have some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provides the facility that makes Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, it's corresponding number is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11594</id>
      <timestamp>2007-11-17T22:02:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Introduction */ typos</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the befunge command for entering text mode. In this mode, the ASCII-value of all characters encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The push ''push'' operation is implicit for any numbers.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge have some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provides the facility that makes Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, it's corresponding number is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11595</id>
      <timestamp>2007-11-17T22:06:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Handling commands */ typos</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of all characters encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any numbers.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge have some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provides the facility that makes Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, it's corresponding number is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11596</id>
      <timestamp>2007-11-17T22:10:55Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Implementation */ typos</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of all characters encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11597</id>
      <timestamp>2007-11-18T13:03:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Handling commands */ typo</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11598</id>
      <timestamp>2007-11-18T13:08:06Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Implementation */ moved srand() to the random command</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
			default:
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11599</id>
      <timestamp>2007-11-18T13:09:07Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Implementation */ moved default case</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11600</id>
      <timestamp>2007-11-18T13:18:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Program flow */ more text</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11601</id>
      <timestamp>2007-11-18T13:29:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Stack functions */ description</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

The stack manipulation functions are like they are in most other stack-based language, with one exception: When ''pop''ing from an ampty stack, we get ''0''.

&lt;codeblock language=c&gt;
&lt;&lt;pop&gt;&gt;=
long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}
&lt;/codeblock&gt;

The ''push()'' function uses a dynamic array, which is ''realloc''ed by ''INITSTACK'' words when needed. This stack will grow as big as needed (unless we are out of memory), but will never release any memory when not needed anymore.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

&lt;&lt;pop&gt;&gt;
&lt;/codeblock&gt;

The ''dup()'' and ''swap()'' functions are implemented with ''push()'' and ''pop()''. This doesn't give optimal performance, but ensures that the special case of an empty stack is handled the same way as for ''pop()''.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

#define NCOLS         80
#define NLINES        25
#define INITSTACK   4096
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11602</id>
      <timestamp>2007-11-18T13:35:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>wrapping up</comment>
      <text xml:space="preserve">{{codedump}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

The stack manipulation functions are like they are in most other stack-based language, with one exception: When ''pop''ing from an ampty stack, we get ''0''.

&lt;codeblock language=c&gt;
&lt;&lt;pop&gt;&gt;=
long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}
&lt;/codeblock&gt;

The ''push()'' function uses a dynamic array, which is ''realloc''ed by ''INITSTACK'' words when needed. This stack will grow as big as needed (unless we are out of memory), but will never release any memory when not needed anymore.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

&lt;&lt;pop&gt;&gt;
&lt;/codeblock&gt;

The ''dup()'' and ''swap()'' functions are implemented with ''push()'' and ''pop()''. This doesn't give optimal performance, but ensures that the special case of an empty stack is handled the same way as for ''pop()''.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

=== Wrapping up ===

Befunge-93 is limited to a program-size of 25 lines with maximum 80 columns in each.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define NCOLS         80
#define NLINES        25
&lt;/codeblock&gt;

To avoid lots of ''realloc''s, we use a big(4096 words) initial stack.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define INITSTACK   4096
&lt;/codeblock&gt;

To compile the interpreter, it must have some includes and global variables.

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

&lt;&lt;limits&gt;&gt;
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11603</id>
      <timestamp>2007-11-18T13:38:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>s/{{codedump}}/{{develop}}/ - Not finished yet, but not really a codedump</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

The stack manipulation functions are like they are in most other stack-based language, with one exception: When ''pop''ing from an ampty stack, we get ''0''.

&lt;codeblock language=c&gt;
&lt;&lt;pop&gt;&gt;=
long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}
&lt;/codeblock&gt;

The ''push()'' function uses a dynamic array, which is ''realloc''ed by ''INITSTACK'' words when needed. This stack will grow as big as needed (unless we are out of memory), but will never release any memory when not needed anymore.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

&lt;&lt;pop&gt;&gt;
&lt;/codeblock&gt;

The ''dup()'' and ''swap()'' functions are implemented with ''push()'' and ''pop()''. This doesn't give optimal performance, but ensures that the special case of an empty stack is handled the same way as for ''pop()''.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

=== Wrapping up ===

Befunge-93 is limited to a program-size of 25 lines with maximum 80 columns in each.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define NCOLS         80
#define NLINES        25
&lt;/codeblock&gt;

To avoid lots of ''realloc''s, we use a big(4096 words) initial stack.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define INITSTACK   4096
&lt;/codeblock&gt;

To compile the interpreter, it must have some includes and global variables.

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

&lt;&lt;limits&gt;&gt;
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11796</id>
      <timestamp>2007-12-08T16:17:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Stack functions */ typo</comment>
      <text xml:space="preserve">{{develop}}

== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

The stack manipulation functions are like they are in most other stack-based language, with one exception: When ''pop''ing from an empty stack, we get ''0''.

&lt;codeblock language=c&gt;
&lt;&lt;pop&gt;&gt;=
long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}
&lt;/codeblock&gt;

The ''push()'' function uses a dynamic array, which is ''realloc''ed by ''INITSTACK'' words when needed. This stack will grow as big as needed (unless we are out of memory), but will never release any memory when not needed anymore.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

&lt;&lt;pop&gt;&gt;
&lt;/codeblock&gt;

The ''dup()'' and ''swap()'' functions are implemented with ''push()'' and ''pop()''. This doesn't give optimal performance, but ensures that the special case of an empty stack is handled the same way as for ''pop()''.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

=== Wrapping up ===

Befunge-93 is limited to a program-size of 25 lines with maximum 80 columns in each.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define NCOLS         80
#define NLINES        25
&lt;/codeblock&gt;

To avoid lots of ''realloc''s, we use a big(4096 words) initial stack.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define INITSTACK   4096
&lt;/codeblock&gt;

To compile the interpreter, it must have some includes and global variables.

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

&lt;&lt;limits&gt;&gt;
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>11797</id>
      <timestamp>2007-12-08T16:18:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>rm {{develop}}</comment>
      <text xml:space="preserve">
== Introduction ==

This article describes a simple interpreter for the [http://en.wikipedia.org/wiki/Befunge Befunge]-93 esoteric programming language. 

The language, which, by design, is extremely difficult to compile to machine code, is actually very easy to interpret. A program in Befunge is actually a two-dimensional grid of one-byte commands. This makes it very different from most other languages, which are programmed with a sequence of tokens. The program execution can go in any direction (up, down, left or right). This complicates the task of compiling it to a machine code, which only allows one direction. Another feature causing trouble for a compiler is Befunge's ability to change its own code in runtime.

These complications are not a problem for an interpreter. In fact, the very simple syntax of Befunge, with all commands being exactly one byte long, makes the task of writing an interpreter simple.

== Implementation ==

=== Reading the program code ===
This implementation reads a program from ''stdin'' or a file specified on the command line. The code is stored in the ''prog'' array.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

int main(int argc, char *argv[])
{
	char prog[NLINES][NCOLS+1]={{0}};
	int ncol=0, nline=0;
	int cmd=0;
	int dir=dir_right;
	long tmp;
	int textmode=0;
	int step=1;
	int y, x;
	FILE *fp;

	if(argc&gt;1) {
		if(!(fp=fopen(argv[1], &quot;r&quot;))) {
			fprintf(stderr, &quot;ERROR: Can\'t open file %s\n&quot;, argv[1]);
			exit(EXIT_FAILURE);
		}
	} else fp=stdin;

	while(nline&lt;NLINES &amp;&amp; fgets(prog[nline], NCOLS+1, fp)) ++nline;

	if(fp!=stdin) fclose(fp);

&lt;&lt;init random&gt;&gt;
&lt;/codeblock&gt;

=== Handling commands ===

A Befunge program starts in the upper-left corner of the code. Initially, the execution direction is right. We use ''nline'' and ''ncol'' as the &quot;program counter&quot;. These are zero-based indexes into the ''prog'' array containing the program.

The main loop is terminated by ''@'', which is the Befunge command to end a program.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=

	nline=0;
	while((cmd=prog[nline][ncol])!='@' || textmode) {
&lt;/codeblock&gt;

A ''&quot;''-character is the Befunge command for entering text mode. In this mode, the ASCII-value of any character encountered until the next '&quot;' is pushed on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		if(textmode) {
			if(cmd=='\&quot;') textmode=0;
			else push(cmd);
		} else {
&lt;/codeblock&gt;

==== Arithmetic and logic commands ====
As Befunge is a stack-based language, most commands involve stack-manipulation. The basic arithmetic command will pop two values from the stack, evaluate the specific arithmetic operation, and push the result back.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			switch(cmd) {
			case '+': push(pop()+pop()); break;
			case '-': tmp=pop(); push(pop()-tmp); break;
			case '*': push(pop()*pop()); break;
			case '/': tmp=pop(); push(pop()/tmp); break;
			case '%': tmp=pop(); push(pop()%tmp); break;
&lt;/codeblock&gt;

The negation command (''!'') works in the same way as the corresponding C operator, resulting in ''0'' for all non-zero values, or ''1'' for ''0''.
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '!': push(!pop()); break;
&lt;/codeblock&gt;

The only comparison command in Befunge is ''`'', which will pop two values, and push ''1'' if the second is larger than the first (''0'' otherwise).
&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '`': tmp=pop(); push(pop()&gt;tmp); break;
&lt;/codeblock&gt;

==== Program direction commands ====
There are two kinds of predictive commands for changing program direction. The first kind (''_'' and ''|'') will first pop a value, and change direction based on the value. This can be used to implement branching and loops.

The other kind will change the direction unconditionally.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '_': dir=pop()?dir_left:dir_right; break;
			case '|': dir=pop()?dir_up:dir_down; break;
			case '&lt;': dir=dir_left; break;
			case '&gt;': dir=dir_right; break;
			case '^': dir=dir_up; break;
			case 'v': dir=dir_down; break;
&lt;/codeblock&gt;

==== Stack operations ====
Befunge also supports the common operations (push, pop, dup and swap) that are available in all stack-based language. The ''push'' operation is implicit for any number.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case ':': dup(); break;
			case '\\': swap(); break;
			case '$': pop(); break;
&lt;/codeblock&gt;

==== Output ====
A very basic functionality for writing to ''stdout'' is provided with the ''.'' and '','' commands.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '.': printf(&quot;%ld&quot;, pop()); break;
			case ',': putchar(pop()); break;
&lt;/codeblock&gt;

==== Special commands ====

Befunge has some special commands that influence how the code is handled. ''&quot;'' is used to enter text mode, where all commands are pushed on the stack (by ASCII-value). The ''#'' command is used to &quot;jump&quot; over another command. Finally, the ''@'' command will just stop program execution.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&quot;': textmode=1; break;
			case '#': step=2; break;
			case '@': exit(EXIT_SUCCESS);
&lt;/codeblock&gt;

==== Self-modifying code ====

The ''p'' and ''g'' commands provide the facilities that make Befunge programs really difficult to compile. These commands allow the user to change the program-code itself while the program is running.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case 'p': y=pop(); x=pop(); prog[y][x]=pop(); break;
			case 'g': y=pop(); x=pop(); push(prog[y][x]); break;
&lt;/codeblock&gt;

==== Input ====

Befunge has two commands for reading from ''stdin''. These will read either a character or a number, and push it on the stack.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '&amp;': scanf(&quot;%ld&quot;, &amp;tmp); push(tmp); break;
			case '~': push(getchar()); break;
&lt;/codeblock&gt;

==== Random ====

The random command will just change the program direction randomly.

&lt;codeblock language=c&gt;
&lt;&lt;init random&gt;&gt;=

	srand(time(NULL));
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			case '?': dir=(rand()/7)&amp;3; break;
&lt;/codeblock&gt;

==== Pushing numbers ====

When a digit is encountered, its corresponding numeric value is pushed.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
			default:
				if(cmd&gt;='0' &amp;&amp; cmd&lt;='9') push(cmd-'0');
			}
		}

&lt;/codeblock&gt;

=== Program flow ===

The ''ncol'' and ''nline'' variables makes up the &quot;program counter&quot;. These variables are manipulated according to the current program direction stored in ''dir''. The ''step'' variable (normaloly ''1'') is set to ''2'' by the ''#'' command to indicate a &quot;jump&quot; over the next command.

When we reach the end of code in any direction, we continue from the other end.

&lt;codeblock language=c&gt;
&lt;&lt;main&gt;&gt;=
		while(step) {
			switch(dir) {
			case dir_left: 
				if(--ncol&lt;0) ncol=NCOLS-1;
				break;
			case dir_right: 
				if(++ncol&gt;=NCOLS) ncol=0;
				break;
			case dir_up: 
				if(--nline&lt;0) nline=NLINES-1;
				break;
			case dir_down: 
				if(++nline&gt;=NLINES) nline=0;
				break;
			}
			--step;
		}
		++step;
	}

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;

=== Stack functions ===

The stack manipulation functions are like they are in most other stack-based language, with one exception: When ''pop''ing from an empty stack, we get ''0''.

&lt;codeblock language=c&gt;
&lt;&lt;pop&gt;&gt;=
long pop(void)
{
	if(nstack&gt;0) return stack[--nstack];
	else return 0;
}
&lt;/codeblock&gt;

The ''push()'' function uses a dynamic array, which is ''realloc''ed by ''INITSTACK'' words when needed. This stack will grow as big as needed (unless we are out of memory), but will never release any memory when not needed anymore.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=
void push(long v)
{
	if(!stack) {
		if(!maxstack) maxstack=INITSTACK;
		if(!(stack=malloc(sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	} else if(nstack&lt;maxstack) stack[nstack++]=v;
	else {
		maxstack+=INITSTACK;
		if(!(stack=realloc(stack, sizeof *stack * maxstack))) {
			fprintf(stderr, &quot;ERROR: Not enough memory.\n&quot;);
			exit(EXIT_FAILURE);
		}
	}
}

&lt;&lt;pop&gt;&gt;
&lt;/codeblock&gt;

The ''dup()'' and ''swap()'' functions are implemented with ''push()'' and ''pop()''. This doesn't give optimal performance, but ensures that the special case of an empty stack is handled the same way as for ''pop()''.

&lt;codeblock language=c&gt;
&lt;&lt;stack functions&gt;&gt;=

void dup(void)
{
	long tmp;
	
	tmp=pop();
	push(tmp);
	push(tmp);
}

void swap(void)
{
	long tmp, tmp2;
	
	tmp=pop();
	tmp2=pop();
	push(tmp);
	push(tmp2);
}
&lt;/codeblock&gt;

=== Wrapping up ===

Befunge-93 is limited to a program-size of 25 lines with maximum 80 columns in each.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define NCOLS         80
#define NLINES        25
&lt;/codeblock&gt;

To avoid lots of ''realloc''s, we use a big(4096 words) initial stack.

&lt;codeblock language=c&gt;
&lt;&lt;limits&gt;&gt;=
#define INITSTACK   4096
&lt;/codeblock&gt;

To compile the interpreter, it must have some includes and global variables.

&lt;codeblock language=c&gt;
&lt;&lt;befunge.c&gt;&gt;=
#include&lt;stdio.h&gt;
#include&lt;stdlib.h&gt;
#include&lt;ctype.h&gt;
#include&lt;time.h&gt;

&lt;&lt;limits&gt;&gt;
enum {dir_left=0, dir_right=1, dir_up=2, dir_down=3};

long *stack=NULL;
int maxstack=0;
int nstack=0;


&lt;&lt;stack functions&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;


[[Category:Compilers and programming languages]]
[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Bernoulli numbers (Erlang)</title>
    <id>3148</id>
    <revision>
      <id>10282</id>
      <timestamp>2007-05-19T17:36:48Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

==Rational Numbers==
For generating Bernoulli numbers we first need a way to represent rational numbers. We'll make a module for handling regular number functions: add, subtract, multiply, divide, inverse, and negation.

&lt;codeblock language=erlang&gt;
&lt;&lt;rational.erl&gt;&gt;=
-module(rational).
-export([is_rational/1, make/2, make/1, add/2,
         sub/2, mult/2, divide/2, inv/1, neg/1,
         to_float/1, to_decimal_string/2]).

-record(rational, {top, bot}).

gcd(A, 0) -&gt; A;
gcd(A, B) -&gt; gcd(B, A rem B).

lcm(A, B) -&gt; (A*B) div gcd(A, B).

is_rational(X) when record(X, rational) -&gt; true;
is_rational(_) -&gt; false.

make(Top, Bot) -&gt;
    Gcd = gcd(Top, Bot),
    #rational{top = Top div Gcd, bot = Bot div Gcd}.

make(Num) when is_integer(Num) -&gt; make(Num, 1);
make(Num) when record(Num, rational) -&gt; Num.

inv(X) -&gt;
    A = make(X),
    make(A#rational.bot, A#rational.top).

neg(X) -&gt;
    A = make(X),
    make(-A#rational.top, A#rational.bot).

mult(X, Y) -&gt;
    A = make(X),
    B = make(Y),
    Top = A#rational.top * B#rational.top,
    Bot = A#rational.bot * B#rational.bot,
    Gcd = gcd(Top, Bot),
    make(Top div Gcd, Bot div Gcd).

divide(X, Y) -&gt; mult(X, inv(Y)).

add(X, Y) -&gt;
    A = make(X),
    B = make(Y),
    Lcm = lcm(A#rational.bot, B#rational.bot),
    Top = A#rational.top * (Lcm div A#rational.bot) +
          B#rational.top * (Lcm div B#rational.bot),
    make(Top, Lcm).

sub(X, Y) -&gt; add(X, neg(Y)).
&lt;/codeblock&gt;

==Memoize==

The values of the bernoulli numbers need to be memoized to avoid recalculation over and over of the same number. Ets can handle this:
&lt;codeblock language=erlang&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli(N) -&gt;
    Name = bernoulli,
    case ets:info(Name) of
    undefined -&gt;
        ets:new(Name, [public, named_table]);
    _ -&gt; true
    end,
    case ets:lookup(Name, N) of
    [] -&gt;
        Val = bernoulli_i(N),
        ets:insert(Name, {N, Val}),
        Val;
    [{N, Val}] -&gt; Val;
    Else -&gt; Else
    end.
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli_i(0) -&gt; 1;
bernoulli_i(1) -&gt; rational:make(-1,2);
bernoulli_i(N) when N rem 2 == 1 -&gt; 0;
bernoulli_i(N) when N rem 6 == 0 -&gt;
    Val = rational:sub(rational:make(N+3, 3), bernoulli_a(N, N div 6)),
    rational:divide(Val, choose(N+3, N));
bernoulli_i(N) when N rem 6 == 2 -&gt;
    Val = rational:sub(rational:make(N+3, 3), bernoulli_a(N, (N-2) div 6)),
    rational:divide(Val, choose(N+3, N));
bernoulli_i(N) when N rem 6 == 4 -&gt;
    Val = rational:sub(rational:make(-(N+3), 6), bernoulli_a(N, (N-4) div 6)),
    rational:divide(Val, choose(N+3, N)).
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=erlang&gt;
&lt;&lt;a&gt;&gt;=
%This can be sped up by not re-calculating the binary coefficient every time or
%memoizing that function.
bernoulli_a(N, M) -&gt; bernoulli_a(N, M, 0).

bernoulli_a(_N, 0, Sum) -&gt; Sum;
bernoulli_a(N, M, Sum) -&gt;
    Val = rational:mult(choose(N+3, N-6*M), bernoulli(N-6*M)),
    bernoulli_a(N, M-1, rational:add(Sum, Val)).
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=erlang&gt;
&lt;&lt;bincoef&gt;&gt;=
min(X, Y) when X&lt;Y -&gt; X;
min(_X, Y) -&gt; Y.

choose(N, R) -&gt;
    choose(N, min(R, N-R), 1, 1).
choose(_N, 0, Top, Bottom) -&gt; Top div Bottom;
choose(N, R, Top, Bottom) -&gt; choose(N-1, R-1, Top*N, Bottom*R).
&lt;/codeblock&gt;

Now we put it all together in a module:
&lt;codeblock language=erlang&gt;
&lt;&lt;bernoulli.erl&gt;&gt;=
-module(bernoulli).
-export([bernoulli/1]).

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10283</id>
      <timestamp>2007-05-19T17:47:13Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <comment>little fixes, added running section</comment>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

==Rational Numbers==
For generating Bernoulli numbers we first need a way to represent rational numbers. We'll make a module for handling regular number functions: add, subtract, multiply, divide, inverse, and negation.

&lt;codeblock language=erlang&gt;
&lt;&lt;rational.erl&gt;&gt;=
-module(rational).
-export([is_rational/1, make/2, make/1, add/2,
         sub/2, mult/2, divide/2, inv/1, neg/1]).

-record(rational, {top, bot}).

gcd(A, 0) -&gt; A;
gcd(A, B) -&gt; gcd(B, A rem B).

lcm(A, B) -&gt; (A*B) div gcd(A, B).

is_rational(X) when record(X, rational) -&gt; true;
is_rational(_) -&gt; false.

make(Top, Bot) -&gt;
    Gcd = gcd(Top, Bot),
    #rational{top = Top div Gcd, bot = Bot div Gcd}.

make(Num) when is_integer(Num) -&gt; make(Num, 1);
make(Num) when record(Num, rational) -&gt; Num.

inv(X) -&gt;
    A = make(X),
    make(A#rational.bot, A#rational.top).

neg(X) -&gt;
    A = make(X),
    make(-A#rational.top, A#rational.bot).

mult(X, Y) -&gt;
    A = make(X),
    B = make(Y),
    Top = A#rational.top * B#rational.top,
    Bot = A#rational.bot * B#rational.bot,
    Gcd = gcd(Top, Bot),
    make(Top div Gcd, Bot div Gcd).

divide(X, Y) -&gt; mult(X, inv(Y)).

add(X, Y) -&gt;
    A = make(X),
    B = make(Y),
    Lcm = lcm(A#rational.bot, B#rational.bot),
    Top = A#rational.top * (Lcm div A#rational.bot) +
          B#rational.top * (Lcm div B#rational.bot),
    make(Top, Lcm).

sub(X, Y) -&gt; add(X, neg(Y)).
&lt;/codeblock&gt;

==Memoize==

The values of the bernoulli numbers need to be memoized to avoid recalculation over and over of the same number. This should be transparent to the caller of this function. Ets can handle this. We check if the ets table exists and create one if it does not. We then check if the value has already been calculated and return it if it has. Otherwise we calculate it, store it in the ets table, and then return it.
&lt;codeblock language=erlang&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli(N) -&gt;
    Name = bernoulli,
    case ets:info(Name) of
    undefined -&gt;
        ets:new(Name, [public, named_table]);
    _ -&gt; true
    end,
    case ets:lookup(Name, N) of
    [] -&gt;
        Val = bernoulli_i(N),
        ets:insert(Name, {N, Val}),
        Val;
    [{N, Val}] -&gt; Val;
    Else -&gt; Else
    end.
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli_i(0) -&gt; 1;
bernoulli_i(1) -&gt; rational:make(-1,2);
bernoulli_i(N) when N rem 2 == 1 -&gt; 0;
bernoulli_i(N) when N rem 6 == 0 -&gt;
    Val = rational:sub(rational:make(N+3, 3), bernoulli_a(N, N div 6)),
    rational:divide(Val, choose(N+3, N));
bernoulli_i(N) when N rem 6 == 2 -&gt;
    Val = rational:sub(rational:make(N+3, 3), bernoulli_a(N, (N-2) div 6)),
    rational:divide(Val, choose(N+3, N));
bernoulli_i(N) when N rem 6 == 4 -&gt;
    Val = rational:sub(rational:make(-(N+3), 6), bernoulli_a(N, (N-4) div 6)),
    rational:divide(Val, choose(N+3, N)).
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=erlang&gt;
&lt;&lt;a&gt;&gt;=
%This can be sped up by not re-calculating the binary coefficient every time or
%memoizing that function.
bernoulli_a(N, M) -&gt; bernoulli_a(N, M, 0).

bernoulli_a(_N, 0, Sum) -&gt; Sum;
bernoulli_a(N, M, Sum) -&gt;
    Val = rational:mult(choose(N+3, N-6*M), bernoulli(N-6*M)),
    bernoulli_a(N, M-1, rational:add(Sum, Val)).
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=erlang&gt;
&lt;&lt;bincoef&gt;&gt;=
min(X, Y) when X&lt;Y -&gt; X;
min(_X, Y) -&gt; Y.

choose(N, R) -&gt;
    choose(N, min(R, N-R), 1, 1).
choose(_N, 0, Top, Bottom) -&gt; Top div Bottom;
choose(N, R, Top, Bottom) -&gt; choose(N-1, R-1, Top*N, Bottom*R).
&lt;/codeblock&gt;

Now we put it all together in a module:
&lt;codeblock language=erlang&gt;
&lt;&lt;bernoulli.erl&gt;&gt;=
-module(bernoulli).
-export([bernoulli/1]).

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

==Running==

Now the code can be run from the erlang shell:
 1&gt; c(rational).
 {ok,rational}
 2&gt; c(bernoulli).
 {ok,bernoulli}
 3&gt; bernoulli:bernoulli(6).
 {rational,1,42}


[[Category:Bernoulli numbers]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bernoulli numbers (Haskell)</title>
    <id>3639</id>
    <revision>
      <id>15149</id>
      <timestamp>2008-10-20T05:22:40Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>translated from erlang</comment>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

==Memoize==

We use a lazy list to memoize calculations. This takes linear time to lookup, instead of constant time, but oh well; it's not a big deal for small numbers.

&lt;codeblock language=haskell&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli = (bernoulli_table !!)
bernoulli_table = map bernoulli' [0..]
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=haskell&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli' 0 = 1
bernoulli' 1 = -1 % 2
bernoulli' n | n `mod` 2 == 1 = 0
             | n `mod` 6 == 0 = let val = (n+3) % 3 - bernoulliA n (n `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 2 = let val = (n+3) % 3 - bernoulliA n ((n-2) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 4 = let val = -(n+3) % 6 - bernoulliA n ((n-4) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=haskell&gt;
&lt;&lt;a&gt;&gt;=
--This can be sped up by not re-calculating the binary coefficient every time or
--memoizing that function.
bernoulliA n m = sum (map foo [1..m])
  where foo j = fromIntegral (choose (n+3) (n-6*j)) * bernoulli (n-6*j)
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=haskell&gt;
&lt;&lt;bincoef&gt;&gt;=
choose n r = choose' n (min r (n-r)) 1 1
  where
    choose' _ 0 top bottom = top `div` bottom
    choose' n r top bottom = choose' (n-1) (r-1) (top*n) (bottom*r)
&lt;/codeblock&gt;

Now we put it all together; remembering to import Data.Ratio to use the &quot;%&quot; ratio operator:
&lt;codeblock language=haskell&gt;
&lt;&lt;bernoulli.hs&gt;&gt;=
import Data.Ratio

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

==Running==

Now the code can be run from the Haskell shell:
 Prelude&gt; :l bernoulli.hs
 [1 of 1] Compiling Main             ( bernoulli.hs, interpreted )
 Ok, modules loaded: Main.
 *Main&gt; bernoulli 6
 1%42
 *Main&gt; bernoulli 12
 (-691)%2730


[[Category:Bernoulli numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15150</id>
      <timestamp>2008-10-20T05:33:47Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

==Memoize==

We use a lazy list to memoize calculations. This takes linear time to lookup, instead of constant time, but oh well; it's not a big deal for small numbers. We use &quot;genericIndex&quot; instead of the (!!) operator because (!!) only takes Ints, which will force the rest of our program to use Ints, which will overflow when numbers get sufficiently big, producing incorrect answers; whereas if arbitrary-precision Integers are used, it will not overflow.

&lt;codeblock language=haskell&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli = genericIndex bernoulli_table
bernoulli_table = map bernoulli' [0..]
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=haskell&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli' 0 = 1
bernoulli' 1 = -1 % 2
bernoulli' n | odd n          = 0
             | n `mod` 6 == 0 = let val = (n+3) % 3 - bernoulliA n (n `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 2 = let val = (n+3) % 3 - bernoulliA n ((n-2) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 4 = let val = -(n+3) % 6 - bernoulliA n ((n-4) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=haskell&gt;
&lt;&lt;a&gt;&gt;=
--This can be sped up by not re-calculating the binary coefficient every time or
--memoizing that function.
bernoulliA n m = sum (map foo [1..m])
  where foo j = fromIntegral (choose (n+3) (n-6*j)) * bernoulli (n-6*j)
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=haskell&gt;
&lt;&lt;bincoef&gt;&gt;=
choose n r = choose' n (min r (n-r)) 1 1
  where
    choose' _ 0 top bottom = top `div` bottom
    choose' n r top bottom = choose' (n-1) (r-1) (top*n) (bottom*r)
&lt;/codeblock&gt;

Now we put it all together; remembering to import Data.Ratio to use the &quot;%&quot; ratio operator, and Data.List for genericIndex:
&lt;codeblock language=haskell&gt;
&lt;&lt;bernoulli.hs&gt;&gt;=
import Data.Ratio
import Data.List

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

==Running==

Now the code can be run from the Haskell shell:
 Prelude&gt; :l bernoulli.hs
 [1 of 1] Compiling Main             ( bernoulli.hs, interpreted )
 Ok, modules loaded: Main.
 *Main&gt; bernoulli 6
 1%42
 *Main&gt; bernoulli 12
 (-691)%2730
 *Main&gt; bernoulli 16
 (-3617)%510
 *Main&gt; bernoulli 18
 43867%798


[[Category:Bernoulli numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15152</id>
      <timestamp>2008-10-20T06:15:36Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

[http://okmij.org/ftp/Haskell/Bernoulli.hs This version] is probably better though.

==Memoize==

We use a lazy list to memoize calculations. This takes linear time to lookup, instead of constant time, but oh well; it's not a big deal for small numbers. We use &quot;genericIndex&quot; instead of the (!!) operator because (!!) only takes Ints, which will force the rest of our program to use Ints, which will overflow when numbers get sufficiently big, producing incorrect answers; whereas if arbitrary-precision Integers are used, it will not overflow.

&lt;codeblock language=haskell&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli = genericIndex bernoulli_table
bernoulli_table = map bernoulli' [0..]
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=haskell&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli' 0 = 1
bernoulli' 1 = -1 % 2
bernoulli' n | odd n          = 0
             | n `mod` 6 == 0 = let val = (n+3) % 3 - bernoulliA n (n `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 2 = let val = (n+3) % 3 - bernoulliA n ((n-2) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 4 = let val = -(n+3) % 6 - bernoulliA n ((n-4) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=haskell&gt;
&lt;&lt;a&gt;&gt;=
--This can be sped up by not re-calculating the binary coefficient every time or
--memoizing that function.
bernoulliA n m = sum (map foo [1..m])
  where foo j = fromIntegral (choose (n+3) (n-6*j)) * bernoulli (n-6*j)
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=haskell&gt;
&lt;&lt;bincoef&gt;&gt;=
choose n r = choose' n (min r (n-r)) 1 1
  where
    choose' _ 0 top bottom = top `div` bottom
    choose' n r top bottom = choose' (n-1) (r-1) (top*n) (bottom*r)
&lt;/codeblock&gt;

Now we put it all together; remembering to import Data.Ratio to use the &quot;%&quot; ratio operator, and Data.List for genericIndex:
&lt;codeblock language=haskell&gt;
&lt;&lt;bernoulli.hs&gt;&gt;=
import Data.Ratio
import Data.List

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

==Running==

Now the code can be run from the Haskell shell:
 Prelude&gt; :l bernoulli.hs
 [1 of 1] Compiling Main             ( bernoulli.hs, interpreted )
 Ok, modules loaded: Main.
 *Main&gt; bernoulli 6
 1%42
 *Main&gt; bernoulli 12
 (-691)%2730
 *Main&gt; bernoulli 16
 (-3617)%510
 *Main&gt; bernoulli 18
 43867%798


[[Category:Bernoulli numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15245</id>
      <timestamp>2008-10-23T19:05:10Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

[http://okmij.org/ftp/Haskell/Bernoulli.hs This version] is probably better though.

==Memoize==

We use a lazy list to memoize calculations. This takes linear time to lookup, instead of constant time, but oh well; it's not a big deal for small numbers. We use &quot;genericIndex&quot; instead of the (!!) operator because (!!) only takes Ints, which will force the rest of our program to use Ints, which will overflow when numbers get sufficiently big, producing incorrect answers; whereas if arbitrary-precision Integers are used, it will not overflow.

&lt;codeblock language=haskell&gt;
&lt;&lt;memoize&gt;&gt;=
bernoulli :: Integer -&gt; Ratio Integer
bernoulli = genericIndex bernoulli_table
bernoulli_table = map bernoulli' [0..]
&lt;/codeblock&gt;

==Implementation==

Now to implement the actual function. The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

&lt;codeblock language=haskell&gt;
&lt;&lt;impl&gt;&gt;=
bernoulli' :: Integer -&gt; Ratio Integer
bernoulli' 0 = 1
bernoulli' 1 = -1 % 2
bernoulli' n | odd n          = 0
             | n `mod` 6 == 0 = let val = (n+3) % 3 - bernoulliA n (n `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 2 = let val = (n+3) % 3 - bernoulliA n ((n-2) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
             | n `mod` 6 == 4 = let val = -(n+3) % 6 - bernoulliA n ((n-4) `div` 6) in
                                  val / fromIntegral (choose (n+3) n)
&lt;/codeblock&gt;

Now we implement A:
&lt;codeblock language=haskell&gt;
&lt;&lt;a&gt;&gt;=
--This can be sped up by not re-calculating the binary coefficient every time or
--memoizing that function.
bernoulliA :: Integer -&gt; Integer -&gt; Ratio Integer
bernoulliA n m = sum (map foo [1..m])
  where foo j = fromIntegral (choose (n+3) (n-6*j)) * bernoulli (n-6*j)
&lt;/codeblock&gt;

The last piece we need is to calculate the binary coefficient:
&lt;codeblock language=haskell&gt;
&lt;&lt;bincoef&gt;&gt;=
choose :: (Integral a) =&gt; a -&gt; a -&gt; a
choose n r = product [n-r'+1..n] `div` product [1..r']
  where r' = min r (n-r)
&lt;/codeblock&gt;

Now we put it all together; remembering to import Data.Ratio to use the &quot;%&quot; ratio operator, and Data.List for genericIndex:
&lt;codeblock language=haskell&gt;
&lt;&lt;bernoulli.hs&gt;&gt;=
import Data.Ratio
import Data.List

&lt;&lt;memoize&gt;&gt;
&lt;&lt;impl&gt;&gt;
&lt;&lt;a&gt;&gt;
&lt;&lt;bincoef&gt;&gt;
&lt;/codeblock&gt;

==Running==

Now the code can be run from the Haskell shell:
 Prelude&gt; :l bernoulli.hs
 [1 of 1] Compiling Main             ( bernoulli.hs, interpreted )
 Ok, modules loaded: Main.
 *Main&gt; bernoulli 6
 1%42
 *Main&gt; bernoulli 12
 (-691)%2730
 *Main&gt; bernoulli 16
 (-3617)%510
 *Main&gt; bernoulli 18
 43867%798


[[Category:Bernoulli numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bernoulli numbers (Python)</title>
    <id>1992</id>
    <revision>
      <id>4648</id>
      <timestamp>2006-05-13T12:24:24Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>new. some murky stuff in here to be polished...</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] ''B''&lt;sub&gt;m&lt;/sub&gt; are a sequence of rational numbers defined by the identity

:&lt;math&gt;\sum_{j=0}^m {{m+1}\choose{j}} B_j = 0&lt;/math&gt; 

with the initial condition ''B''&lt;sub&gt;0&lt;/sub&gt; = 1. Here, &lt;math&gt;{{n}\choose{k}}&lt;/math&gt; denotes a [http://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficient]. The sequence, which continues -1/2, 1/6, 0, -1/30, 0, 1/42, ..., obeys no simple pattern, and computing ''B&lt;sub&gt;m&lt;/sub&gt;'' for ''m'' as small as a few hundred is a relatively time-consuming task.

The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - combsum(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - combsum(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - combsum(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4649</id>
      <timestamp>2006-05-13T12:24:54Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>/* A faster implementation */ filename fix</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] ''B''&lt;sub&gt;m&lt;/sub&gt; are a sequence of rational numbers defined by the identity

:&lt;math&gt;\sum_{j=0}^m {{m+1}\choose{j}} B_j = 0&lt;/math&gt; 

with the initial condition ''B''&lt;sub&gt;0&lt;/sub&gt; = 1. Here, &lt;math&gt;{{n}\choose{k}}&lt;/math&gt; denotes a [http://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficient]. The sequence, which continues -1/2, 1/6, 0, -1/30, 0, 1/42, ..., obeys no simple pattern, and computing ''B&lt;sub&gt;m&lt;/sub&gt;'' for ''m'' as small as a few hundred is a relatively time-consuming task.

The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - combsum(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - combsum(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - combsum(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4650</id>
      <timestamp>2006-05-13T12:26:04Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>/* A faster implementation */ forgot to rename a function</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] ''B''&lt;sub&gt;m&lt;/sub&gt; are a sequence of rational numbers defined by the identity

:&lt;math&gt;\sum_{j=0}^m {{m+1}\choose{j}} B_j = 0&lt;/math&gt; 

with the initial condition ''B''&lt;sub&gt;0&lt;/sub&gt; = 1. Here, &lt;math&gt;{{n}\choose{k}}&lt;/math&gt; denotes a [http://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficient]. The sequence, which continues -1/2, 1/6, 0, -1/30, 0, 1/42, ..., obeys no simple pattern, and computing ''B&lt;sub&gt;m&lt;/sub&gt;'' for ''m'' as small as a few hundred is a relatively time-consuming task.

The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - A(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - A(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - A(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4651</id>
      <timestamp>2006-05-13T12:27:10Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>/* Testing */ import clock</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] ''B''&lt;sub&gt;m&lt;/sub&gt; are a sequence of rational numbers defined by the identity

:&lt;math&gt;\sum_{j=0}^m {{m+1}\choose{j}} B_j = 0&lt;/math&gt; 

with the initial condition ''B''&lt;sub&gt;0&lt;/sub&gt; = 1. Here, &lt;math&gt;{{n}\choose{k}}&lt;/math&gt; denotes a [http://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficient]. The sequence, which continues -1/2, 1/6, 0, -1/30, 0, 1/42, ..., obeys no simple pattern, and computing ''B&lt;sub&gt;m&lt;/sub&gt;'' for ''m'' as small as a few hundred is a relatively time-consuming task.

The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - A(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - A(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - A(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2
from time import clock

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4656</id>
      <timestamp>2006-05-13T17:54:20Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>transclude common content from cat page</comment>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}

The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - A(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - A(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - A(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2
from time import clock

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4657</id>
      <timestamp>2006-05-13T17:54:57Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>spacing</comment>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}
The following two programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - A(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - A(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - A(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;

def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

==Testing==

A good way to check that both implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2
from time import clock

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;
&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
&lt;/pre&gt;

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5312</id>
      <timestamp>2006-05-29T11:59:05Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>much faster version</comment>
      <text xml:space="preserve">{{Category:Bernoulli numbers}}
The following programs for calculating Bernoulli numbers will assume the presence of a rational type &lt;tt&gt;mpq&lt;/tt&gt; (with support for basic arithmetic) and a function &lt;tt&gt;bincoef&lt;/tt&gt; for calculating binomial coefficients, neither of which is available in Python's standard library. The [http://sourceforge.net/projects/gmpy/ GMPY] library provides these, however.

We will have to create a trivial wrapper around GMPY's &lt;tt&gt;bincoef&lt;/tt&gt; since for some reason it does not handle the case when ''k'' &lt; 0, which will be of use later on.
&lt;codeblock language=python&gt;
&lt;&lt;dependencies&gt;&gt;=
from gmpy import mpq, bincoef as _bincoef

def bincoef(n, k):
    if k &lt; 0:
        return 0
    else:
        return _bincoef(n, k)
&lt;/codeblock&gt;

==Basic implementation==

The ''m'':th Bernoulli number can be obtained by extracting the last term from the sum we used to define the sequence, but this requires that ''B''&lt;sub&gt;1&lt;/sub&gt; ... ''B''&lt;sub&gt;m-1&lt;/sub&gt; are already known. This is a perfect opportunity to employ recursion: &lt;tt&gt;bernoulli(m)&lt;/tt&gt; will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;, which in turn will call &lt;tt&gt;bernoulli(0) ... bernoulli(m-2)&lt;/tt&gt; and so on, until all fall back on &lt;tt&gt;bernoulli(0)&lt;/tt&gt;. The number of computations needed will grow exponentially with ''m'', so a practical implementation must use memoization. We will create a decorator for this purpose:

&lt;codeblock language=python&gt;
&lt;&lt;memo&gt;&gt;=
class memo:
    def __init__(self, f):
        self.func = f
        self.cache = {}
        self.highest = 0
    def __call__(self, m):
        if m &lt; self.highest:
            return self.cache[m]
        else:
            x = self.func(m)
            self.cache[m] = x
            self.highest = m
            return x
&lt;/codeblock&gt;

Now the main function. As a final optimization, we will exploit the fact that ''B&lt;sub&gt;m&lt;/sub&gt;'' = 0 if ''m'' &gt; 1 is odd.

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_simple.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;

@memo
def bernoulli(m):
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 2: return 0
    s = 0
    for j in range(0, m):
        s += bincoef(m+1, j) * bernoulli(j)
    b = -mpq(s)/bincoef(m+1, m)
    return b
&lt;/codeblock&gt;

The function can be used as follows:
&lt;pre&gt;
&gt;&gt;&gt; [bernoulli(n) for n in range(10)]
[1, mpq(-1,2), mpq(1,6), 0, mpq(-1,30), 0, mpq(1,42), 0, mpq(-1,30), 0]
&lt;/pre&gt;

==A faster implementation==
The computation can be performed more efficiently according to the following identities due to [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Srinivasa Ramanujan]:

:&lt;math&gt;m\equiv 0\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, m/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 2\,\bmod\,6\qquad {{m+3}\choose{m}}B_m={{m+3}\over3}-A(m, (m-2)/6)&lt;/math&gt;

:&lt;math&gt;m\equiv 4\,\bmod\, 6\qquad{{m+3}\choose{m}}B_m=-{{m+3}\over6}-A(m, (m-4)/6)&lt;/math&gt;

where

:&lt;math&gt;A(m, M) = \sum_{j=1}^M {m+3\choose{m-6j}}B_{m-6j}.&lt;/math&gt;

So instead of summing over ''m'' Bernoulli numbers and binomial coefficients, a sum over ''m''/6 terms suffices.

We implement ''A'':

&lt;codeblock language=python&gt;
&lt;&lt;A&gt;&gt;=
def A(m, M):
    s = 0
    for j in range(1, M+1):
        s += bincoef(m+3, m-6*j) * bernoulli(m-6*j)
    return s
&lt;/codeblock&gt;

We may now implement the three different cases modulo 6 as three separately memoized functions. (Separating them is necessary since the &lt;tt&gt;memo&lt;/tt&gt; decorator assumes that if &lt;tt&gt;bernoulli(m)&lt;/tt&gt; has been computed, then so have ''all'' of &lt;tt&gt;bernoulli(0) ... bernoulli(m-1)&lt;/tt&gt;. But here we want to rely only on ''m'' that are congruent modulo 6.)

&lt;codeblock language=python&gt;
&lt;&lt;modular cases&gt;&gt;=
@memo
def b0mod6(m):
    return (mpq(m+3, 3) - A(m, m//6)) / bincoef(m+3, m)

@memo
def b2mod6(m):
    return (mpq(m+3, 3) - A(m, (m-2)//6)) / bincoef(m+3, m)

@memo
def b4mod6(m):
    return (-mpq(m+3, 6) - A(m, (m-4)//6)) / bincoef(m+3, m)
&lt;/codeblock&gt;

Wrapping things up:

&lt;codeblock language=python&gt;
&lt;&lt;main faster&gt;&gt;=
def bernoulli(m):
    assert m &gt;= 0
    if m == 0: return 1
    if m == 1: return -mpq(1,2)
    if m % 6 == 0: return b0mod6(m)
    if m % 6 == 2: return b2mod6(m)
    if m % 6 == 4: return b4mod6(m)
    return 0
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A&gt;&gt;
&lt;&lt;modular cases&gt;&gt;
&lt;&lt;main faster&gt;&gt;
&lt;/codeblock&gt;

==A further enhancement==

There is some inefficiency in the implementation of ''A'', namely that it calculates a new binomial coefficient &quot;from scratch&quot; for each term of the sum. For large inputs, it is faster to compute each binomial coefficient from the previous one. &lt;!-- TODO: write down formulas for the differences --&gt;

&lt;codeblock language=python&gt;
&lt;&lt;A faster&gt;&gt;=
def product(low, high):
    p = 1
    for k in range(low, high+1):
        p *= k
    return p

def A(m, mtop):
    s = 0
    a = bincoef(m+3, m-6)
    for j in range(1, mtop+1):
        s += a*bernoulli(m-6*j)
        a *= product(m-6 - 6*j + 1, m-6*j)
        a //= product(6*j+4, 6*j+9)
    return s
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;bernoulli_faster_yet.py&gt;&gt;=
&lt;&lt;dependencies&gt;&gt;
&lt;&lt;memo&gt;&gt;
&lt;&lt;A faster&gt;&gt;
&lt;&lt;modular cases&gt;&gt;
&lt;&lt;main faster&gt;&gt;
&lt;/codeblock&gt;

==Testing==

A good way to check that all implementations are correct is to test them against each other. We will also time the computation of ''B''&lt;sub&gt;1000&lt;/sub&gt; with each method.

&lt;codeblock language=python&gt;
&lt;&lt;test.py&gt;&gt;=
from bernoulli_simple import bernoulli as bernoulli1
from bernoulli_faster import bernoulli as bernoulli2
from bernoulli_faster_yet import bernoulli as bernoulli3
from time import clock

for i in range(50):
    assert bernoulli1(i) == bernoulli2(i) == bernoulli3(i)

a = clock()
temp = bernoulli1(1000)
print &quot;simple:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli2(1000)
print &quot;faster:&quot;, clock() - a, &quot;seconds&quot;

a = clock()
temp = bernoulli3(1000)
print &quot;faster yet:&quot;, clock() - a, &quot;seconds&quot;

&lt;/codeblock&gt;

The output will probably resemble the following:
&lt;pre&gt;
simple: 15.7621247952 seconds
faster: 1.00002039365 seconds
faster yet: 0.568878726207 seconds
&lt;/pre&gt;

The difference will become even more significant with larger input. In fact, the third version was used to compute the [http://fredrikj.net/math/bernoulli.html 10,000 first Bernoulli numbers] in less than an hour on a 1400 MHz Athlon (version two needed four hours). By contrast, ''[http://en.wikipedia.org/wiki/Mathematica Mathematica]'' took 1.5 hours to perform the same calculation and the specialized program [http://bernoulli.org calcbn] needed 2.5 hours. However, it should be noted that the program implemented here is not well suited for calculating individual extremely large Bernoulli numbers, say, B&lt;sub&gt;100,000&lt;/sub&gt;.

[[Category:Bernoulli numbers]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Betti numbers (Python)</title>
    <id>2905</id>
    <revision>
      <id>8531</id>
      <timestamp>2007-01-13T17:12:13Z</timestamp>
      <contributor>
        <ip>213.3.88.9</ip>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{codedump}}
An exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided torus, it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>8747</id>
      <timestamp>2007-01-30T01:57:01Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>-codedump</comment>
      <text xml:space="preserve">This article is an exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided torus, it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>8869</id>
      <timestamp>2007-02-07T16:07:31Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>+cat: symbolic mathematics</comment>
      <text xml:space="preserve">This article is an exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided torus, it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Discrete_and_symbolic_mathematics]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>8977</id>
      <timestamp>2007-02-10T11:36:28Z</timestamp>
      <contributor>
        <ip>62.202.114.181</ip>
      </contributor>
      <comment>/* a module */ link to javascript rendered torus as illustration</comment>
      <text xml:space="preserve">This article is an exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided [http://www.canonical.org/~kragen/sw/torus.html torus], it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Discrete_and_symbolic_mathematics]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>16857</id>
      <timestamp>2010-09-23T13:07:41Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">OMG, I ACCDIDENTLY THE WHOLE THING!</text>
    </revision>
    <revision>
      <id>16858</id>
      <timestamp>2010-09-23T13:08:27Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">OMG, I ACCIDENTLY THE WHOLE THING!</text>
    </revision>
    <revision>
      <id>16911</id>
      <timestamp>2010-09-23T15:54:40Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This article is an exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided [http://www.canonical.org/~kragen/sw/torus.html torus], it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Discrete_and_symbolic_mathematics]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>17060</id>
      <timestamp>2011-02-19T18:41:33Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">This article is an exercise inspired by SIGFPE's exploration of  [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell].  Please feel free to expand upon it.

==theory==
The [http://en.wikipedia.org/wiki/Betti_number Betti numbers] are a topological invariant that allow us to measure either the number of holes of various dimensions present in a structure, or equivalently, the number of times the structure loops back upon itself.
==practice==

===boundaries===
The [http://en.wikipedia.org/wiki/Chain_complex boundary] of a n-simplex consists of a chain of ''oriented'' (n-1)-simplices.  We represent these chains as a dictionary of orientations keyed by the simplices.
* '''matrix''' constructs an outer product, connecting each basis element in b0 to a basis element in b1
* '''boundary''' is a straightforward translation of &lt;math&gt;\partial (s_0...s_d) = \sum_{i=0}^d (-1)^i (s_0, ..., \hat{s_i}, ... s_d) &lt;/math&gt;
* '''dmatrix''' builds the matrix connecting the boundary of the n-simplices in a complex to the (n-1)-simplices.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;boundary&gt;&gt;=
matrix = lambda b1,b0,op: [[op(x,y) for x in b1] for y in b0]
boundary = lambda s: dict([(tuple(s[:i]+s[i+1:]), (-1)**i)
                                for i in range(len(s))])
dmatrix = lambda c,n: matrix(grade(c,n), (grade(c,n-1) or [[None]]),
                        lambda x,y: boundary(x).get(tuple(y),0))
&lt;/codeblock&gt;

The boundary of any n-simplex is an n-1 dimensional cycle.

===Betti numbers===

However, there may also be cycles which do not arise as a boundary of higher-dimensional elements of the complex.   ''(a topological space contains all unions of its subsets.  Complexes may be missing some unions (alternatively, containing albeit with multiplicity 0), and it is the presence of these holes (alternatively, the absence of connectivity), which the Betti numbers measure)''

This is also a straightforward calculation comparing the kernel of each &lt;math&gt;\partial_n&lt;/math&gt; with the image of &lt;math&gt;\partial_{n-1}&lt;/math&gt; &amp;mdash; any rank deficiency in the &lt;math&gt;\partial&lt;/math&gt;-matrices contributes to the final result.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti numbers&gt;&gt;=
def betti(c):
    d = ctdim(c)
    ranks = array([rank(dmatrix(c,n)) for n in range(d)]+[0])
    dims  = array([  len(grade(c,n))  for n in range(d)]+[0])
    return dims[:-1] - ranks[:-1] - ranks[1:]
&lt;/codeblock&gt;

At 0-dimensions, the Betti number counts connected components, and higher values count the n-holes.  These are [http://en.wikipedia.org/wiki/Topological_invariant topologically invariant] which means that if one changes the mesh without altering its connectivity, the Betti numbers remain unchanged.

To test this, we include some barycentric subdivision code.  The new members of a simplex in the subdivision are formed by combining the existing vertices.  In a geometric context, this would be done using affine coordinates, here we simply pack old vertices into tuples to form new vertices.  Each new element of the simplex forms a chain, consisting of one old vertex and ascending to the largest combination of vertices in that dimension: eg. [0, (0,1), (0,1,2)] might be a typical 2-simplex in a subdivision.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;=
def bary(c):
    def chains(xs):
        if len(xs) &lt; 2:  return [xs]
        else: return [cs+[tuple(xs)]
                        for ps in subsets(xs)[:-1]
                        for cs in chains(ps)]
    return reduce(concat,map(chains,c))
&lt;/codeblock&gt;
The [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Haskell implementation] is notable here for the use of the List monad to succinctly generate multiple values at each dimension.  Not having monadic '''do'''s in Python, we must make the &lt;code&gt;reduce(concat,map(...,...))&lt;/code&gt; explicit.

==wrapping up==
We will require a few supporting definitions.
===miscellanea===
Following Iverson, we use the '''binary''' expansion to generate masks for all possible subsets of d items, at which point '''subset''' is simply a selection with each of those masks.  Being in counting order, the result always starts with the empty subset and ends with the improper subset.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
binary = lambda d: (lambda a: (a[0]/(2**a[1])) % 2)(indices((2**d,d)))
subsets = lambda l: [list(repeat(l,r)) for r in binary(len(l))]
&lt;/codeblock&gt;
We are lazy, and outsource '''rank''' (the mathematical rank, ignoring dependent vectors, not the physical size of the matrix) to the LinearAlgebra module.
'''grade''' picks only the simplices of a given dimension from the complex, and
'''ctdim''' computes the dimension of the simplex as a whole.  (we follow the category theorists here, and hence are off-by-one from the topologists' view of dimension)
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillary&gt;&gt;=
rank  = lambda m: sum(singular_value_decomposition(array(m))[1] &gt; 1e-12)
grade = lambda c, n: [s for s in c if len(s)==n+1]
ctdim = lambda c: maximum.reduce(map(len,c))
&lt;/codeblock&gt;
A few extra definitions:
* the n-'''ball''' &amp;mdash; completely connected, but ignoring the single empty element, at (topologists') dimension -1.
* the n-'''sphere''' &amp;mdash; as above, but with a hollow interior (missing the maximal simplex).  Again, we take advantage of the ordering of the binary subsets to trim instead of search.
* the '''euler''' number, calculated the hard way as the alternating sum of betti coefficients.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;supplements&gt;&gt;=
ball   = lambda n: subsets(range(n+1))[1:]
sphere = lambda n: subsets(range(n+2))[1:-1]

euler  = lambda c: (lambda b: sum(b[0::2])-sum(b[1::2]))(betti(c))
&lt;/codeblock&gt;

===a module===

Finally we put together a module, using examples and problems from the [http://www.reed.edu/~davidp/411/handouts/simplicial.pdf handout] mentioned by SIGFPE as test vectors.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;betti.py&gt;&gt;=
from Numeric import *
from LinearAlgebra import singular_value_decomposition
from operator import add as concat
# after http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html

&lt;&lt;ancillary&gt;&gt;
&lt;&lt;boundary&gt;&gt;
&lt;&lt;betti numbers&gt;&gt;
&lt;&lt;barycentric subdivision&gt;&gt;
&lt;&lt;supplements&gt;&gt;

if __name__ == &quot;__main__&quot;:
        # examples from http://www.reed.edu/~davidp/411/handouts/simplicial.pdf
        example = [
            [1,2,3],
            [1,2],[1,3],[2,3],[2,4],[3,4],
            [1],[2],[3],[4],[5]]

        print &quot;example.&quot;, betti(example)
        print &quot;exercise 1.&quot;, betti(example[1:])

        point = [[0]]
        line = [[0],[1],[0,1]]
        tri = ball(2)
        torus = [[1],[2],[3],[4],[5],[6],[7],[8],[9],
            [1,2],[2,3],[1,3],
            [5,9],[8,9],[5,8],
            [4,6],[6,7],[4,7],

            [1,5],[4,5],[1,4],
            [2,9],[6,9],[2,6],
            [3,8],[7,8],[3,7],

            [1,9],[3,9],[1,8],
            [4,9],[6,8],[5,7],
            [1,6],[2,7],[1,7],

            [1,5,9],[1,2,9],[2,3,9],[3,8,9],[1,3,8],[1,5,8],
            [4,5,9],[4,6,9],[6,8,9],[6,7,8],[5,7,8],[4,5,7],
            [1,4,6],[1,2,6],[2,6,7],[2,3,7],[1,3,7],[1,4,7]]

        example2 = [[1],[2],[3],[4],[5],[6],
                [1,4],[1,6],[1,5],[1,3],
                [3,4],[2,3],[3,5],
                [2,4],[4,6],
                [2,5],[2,6],[5,6],
                [1,4,6],[2,4,6],[2,3,4],[2,3,5],[1,3,5],[1,5,6],[2,5,6],[1,3,4]]

        print &quot;exercise 5.&quot;, betti(example2), betti(sphere(2))

        print &quot;point&quot;, betti(point)
        print &quot;line&quot;, betti(line)
        print &quot;3-sphere&quot;, betti(sphere(3))
        print &quot;0-sphere&quot;, betti(sphere(0))
        print &quot;exercise 6.&quot;, betti(torus)

        print &quot;bary(point), point&quot;, betti(bary(point)), betti(point)
        print &quot;bary(line), line&quot;, betti(bary(line)), betti(line)
        print &quot;bary(tri), tri&quot;, betti(bary(tri)), betti(tri)

        btorus=bary(torus)
        print &quot;size of bary(torus)&quot;, len(btorus)
        print &quot;bary(torus), torus&quot;, betti(btorus), betti(torus)
        print &quot;euler(2-sphere)&quot;, euler(sphere(2))
        print &quot;euler(torus)&quot;, euler(torus)
&lt;/codeblock&gt;

and, after waiting a second or so for the subdivided [http://www.canonical.org/~kragen/sw/torus.html torus], it yields the following.

&lt;pre&gt;
example. [2 1 0]
exercise 1. [2 2]
exercise 5. [1 0 1] [1 0 1]
point [1]
line [1 0]
3-sphere [1 0 0 1]
0-sphere [2]
exercise 6. [1 2 1]
bary(point), point [1] [1]
bary(line), line [1 0] [1 0]
bary(tri), tri [1 0 0] [1 0 0]
size of bary(torus) 324
bary(torus), torus [1 2 1] [1 2 1]
euler(2-sphere) 2
euler(torus) 0
&lt;/pre&gt;

Not exactly fast enough for production datasets, but not bad for roughly 30 lines of definitions.

[[Category:Computer algebra systems]]
[[Category:Discrete_and_symbolic_mathematics]]
[[Category:Homology]]
[[Category:Topology]]
[[Category:Programming language:Python]]</text>
    </revision>
  </page>
  <page>
    <title>Binary Search (C Plus Plus)</title>
    <id>2274</id>
    <revision>
      <id>5962</id>
      <timestamp>2006-06-05T22:11:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Binary Search (C Plus Plus)]] moved to [[Binary search (C Plus Plus)]]: Capitalization convention</comment>
      <text xml:space="preserve">#REDIRECT [[Binary search (C Plus Plus)]]</text>
    </revision>
  </page>
  <page>
    <title>Binary Search Tree (Haskell)</title>
    <id>3340</id>
    <revision>
      <id>12831</id>
      <timestamp>2008-03-16T03:57:04Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>[[Binary Search Tree (Haskell)]] moved to [[Binary search tree (Haskell)]]: consistency with other languages</comment>
      <text xml:space="preserve">#REDIRECT [[Binary search tree (Haskell)]]</text>
    </revision>
  </page>
  <page>
    <title>Binary heap (Scheme)</title>
    <id>2679</id>
    <revision>
      <id>7552</id>
      <timestamp>2006-09-02T17:26:07Z</timestamp>
      <contributor>
        <username>S. Carton</username>
        <id>82</id>
      </contributor>
      <comment>working but crude first draft</comment>
      <text xml:space="preserve">{{develop}}
This is an implementation of a [http://en.wikipedia.org/wiki/Binary_heap binary min-heap] that uses a user-supplied comparison predicate so it can hold different types of elements.

We'll use an array representation of the binary heap; scheme vectors are heterogenous. We also have to store the current heap size and the heap comparison predicate. So our heap data structure will be a three-element vector: a comparison predicate, the array holding the heap's elements and a number representing the heap size. The choice of a vector instead of a fancier record type ensures R5RS standard compliance.

First, some convenient accessor and utility functions for our heap data structure:

&lt;codeblock language=scheme&gt;
(define (heap-size heap)
  (vector-ref heap 2))

(define (heap-vect heap)
  (vector-ref heap 1))

(define (heap-read heap)
  (vector-ref (vector-ref heap 1) 0))

(define (heap-&lt; heap index1 index2)
  (let ((vect (heap-vect heap)))
    ((vector-ref heap 0) (vector-ref vect index1) (vector-ref vect index2))))

(define (heap-swap! heap index1 index2) 
  (let* ((vect (heap-vect heap))
         (val1 (vector-ref vect index1)))
         (begin
           (vector-set! vect index1 (vector-ref vect index2))
           (vector-set! vect index2 val1))))
&lt;/codeblock&gt;

The heap-&lt; function lets us conveniently compare elements by their index.

Our heap implementation must take care of managing the vector representation of the heap, so we provide a vector-resize function so our heap can grow:

&lt;codeblock language=scheme&gt;
(define (vector-resize vect new-size)
  (define (overwrite-vector alist avector position)
    (if (null? alist) avector
        (begin
          (vector-set! avector position (car alist))
          (overwrite-vector (cdr alist) avector (+ position 1)))))
  (overwrite-vector (vector-&gt;list vect) (make-vector new-size) 0))
&lt;/codeblock&gt;

With the preliminaries out of the way, we can implement the actual heap. Our heap will support two operations: heap insertion and root deletion.

Heap insertion is accomplished by adding the element at the bottom of the heap and moving it up until the heap property is satisfied (that is, until its parent is smaller than itself).

So we need a function that, given a position in the heap, checks to see if the heap property holds for it and its parent. If it doesn't, it swaps the element at this position with its parent, moving it up, and repeats this until the heap property is satisfied.

The heap property is satisfied if:

1) The element is at the root position (has no parent).
2) The element is larger than its parent.

The code IS redundant, but prevents an infinite loop if the predicate is &lt;= instead of &lt;. Suggestions?

&lt;codeblock language=scheme&gt;
(define (heap-move-up heap position)
    (let ((parent (quotient (- position 1) 2)))
      (cond ((or (= position 0) (heap-&lt; heap parent position))  
             'end-move-up)
            ((heap-&lt; heap position parent)
             (begin
               (heap-swap! heap position parent)
               (heap-move-up heap parent)))
            (else 'end-move-up))))
&lt;/codeblock&gt;

Once we have this function, insertion is easy: we first check to see if the array holding our heap is big enough to accomodate the new element. If it isn't, we resize it to twice its old size (the + 1 copes with with the size=0 initial case).

Then we insert the new element at the last position in the heap, update the heap size, and call the heap-move-up function to restore the heap structure.

&lt;codeblock language=scheme&gt;
(define (heap-insert! heap elem)
  (let ((size (heap-size heap)))
    (begin 
      (if (&gt; (+ size 1) (vector-length (vector-ref heap 1)))
          (vector-set! heap 1 (vector-resize (vector-ref heap 1) (* 2 (+ 1 size)))))
      (vector-set! (vector-ref heap 1) size elem)
      (vector-set! heap 2 (+ size 1))
      (heap-move-up heap size))))
&lt;/codeblock&gt;

Root deletion is accomplished by deleting the root element, moving the last element in the heap into root position, and then restoring heap structure. So we need a function that, given a position in the heap, restores the heap property by moving the element down until the heap property holds. There are 3 cases:

1) The position being considered is the last position in the heap. In that case, the heap property holds trivially.

2) The position being considered is the last position in the heap but one. In that case, check its single child: if the child is smaller, swap the elements. If not, the heap property holds.

3) The position being considered has two children. If a child is smaller, swap the element with the smallest of its two children. If not, the heap property holds.

&lt;codeblock language=scheme&gt;
(define (heap-move-down heap position)
    (let ((lchild (+ (* 2 position) 1))
          (rchild (+ (* 2 position) 2))
          (size (heap-size heap))
          (swap! (lambda (pos child)
                   (begin
                     (heap-swap! heap pos child)
                     (heap-move-down heap child)))))
      (cond ((&gt; lchild (- size 1))
             'end-move-down)
            ((&gt; rchild (- size 1))
             (if (heap-&lt; heap lchild position)
                 (swap! position lchild)
                 'end-move-down))
             (else
              (let ((smallest-child (if (heap-&lt; heap lchild rchild) lchild rchild)))
                (if (heap-&lt; heap smallest-child position)
                    (swap! position smallest-child)
                    'end-move-down))))))
&lt;/codeblock&gt;

Now we have heap-move-down, root deletion is easy. We simply

1) remember the element at the root, 

2) swap the root element and the last element in the heap

3) decrease the heap size by 1

4) restore heap structure using heap-move-down

5) return the element that was the root before deletion.

&lt;codeblock language=scheme&gt;
(define (heap-extract-root! heap)
  (let ((size (heap-size heap)) (old-root (heap-read heap)))
    (begin
      (heap-swap! heap 0 (- size 1))
      (vector-set! heap 2 (- size 1))
      (heap-move-down heap 0)
      old-root)))
&lt;/codeblock&gt;

The important binary heap logic is done. Now, we need a function that makes a heap structure given a list of elements and a comparison predicate:

&lt;codeblock language=scheme&gt;
(define (make-heap elem-list lt-predicate)
  (define (heap-fill heap alist)
    (if (null? alist) heap
        (begin
          (heap-insert! heap (car alist))
          (heap-fill heap (cdr alist)))))
  (let ((new-heap (make-vector 3)))
    (begin
      (vector-set! new-heap 0 lt-predicate)
      (vector-set! new-heap 1 (make-vector 0))
      (vector-set! new-heap 2 0)
      (heap-fill new-heap elem-list))))
&lt;/codeblock&gt;

The heap implementation is complete.

Now, let's implement heapsort to test our heap implementation:

&lt;codeblock language=scheme&gt;
(define (heap-sort alist apred)
  (define (extract-until aheap)
    (if (= 0 (heap-size aheap)) '()
        (cons (heap-extract-root! aheap) (extract-until aheap))))
  (extract-until (make-heap alist apred)))
&lt;/codeblock&gt;

And let's test it in the repl:

&lt;codeblock&gt;
&gt; (heap-sort '(3 5 7 0 6 5 34 3 6 9 67 5 4 4 3 1 2 3) &lt;)
(0 1 2 3 3 3 3 4 4 5 5 5 6 6 7 9 34 67)
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11226</id>
      <timestamp>2007-10-16T01:02:58Z</timestamp>
      <contributor>
        <ip>158.104.216.48</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
This is an implementation of a [http://en.wikipedia.org/wiki/Binary_heap binary min-heap] that uses a user-supplied comparison predicate so it can hold different types of elements.

We'll use an array representation of the binary heap; scheme vectors are heterogenous. We also have to store the current heap size and the heap comparison predicate. So our heap data structure will be a three-element vector: a comparison predicate, the array holding the heap's elements and a number representing the heap size. The choice of a vector instead of a fancier record type ensures R5RS standard compliance.

First, some convenient accessor and utility functions for our heap data structure:

&lt;codeblock language=scheme&gt;
(define (heap-size heap)
  (vector-ref heap 2))

(define (heap-vect heap)
  (vector-ref heap 1))

(define (heap-read heap)
  (vector-ref (vector-ref heap 1) 0))

(define (heap-&lt; heap index1 index2)
  (let ((vect (heap-vect heap)))
    ((vector-ref heap 0) (vector-ref vect index1) (vector-ref vect index2))))

(define (heap-swap! heap index1 index2) 
  (let* ((vect (heap-vect heap))
         (val1 (vector-ref vect index1)))
         (begin
           (vector-set! vect index1 (vector-ref vect index2))
           (vector-set! vect index2 val1))))
&lt;/codeblock&gt;

The heap-&lt; function lets us conveniently compare elements by their index.

Our heap implementation must take care of managing the vector representation of the heap, so we provide a vector-resize function so our heap can grow:

&lt;codeblock language=scheme&gt;
(define (vector-resize vect new-size)
  (define (overwrite-vector alist avector position)
    (if (null? alist) avector
        (begin
          (vector-set! avector position (car alist))
          (overwrite-vector (cdr alist) avector (+ position 1)))))
  (overwrite-vector (vector-&gt;list vect) (make-vector new-size) 0))
&lt;/codeblock&gt;

With the preliminaries out of the way, we can implement the actual heap. Our heap will support two operations: heap insertion and root deletion.

Heap insertion is accomplished by adding the element at the bottom of the heap and moving it up until the heap property is satisfied (that is, until its parent is smaller than itself).

So we need a function that, given a position in the heap, checks to see if the heap property holds for it and its parent. If it doesn't, it swaps the element at this position with its parent, moving it up, and repeats this until the heap property is satisfied.

The heap property is satisfied if:

1) The element is at the root position (has no parent).
2) The element is larger than its parent.

The code IS redundant, but prevents an infinite loop if the predicate is &lt;= instead of &lt;. Suggestions?

&lt;codeblock language=scheme&gt;
(define (heap-move-up heap position)
    (let ((parent (quotient (- position 1) 2)))
      (cond ((or (= position 0) (heap-&lt; heap parent position))  
             'end-move-up)
            ((heap-&lt; heap position parent)
             (begin
               (heap-swap! heap position parent)
               (heap-move-up heap parent)))
            (else 'end-move-up))))
&lt;/codeblock&gt;

Once we have this function, insertion is easy: we first check to see if the array holding our heap is big enough to accomodate the new element. If it isn't, we resize it to twice its old size (the + 1 copes with with the size=0 initial case).

Then we insert the new element at the last position in the heap, update the heap size, and call the heap-move-up function to restore the heap structure.

&lt;codeblock language=scheme&gt;
(define (heap-insert! heap elem)
  (let ((size (heap-size heap)))
    (begin 
      (if (&gt; (+ size 1) (vector-length (vector-ref heap 1)))
          (vector-set! heap 1 (vector-resize (vector-ref heap 1) (* 2 (+ 1 size)))))
      (vector-set! (vector-ref heap 1) size elem)
      (vector-set! heap 2 (+ size 1))
      (heap-move-up heap size))))
&lt;/codeblock&gt;

Root deletion is accomplished by deleting the root element, moving the last element in the heap into root position, and then restoring heap structure. So we need a function that, given a position in the heap, restores the heap property by moving the element down until the heap property holds. There are 3 cases:

1) The position being considered is the last position in the heap. In that case, the heap property holds trivially.

2) The position being considered is the last position in the heap but one. In that case, check its single child: if the child is smaller, swap the elements. If not, the heap property holds.

3) The position being considered has two children. If a child is smaller, swap the element with the smallest of its two children. If not, the heap property holds.

&lt;codeblock language=scheme&gt;
(define (heap-move-down heap position)
    (let ((lchild (+ (* 2 position) 1))
          (rchild (+ (* 2 position) 2))
          (size (heap-size heap))
          (swap! (lambda (pos child)
                   (begin
                     (heap-swap! heap pos child)
                     (heap-move-down heap child)))))
      (cond ((&gt; lchild (- size 1))
             'end-move-down)
            ((&gt; rchild (- size 1))
             (if (heap-&lt; heap lchild position)
                 (swap! position lchild)
                 'end-move-down))
             (else
              (let ((smallest-child (if (heap-&lt; heap lchild rchild) lchild rchild)))
                (if (heap-&lt; heap smallest-child position)
                    (swap! position smallest-child)
                    'end-move-down))))))
&lt;/codeblock&gt;

Now we have heap-move-down, root deletion is easy. We simply

1) remember the element at the root, 

2) swap the root element and the last element in the heap

3) decrease the heap size by 1

4) restore heap structure using heap-move-down

5) return the element that was the root before deletion.

&lt;codeblock language=scheme&gt;
(define (heap-extract-root! heap)
  (let ((size (heap-size heap)) (old-root (heap-read heap)))
    (begin
      (heap-swap! heap 0 (- size 1))
      (vector-set! heap 2 (- size 1))
      (heap-move-down heap 0)
      old-root)))
&lt;/codeblock&gt;

The important binary heap logic is done. Now, we need a function that makes a heap structure given a list of elements and a comparison predicate:

&lt;codeblock language=scheme&gt;
(define (make-heap elem-list lt-predicate)
  (define (heap-fill heap alist)
    (if (null? alist) heap
        (begin
          (heap-insert! heap (car alist))
          (heap-fill heap (cdr alist)))))
  (let ((new-heap (make-vector 3)))
    (begin
      (vector-set! new-heap 0 lt-predicate)
      (vector-set! new-heap 1 (make-vector 0))
      (vector-set! new-heap 2 0)
      (heap-fill new-heap elem-list))))
&lt;/codeblock&gt;

The heap implementation is complete.

Now, let's implement heapsort to test our heap implementation:

&lt;codeblock language=scheme&gt;
(define (heap-sort alist apred)
  (define (extract-until aheap)
    (if (= 0 (heap-size aheap)) '()
        (cons (heap-extract-root! aheap) (extract-until aheap))))
  (extract-until (make-heap alist apred)))
&lt;/codeblock&gt;

And let's test it in the repl:

&lt;codeblock&gt;
&gt; (heap-sort '(3 5 7 0 6 5 34 3 6 9 67 5 4 4 3 1 2 3) &lt;)
(0 1 2 3 3 3 3 4 4 5 5 5 6 6 7 9 34 67)
&lt;/codeblock&gt;
[[Category:Programming language:Scheme]]</text>
    </revision>
    <revision>
      <id>13249</id>
      <timestamp>2008-04-30T06:48:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>[[Category:Binary heap]]</comment>
      <text xml:space="preserve">{{develop}}
This is an implementation of a [http://en.wikipedia.org/wiki/Binary_heap binary min-heap] that uses a user-supplied comparison predicate so it can hold different types of elements.

We'll use an array representation of the binary heap; scheme vectors are heterogenous. We also have to store the current heap size and the heap comparison predicate. So our heap data structure will be a three-element vector: a comparison predicate, the array holding the heap's elements and a number representing the heap size. The choice of a vector instead of a fancier record type ensures R5RS standard compliance.

First, some convenient accessor and utility functions for our heap data structure:

&lt;codeblock language=scheme&gt;
(define (heap-size heap)
  (vector-ref heap 2))

(define (heap-vect heap)
  (vector-ref heap 1))

(define (heap-read heap)
  (vector-ref (vector-ref heap 1) 0))

(define (heap-&lt; heap index1 index2)
  (let ((vect (heap-vect heap)))
    ((vector-ref heap 0) (vector-ref vect index1) (vector-ref vect index2))))

(define (heap-swap! heap index1 index2) 
  (let* ((vect (heap-vect heap))
         (val1 (vector-ref vect index1)))
         (begin
           (vector-set! vect index1 (vector-ref vect index2))
           (vector-set! vect index2 val1))))
&lt;/codeblock&gt;

The heap-&lt; function lets us conveniently compare elements by their index.

Our heap implementation must take care of managing the vector representation of the heap, so we provide a vector-resize function so our heap can grow:

&lt;codeblock language=scheme&gt;
(define (vector-resize vect new-size)
  (define (overwrite-vector alist avector position)
    (if (null? alist) avector
        (begin
          (vector-set! avector position (car alist))
          (overwrite-vector (cdr alist) avector (+ position 1)))))
  (overwrite-vector (vector-&gt;list vect) (make-vector new-size) 0))
&lt;/codeblock&gt;

With the preliminaries out of the way, we can implement the actual heap. Our heap will support two operations: heap insertion and root deletion.

Heap insertion is accomplished by adding the element at the bottom of the heap and moving it up until the heap property is satisfied (that is, until its parent is smaller than itself).

So we need a function that, given a position in the heap, checks to see if the heap property holds for it and its parent. If it doesn't, it swaps the element at this position with its parent, moving it up, and repeats this until the heap property is satisfied.

The heap property is satisfied if:

1) The element is at the root position (has no parent).
2) The element is larger than its parent.

The code IS redundant, but prevents an infinite loop if the predicate is &lt;= instead of &lt;. Suggestions?

&lt;codeblock language=scheme&gt;
(define (heap-move-up heap position)
    (let ((parent (quotient (- position 1) 2)))
      (cond ((or (= position 0) (heap-&lt; heap parent position))  
             'end-move-up)
            ((heap-&lt; heap position parent)
             (begin
               (heap-swap! heap position parent)
               (heap-move-up heap parent)))
            (else 'end-move-up))))
&lt;/codeblock&gt;

Once we have this function, insertion is easy: we first check to see if the array holding our heap is big enough to accomodate the new element. If it isn't, we resize it to twice its old size (the + 1 copes with with the size=0 initial case).

Then we insert the new element at the last position in the heap, update the heap size, and call the heap-move-up function to restore the heap structure.

&lt;codeblock language=scheme&gt;
(define (heap-insert! heap elem)
  (let ((size (heap-size heap)))
    (begin 
      (if (&gt; (+ size 1) (vector-length (vector-ref heap 1)))
          (vector-set! heap 1 (vector-resize (vector-ref heap 1) (* 2 (+ 1 size)))))
      (vector-set! (vector-ref heap 1) size elem)
      (vector-set! heap 2 (+ size 1))
      (heap-move-up heap size))))
&lt;/codeblock&gt;

Root deletion is accomplished by deleting the root element, moving the last element in the heap into root position, and then restoring heap structure. So we need a function that, given a position in the heap, restores the heap property by moving the element down until the heap property holds. There are 3 cases:

1) The position being considered is the last position in the heap. In that case, the heap property holds trivially.

2) The position being considered is the last position in the heap but one. In that case, check its single child: if the child is smaller, swap the elements. If not, the heap property holds.

3) The position being considered has two children. If a child is smaller, swap the element with the smallest of its two children. If not, the heap property holds.

&lt;codeblock language=scheme&gt;
(define (heap-move-down heap position)
    (let ((lchild (+ (* 2 position) 1))
          (rchild (+ (* 2 position) 2))
          (size (heap-size heap))
          (swap! (lambda (pos child)
                   (begin
                     (heap-swap! heap pos child)
                     (heap-move-down heap child)))))
      (cond ((&gt; lchild (- size 1))
             'end-move-down)
            ((&gt; rchild (- size 1))
             (if (heap-&lt; heap lchild position)
                 (swap! position lchild)
                 'end-move-down))
             (else
              (let ((smallest-child (if (heap-&lt; heap lchild rchild) lchild rchild)))
                (if (heap-&lt; heap smallest-child position)
                    (swap! position smallest-child)
                    'end-move-down))))))
&lt;/codeblock&gt;

Now we have heap-move-down, root deletion is easy. We simply

1) remember the element at the root, 

2) swap the root element and the last element in the heap

3) decrease the heap size by 1

4) restore heap structure using heap-move-down

5) return the element that was the root before deletion.

&lt;codeblock language=scheme&gt;
(define (heap-extract-root! heap)
  (let ((size (heap-size heap)) (old-root (heap-read heap)))
    (begin
      (heap-swap! heap 0 (- size 1))
      (vector-set! heap 2 (- size 1))
      (heap-move-down heap 0)
      old-root)))
&lt;/codeblock&gt;

The important binary heap logic is done. Now, we need a function that makes a heap structure given a list of elements and a comparison predicate:

&lt;codeblock language=scheme&gt;
(define (make-heap elem-list lt-predicate)
  (define (heap-fill heap alist)
    (if (null? alist) heap
        (begin
          (heap-insert! heap (car alist))
          (heap-fill heap (cdr alist)))))
  (let ((new-heap (make-vector 3)))
    (begin
      (vector-set! new-heap 0 lt-predicate)
      (vector-set! new-heap 1 (make-vector 0))
      (vector-set! new-heap 2 0)
      (heap-fill new-heap elem-list))))
&lt;/codeblock&gt;

The heap implementation is complete.

Now, let's implement heapsort to test our heap implementation:

&lt;codeblock language=scheme&gt;
(define (heap-sort alist apred)
  (define (extract-until aheap)
    (if (= 0 (heap-size aheap)) '()
        (cons (heap-extract-root! aheap) (extract-until aheap))))
  (extract-until (make-heap alist apred)))
&lt;/codeblock&gt;

And let's test it in the repl:

&lt;codeblock&gt;
&gt; (heap-sort '(3 5 7 0 6 5 34 3 6 9 67 5 4 4 3 1 2 3) &lt;)
(0 1 2 3 3 3 3 4 4 5 5 5 6 6 7 9 34 67)
&lt;/codeblock&gt;
[[Category:Programming language:Scheme]]
[[Category:Binary heap]]</text>
    </revision>
    <revision>
      <id>15988</id>
      <timestamp>2009-01-18T00:33:29Z</timestamp>
      <contributor>
        <ip>201.47.42.10</ip>
      </contributor>
      <comment>dEhhFXqTxHaaUT</comment>
      <text xml:space="preserve">pBf0A9  &lt;a href=&quot;http://ubbfuzmkukvy.com/&quot;&gt;ubbfuzmkukvy&lt;/a&gt;, [url=http://kckmwyovkbmv.com/]kckmwyovkbmv[/url], [link=http://pmcpmwzduyap.com/]pmcpmwzduyap[/link], http://mpboqufibyry.com/</text>
    </revision>
    <revision>
      <id>15990</id>
      <timestamp>2009-01-18T06:59:16Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/201.47.42.10|201.47.42.10]] ([[User_talk:201.47.42.10|201.47.42.10]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{develop}}
This is an implementation of a [http://en.wikipedia.org/wiki/Binary_heap binary min-heap] that uses a user-supplied comparison predicate so it can hold different types of elements.

We'll use an array representation of the binary heap; scheme vectors are heterogenous. We also have to store the current heap size and the heap comparison predicate. So our heap data structure will be a three-element vector: a comparison predicate, the array holding the heap's elements and a number representing the heap size. The choice of a vector instead of a fancier record type ensures R5RS standard compliance.

First, some convenient accessor and utility functions for our heap data structure:

&lt;codeblock language=scheme&gt;
(define (heap-size heap)
  (vector-ref heap 2))

(define (heap-vect heap)
  (vector-ref heap 1))

(define (heap-read heap)
  (vector-ref (vector-ref heap 1) 0))

(define (heap-&lt; heap index1 index2)
  (let ((vect (heap-vect heap)))
    ((vector-ref heap 0) (vector-ref vect index1) (vector-ref vect index2))))

(define (heap-swap! heap index1 index2) 
  (let* ((vect (heap-vect heap))
         (val1 (vector-ref vect index1)))
         (begin
           (vector-set! vect index1 (vector-ref vect index2))
           (vector-set! vect index2 val1))))
&lt;/codeblock&gt;

The heap-&lt; function lets us conveniently compare elements by their index.

Our heap implementation must take care of managing the vector representation of the heap, so we provide a vector-resize function so our heap can grow:

&lt;codeblock language=scheme&gt;
(define (vector-resize vect new-size)
  (define (overwrite-vector alist avector position)
    (if (null? alist) avector
        (begin
          (vector-set! avector position (car alist))
          (overwrite-vector (cdr alist) avector (+ position 1)))))
  (overwrite-vector (vector-&gt;list vect) (make-vector new-size) 0))
&lt;/codeblock&gt;

With the preliminaries out of the way, we can implement the actual heap. Our heap will support two operations: heap insertion and root deletion.

Heap insertion is accomplished by adding the element at the bottom of the heap and moving it up until the heap property is satisfied (that is, until its parent is smaller than itself).

So we need a function that, given a position in the heap, checks to see if the heap property holds for it and its parent. If it doesn't, it swaps the element at this position with its parent, moving it up, and repeats this until the heap property is satisfied.

The heap property is satisfied if:

1) The element is at the root position (has no parent).
2) The element is larger than its parent.

The code IS redundant, but prevents an infinite loop if the predicate is &lt;= instead of &lt;. Suggestions?

&lt;codeblock language=scheme&gt;
(define (heap-move-up heap position)
    (let ((parent (quotient (- position 1) 2)))
      (cond ((or (= position 0) (heap-&lt; heap parent position))  
             'end-move-up)
            ((heap-&lt; heap position parent)
             (begin
               (heap-swap! heap position parent)
               (heap-move-up heap parent)))
            (else 'end-move-up))))
&lt;/codeblock&gt;

Once we have this function, insertion is easy: we first check to see if the array holding our heap is big enough to accomodate the new element. If it isn't, we resize it to twice its old size (the + 1 copes with with the size=0 initial case).

Then we insert the new element at the last position in the heap, update the heap size, and call the heap-move-up function to restore the heap structure.

&lt;codeblock language=scheme&gt;
(define (heap-insert! heap elem)
  (let ((size (heap-size heap)))
    (begin 
      (if (&gt; (+ size 1) (vector-length (vector-ref heap 1)))
          (vector-set! heap 1 (vector-resize (vector-ref heap 1) (* 2 (+ 1 size)))))
      (vector-set! (vector-ref heap 1) size elem)
      (vector-set! heap 2 (+ size 1))
      (heap-move-up heap size))))
&lt;/codeblock&gt;

Root deletion is accomplished by deleting the root element, moving the last element in the heap into root position, and then restoring heap structure. So we need a function that, given a position in the heap, restores the heap property by moving the element down until the heap property holds. There are 3 cases:

1) The position being considered is the last position in the heap. In that case, the heap property holds trivially.

2) The position being considered is the last position in the heap but one. In that case, check its single child: if the child is smaller, swap the elements. If not, the heap property holds.

3) The position being considered has two children. If a child is smaller, swap the element with the smallest of its two children. If not, the heap property holds.

&lt;codeblock language=scheme&gt;
(define (heap-move-down heap position)
    (let ((lchild (+ (* 2 position) 1))
          (rchild (+ (* 2 position) 2))
          (size (heap-size heap))
          (swap! (lambda (pos child)
                   (begin
                     (heap-swap! heap pos child)
                     (heap-move-down heap child)))))
      (cond ((&gt; lchild (- size 1))
             'end-move-down)
            ((&gt; rchild (- size 1))
             (if (heap-&lt; heap lchild position)
                 (swap! position lchild)
                 'end-move-down))
             (else
              (let ((smallest-child (if (heap-&lt; heap lchild rchild) lchild rchild)))
                (if (heap-&lt; heap smallest-child position)
                    (swap! position smallest-child)
                    'end-move-down))))))
&lt;/codeblock&gt;

Now we have heap-move-down, root deletion is easy. We simply

1) remember the element at the root, 

2) swap the root element and the last element in the heap

3) decrease the heap size by 1

4) restore heap structure using heap-move-down

5) return the element that was the root before deletion.

&lt;codeblock language=scheme&gt;
(define (heap-extract-root! heap)
  (let ((size (heap-size heap)) (old-root (heap-read heap)))
    (begin
      (heap-swap! heap 0 (- size 1))
      (vector-set! heap 2 (- size 1))
      (heap-move-down heap 0)
      old-root)))
&lt;/codeblock&gt;

The important binary heap logic is done. Now, we need a function that makes a heap structure given a list of elements and a comparison predicate:

&lt;codeblock language=scheme&gt;
(define (make-heap elem-list lt-predicate)
  (define (heap-fill heap alist)
    (if (null? alist) heap
        (begin
          (heap-insert! heap (car alist))
          (heap-fill heap (cdr alist)))))
  (let ((new-heap (make-vector 3)))
    (begin
      (vector-set! new-heap 0 lt-predicate)
      (vector-set! new-heap 1 (make-vector 0))
      (vector-set! new-heap 2 0)
      (heap-fill new-heap elem-list))))
&lt;/codeblock&gt;

The heap implementation is complete.

Now, let's implement heapsort to test our heap implementation:

&lt;codeblock language=scheme&gt;
(define (heap-sort alist apred)
  (define (extract-until aheap)
    (if (= 0 (heap-size aheap)) '()
        (cons (heap-extract-root! aheap) (extract-until aheap))))
  (extract-until (make-heap alist apred)))
&lt;/codeblock&gt;

And let's test it in the repl:

&lt;codeblock&gt;
&gt; (heap-sort '(3 5 7 0 6 5 34 3 6 9 67 5 4 4 3 1 2 3) &lt;)
(0 1 2 3 3 3 3 4 4 5 5 5 6 6 7 9 34 67)
&lt;/codeblock&gt;
[[Category:Programming language:Scheme]]
[[Category:Binary heap]]</text>
    </revision>
  </page>
  <page>
    <title>Binary matrix (Java)</title>
    <id>1960</id>
    <revision>
      <id>4450</id>
      <timestamp>2006-05-07T09:03:05Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication.

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
	private boolean A[][];
	private int row;
	private int col;
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
  &lt;&lt;Data&gt;&gt;
&lt;/codeblock&gt;
[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4451</id>
      <timestamp>2006-05-07T09:18:13Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication.

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }
&lt;/codeblock&gt;

==Addition==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
&lt;/codeblock&gt;

==Subtraction==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;Data&gt;&gt;
&lt;/codeblock&gt;


[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4453</id>
      <timestamp>2006-05-07T10:58:28Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }
&lt;/codeblock&gt;

==Getter and Setter==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColumnDimension();
    int bRow = B.getRowDimension();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
&lt;/codeblock&gt;


[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4454</id>
      <timestamp>2006-05-07T11:14:00Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }
&lt;/codeblock&gt;

==Getter===
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

===Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4455</id>
      <timestamp>2006-05-07T11:19:44Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from the two-dimensional integer array.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }
&lt;/codeblock&gt;

==Getter==
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4456</id>
      <timestamp>2006-05-07T11:23:44Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Addition */</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from the two-dimensional integer array.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }
&lt;/codeblock&gt;

==Getter==
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4457</id>
      <timestamp>2006-05-07T11:27:50Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Constructors */</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4458</id>
      <timestamp>2006-05-07T11:43:48Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;/codeblock&gt;

==Transpose==
&lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4459</id>
      <timestamp>2006-05-07T11:45:57Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Multiplication */</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Addition==
&lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
&lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
&lt;/codeblock&gt;

==Multiplication==
&lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;/codeblock&gt;

==Transpose==
&lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4460</id>
      <timestamp>2006-05-07T12:14:23Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;==
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Addition==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    BMatrix Bminus = new BMatrix(B.negate().getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiplication==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
  public BMatrix inverse() {
    
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4461</id>
      <timestamp>2006-05-07T12:15:09Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Addition==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Addition&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtraction==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtraction&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    BMatrix Bminus = new BMatrix(B.negate().getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiplication==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiplication&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
  public BMatrix inverse() {
    
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Addition&gt;&gt;
  &lt;&lt;Subtraction&gt;&gt;
  &lt;&lt;Multiplication&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4462</id>
      <timestamp>2006-05-07T12:23:39Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
  public BMatrix inverse() {
    
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4463</id>
      <timestamp>2006-05-07T12:30:51Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>+ Add to do list.</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
  public BMatrix inverse() {
    
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6396</id>
      <timestamp>2006-06-21T22:43:33Z</timestamp>
      <contributor>
        <username>Leland McInnes</username>
        <id>4</id>
      </contributor>
      <comment>Add code for inverse</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }

  public void setMatrix(int i0, int j0, int i1, int j1, BMatrix X){
    try {
      for (int i = i0; i &lt;= i1; i++) {
        for (int j = j0; j &lt;= j1; j++) {
          this.set(i, j, this.get(i - i0, j - j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
Calculating matrix inverses is difficult. An efficient method is to first calculate the LU decomposition and then use back-substitution to solve for the inverse. Thus we first require an implementation of an LU decomposition.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;LU decomposition&gt;&gt;=
  private BMatrix[] pivot() {
    BMatrix output = new BMatrix(A);
    BMatrix permutation = new BMatrix(this.getRowDim());
    BMatrix parity = new BMatrix({{false}});
    	
    for (int j = 0; j &lt; this.getColDim(); j++) {
      if (!this.get(j, j)) {
        for (int i = j; i &lt; this.getRowDim(); i++) {
          if (this.get(i,j)) {
            output.swapRows(i,j);
            permutation.swapRows(i,j);
            parity.set(0, 0, !parity.get(0, 0));
	    break;
          }
        }    
      }
    }
	
    BMatrix[] result = new BMatrix[3];
    result[0] = output;
    result[1] = permutation;
    result[2] = parity;
	
    return result;
  }
    
  public BMatrix[] LUDecomposition() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }
    BMatrix lower = new BMatrix(this.getRowDim, this.getColDim);
    BMatrix upper = new BMatrix(this.getRowDim);
    	
    BMatrix[] input = pivot();
    	
    // Initialise first column of lower, and first row of upper
    for (int i = 0; i &lt; this.getRowDim; i++) {
      lower.set(i, 0, input[0].get(i, 0));
      upper.set(0, i, input[0].get(0, i));
    }
    	
    for (int i = 0; i &lt; this.getRowDim(); i ++) {
      // Determine column i of lower
      for (int j = i; j &lt; this.getColDim(); j++) {
    	for (int n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(j, n) &amp;&amp; upper.get(n, i)) {
    	    parity = !parity;
    	  }
    	}
    	if (parity) {
    	  lower.set(j, i, input[0].get(j, i));
    	} else {
    	  lower.set(j, i, !input[0].get(j, i))
    	}
      }
      // Determine row i of upper
      for (int j = i + 1; j &lt; this.getRowDim(); j++) {
    	for (int n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(i, n) &amp;&amp; upper.get(n, j)) {
    	    parity = !parity;
          }
    	}
    	if (parity) {
    	  lower.set(i, j, input[0].get(i, j));
    	} else {
    	  lower.set(i, j, !input[0].get(i, j))
    	}    			
      }
    }
    	
    BMatrix[] result = new BMatrix[4];
    result[0] = lower;
    result[1] = upper;
    result[2] = input[1];
    result[3] = input[2];
    	
    return result;
  }
&lt;/codeblock&gt;


The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
  private BMatrix backSub(BMatrix[] luDecomp; BMatrix vector) {
    // Correct vector for permutation in LU decomp:
    b = luDecomp[2].multiply(vector);
    	
    // Solve Ly = b by forward substitition
    BMatrix y = new BMatrix(vector.getRowDim(), vector.getColDim());
    y.set(0, 0, b.get(0, 0));
    	
    for (int i = 1; i &lt; vector.getRowDim(); i++) {
      for (int j = 0, parity = true; j &lt; i; j++) {
    	if (luDecomp[0].get(i,j) &amp;&amp; y.get(j,0) {
    	  parity = !parity;
    	}
      }
      if (parity) {
	y.set(i, 0, b.get(i,0));
      } else {
	y.set(i, 0, !b.get(i,0));
      }
    }
    	
    // Solve Ux = y by back substitution
    BMatrix x = new BMatrix(vector.getRowDim(), vector.getColDim());
    x.set(vector.getRowDim(), 0, x.get(0, 0));
    	
    for (int i = vector.getRowDim(); i &gt;= 0; i--) {
      for (int j = i + 1, parity = true; j &lt; vector.getRowDim(); j++) {
    	if (luDecomp[1].get(i,j) &amp;&amp; x.get(j,0) {
    	    parity = !parity;
    	}
      }
      if (parity) {
	x.set(i, 0, y.get(i,0));
      } else {
	x.set(i, 0, !y.get(i,0));
      }
    }
    
    return x;
  }
    
  public BMatrix inverse() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }    	
    BMatrix[] luDecomp = LUDecomposition(this);
    BMatrix result = BMatrix(this.getRowDim(), this.getColDim());
    BMatrix vector = BMatrix(this.getRowDim(), 1);
    	
    for (int i = 0; i &lt; this.getColDim(); i++) {
      vector.set(i, 0, true);
      BMatrix column = backSub(luDecomp, vector);
      result.setMatrix(0, this.getRowDim(), i, i, column);
    		
      // For next pass
      vector.set(i, 0, false);
    }
    	
    return result; 
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6439</id>
      <timestamp>2006-06-22T04:27:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Inverse */ include LU decomp code chunk in output code</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }

  public void setMatrix(int i0, int j0, int i1, int j1, BMatrix X){
    try {
      for (int i = i0; i &lt;= i1; i++) {
        for (int j = j0; j &lt;= j1; j++) {
          this.set(i, j, this.get(i - i0, j - j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
Calculating matrix inverses is difficult. An efficient method is to first calculate the LU decomposition and then use back-substitution to solve for the inverse. Thus we first require an implementation of an LU decomposition.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;LU decomposition&gt;&gt;=
  private BMatrix[] pivot() {
    BMatrix output = new BMatrix(A);
    BMatrix permutation = new BMatrix(this.getRowDim());
    BMatrix parity = new BMatrix({{false}});
    	
    for (int j = 0; j &lt; this.getColDim(); j++) {
      if (!this.get(j, j)) {
        for (int i = j; i &lt; this.getRowDim(); i++) {
          if (this.get(i,j)) {
            output.swapRows(i,j);
            permutation.swapRows(i,j);
            parity.set(0, 0, !parity.get(0, 0));
	    break;
          }
        }    
      }
    }
	
    BMatrix[] result = new BMatrix[3];
    result[0] = output;
    result[1] = permutation;
    result[2] = parity;
	
    return result;
  }
    
  public BMatrix[] LUDecomposition() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }
    BMatrix lower = new BMatrix(this.getRowDim, this.getColDim);
    BMatrix upper = new BMatrix(this.getRowDim);
    	
    BMatrix[] input = pivot();
    	
    // Initialise first column of lower, and first row of upper
    for (int i = 0; i &lt; this.getRowDim; i++) {
      lower.set(i, 0, input[0].get(i, 0));
      upper.set(0, i, input[0].get(0, i));
    }
    	
    for (int i = 0; i &lt; this.getRowDim(); i ++) {
      // Determine column i of lower
      for (int j = i; j &lt; this.getColDim(); j++) {
    	for (int n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(j, n) &amp;&amp; upper.get(n, i)) {
    	    parity = !parity;
    	  }
    	}
    	if (parity) {
    	  lower.set(j, i, input[0].get(j, i));
    	} else {
    	  lower.set(j, i, !input[0].get(j, i))
    	}
      }
      // Determine row i of upper
      for (int j = i + 1; j &lt; this.getRowDim(); j++) {
    	for (int n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(i, n) &amp;&amp; upper.get(n, j)) {
    	    parity = !parity;
          }
    	}
    	if (parity) {
    	  lower.set(i, j, input[0].get(i, j));
    	} else {
    	  lower.set(i, j, !input[0].get(i, j))
    	}    			
      }
    }
    	
    BMatrix[] result = new BMatrix[4];
    result[0] = lower;
    result[1] = upper;
    result[2] = input[1];
    result[3] = input[2];
    	
    return result;
  }
&lt;/codeblock&gt;


The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;&lt;LU decomposition&gt;&gt;
  private BMatrix backSub(BMatrix[] luDecomp; BMatrix vector) {
    // Correct vector for permutation in LU decomp:
    b = luDecomp[2].multiply(vector);
    	
    // Solve Ly = b by forward substitition
    BMatrix y = new BMatrix(vector.getRowDim(), vector.getColDim());
    y.set(0, 0, b.get(0, 0));
    	
    for (int i = 1; i &lt; vector.getRowDim(); i++) {
      for (int j = 0, parity = true; j &lt; i; j++) {
    	if (luDecomp[0].get(i,j) &amp;&amp; y.get(j,0) {
    	  parity = !parity;
    	}
      }
      if (parity) {
	y.set(i, 0, b.get(i,0));
      } else {
	y.set(i, 0, !b.get(i,0));
      }
    }
    	
    // Solve Ux = y by back substitution
    BMatrix x = new BMatrix(vector.getRowDim(), vector.getColDim());
    x.set(vector.getRowDim(), 0, x.get(0, 0));
    	
    for (int i = vector.getRowDim(); i &gt;= 0; i--) {
      for (int j = i + 1, parity = true; j &lt; vector.getRowDim(); j++) {
    	if (luDecomp[1].get(i,j) &amp;&amp; x.get(j,0) {
    	    parity = !parity;
    	}
      }
      if (parity) {
	x.set(i, 0, y.get(i,0));
      } else {
	x.set(i, 0, !y.get(i,0));
      }
    }
    
    return x;
  }
    
  public BMatrix inverse() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }    	
    BMatrix[] luDecomp = LUDecomposition(this);
    BMatrix result = BMatrix(this.getRowDim(), this.getColDim());
    BMatrix vector = BMatrix(this.getRowDim(), 1);
    	
    for (int i = 0; i &lt; this.getColDim(); i++) {
      vector.set(i, 0, true);
      BMatrix column = backSub(luDecomp, vector);
      result.setMatrix(0, this.getRowDim(), i, i, column);
    		
      // For next pass
      vector.set(i, 0, false);
    }
    	
    return result; 
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>6440</id>
      <timestamp>2006-06-22T04:44:57Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Inverse */ fix typos in code</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }

  public void setMatrix(int i0, int j0, int i1, int j1, BMatrix X){
    try {
      for (int i = i0; i &lt;= i1; i++) {
        for (int j = j0; j &lt;= j1; j++) {
          this.set(i, j, this.get(i - i0, j - j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
Calculating matrix inverses is difficult. An efficient method is to first calculate the LU decomposition and then use back-substitution to solve for the inverse. Thus we first require an implementation of an LU decomposition.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;LU decomposition&gt;&gt;=
  private BMatrix[] pivot() {
    BMatrix output = new BMatrix(A);
    BMatrix permutation = new BMatrix(this.getRowDim());
    boolean[][] parityInitializer = {{false}};
    BMatrix parity = new BMatrix(parityInitializer);
    	
    for (int j = 0; j &lt; this.getColDim(); j++) {
      if (!this.get(j, j)) {
        for (int i = j; i &lt; this.getRowDim(); i++) {
          if (this.get(i,j)) {
            output.swapRows(i,j);
            permutation.swapRows(i,j);
            parity.set(0, 0, !parity.get(0, 0));
	    break;
          }
        }    
      }
    }
	
    BMatrix[] result = new BMatrix[3];
    result[0] = output;
    result[1] = permutation;
    result[2] = parity;
	
    return result;
  }
    
  public BMatrix[] LUDecomposition() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }
    BMatrix lower = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix upper = new BMatrix(this.getRowDim());
    	
    BMatrix[] input = pivot();
    	
    // Initialise first column of lower, and first row of upper
    for (int i = 0; i &lt; this.getRowDim(); i++) {
      lower.set(i, 0, input[0].get(i, 0));
      upper.set(0, i, input[0].get(0, i));
    }
    	
    int n;
    boolean parity;
    for (int i = 0; i &lt; this.getRowDim(); i ++) {
      // Determine column i of lower
      for (int j = i; j &lt; this.getColDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(j, n) &amp;&amp; upper.get(n, i)) {
    	    parity = !parity;
    	  }
    	}
    	if (parity) {
    	  lower.set(j, i, input[0].get(j, i));
    	} else {
    	  lower.set(j, i, !input[0].get(j, i));
    	}
      }
      // Determine row i of upper
      for (int j = i + 1; j &lt; this.getRowDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(i, n) &amp;&amp; upper.get(n, j)) {
    	    parity = !parity;
          }
    	}
    	if (parity) {
    	  lower.set(i, j, input[0].get(i, j));
    	} else {
    	  lower.set(i, j, !input[0].get(i, j));
    	}    			
      }
    }
    	
    BMatrix[] result = new BMatrix[4];
    result[0] = lower;
    result[1] = upper;
    result[2] = input[1];
    result[3] = input[2];
    	
    return result;
  }
&lt;/codeblock&gt;


The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;&lt;LU decomposition&gt;&gt;
  private BMatrix backSub(BMatrix[] luDecomp, BMatrix vector) {
    // Correct vector for permutation in LU decomp:
    BMatrix b = luDecomp[2].mul(vector);
      	
    // Solve Ly = b by forward substitition
    BMatrix y = new BMatrix(vector.getRowDim(), vector.getColDim());
    y.set(0, 0, b.get(0, 0));
      	
    boolean parity;
    int j;
    for (int i = 1; i &lt; vector.getRowDim(); i++) {
      for (parity = true, j = 0; j &lt; i; j++) {
        if (luDecomp[0].get(i,j) &amp;&amp; y.get(j,0)) {
      	  parity = !parity;
        }    
      } 
      if (parity) {
        y.set(i, 0, b.get(i,0));
      } else {
        y.set(i, 0, !b.get(i,0));
      }
    }
    // Solve Ux = y by back substitution
    BMatrix x = new BMatrix(vector.getRowDim(), vector.getColDim());
    x.set(vector.getRowDim(), 0, x.get(0, 0));
      	
    for (int i = vector.getRowDim(); i &gt;= 0; i--) {
      for (parity = true, j = i + 1; j &lt; vector.getRowDim(); j++) {
      	if (luDecomp[1].get(i,j) &amp;&amp; x.get(j,0)) {
          parity = !parity;
        }
      }
      if (parity) {
        x.set(i, 0, y.get(i,0));
      } else {
        x.set(i, 0, !y.get(i,0));
      }
    }
    
    return x;
  }
    
  public BMatrix inverse() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }    	
    BMatrix[] luDecomp = this.LUDecomposition();
    BMatrix result = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix vector = new BMatrix(this.getRowDim(), 1);
    	
    for (int i = 0; i &lt; this.getColDim(); i++) {
      vector.set(i, 0, true);
      BMatrix column = backSub(luDecomp, vector);
      result.setMatrix(0, this.getRowDim(), i, i, column);
    		
      // For next pass
      vector.set(i, 0, false);
    }
    	
    return result; 
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>12836</id>
      <timestamp>2008-03-16T11:05:26Z</timestamp>
      <contributor>
        <ip>78.8.128.223</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }

  public void setMatrix(int i0, int j0, int i1, int j1, BMatrix X){
    try {
      for (int i = i0; i &lt;= i1; i++) {
        for (int j = j0; j &lt;= j1; j++) {
          this.set(i, j, this.get(i - i0, j - j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }    
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
Calculating matrix inverses is difficult. An efficient method is to first calculate the LU decomposition and then use back-substitution to solve for the inverse. Thus we first require an implementation of an LU decomposition.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;LU decomposition&gt;&gt;=
  private BMatrix[] pivot() {
    BMatrix output = new BMatrix(A);
    BMatrix permutation = new BMatrix(this.getRowDim());
    boolean[][] parityInitializer = {{false}};
    BMatrix parity = new BMatrix(parityInitializer);
    	
    for (int j = 0; j &lt; this.getColDim(); j++) {
      if (!this.get(j, j)) {
        for (int i = j; i &lt; this.getRowDim(); i++) {
          if (this.get(i,j)) {
            output.swapRows(i,j);
            permutation.swapRows(i,j);
            parity.set(0, 0, !parity.get(0, 0));
	    break;
          }
        }    
      }
    }
	
    BMatrix[] result = new BMatrix[3];
    result[0] = output;
    result[1] = permutation;
    result[2] = parity;
	
    return result;
  }
    
  public BMatrix[] LUDecomposition() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }
    BMatrix lower = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix upper = new BMatrix(this.getRowDim());
    	
    BMatrix[] input = pivot();
    	
    // Initialise first column of lower, and first row of upper
    for (int i = 0; i &lt; this.getRowDim(); i++) {
      lower.set(i, 0, input[0].get(i, 0));
      upper.set(0, i, input[0].get(0, i));
    }
    	
    int n;
    boolean parity;
    for (int i = 0; i &lt; this.getRowDim(); i ++) {
      // Determine column i of lower
      for (int j = i; j &lt; this.getColDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(j, n) &amp;&amp; upper.get(n, i)) {
    	    parity = !parity;
    	  }
    	}
    	if (parity) {
    	  lower.set(j, i, input[0].get(j, i));
    	} else {
    	  lower.set(j, i, !input[0].get(j, i));
    	}
      }
      // Determine row i of upper
      for (int j = i + 1; j &lt; this.getRowDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(i, n) &amp;&amp; upper.get(n, j)) {
    	    parity = !parity;
          }
    	}
    	if (parity) {
    	  lower.set(i, j, input[0].get(i, j));
    	} else {
    	  lower.set(i, j, !input[0].get(i, j));
    	}    			
      }
    }
    	
    BMatrix[] result = new BMatrix[4];
    result[0] = lower;
    result[1] = upper;
    result[2] = input[1];
    result[3] = input[2];
    	
    return result;
  }
&lt;/codeblock&gt;


The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;&lt;LU decomposition&gt;&gt;
  private BMatrix backSub(BMatrix[] luDecomp, BMatrix vector) {
    // Correct vector for permutation in LU decomp:
    BMatrix b = luDecomp[2].mul(vector);
      	
    // Solve Ly = b by forward substitition
    BMatrix y = new BMatrix(vector.getRowDim(), vector.getColDim());
    y.set(0, 0, b.get(0, 0));
      	
    boolean parity;
    int j;
    for (int i = 1; i &lt; vector.getRowDim(); i++) {
      for (parity = true, j = 0; j &lt; i; j++) {
        if (luDecomp[0].get(i,j) &amp;&amp; y.get(j,0)) {
      	  parity = !parity;
        }    
      } 
      if (parity) {
        y.set(i, 0, b.get(i,0));
      } else {
        y.set(i, 0, !b.get(i,0));
      }
    }
    // Solve Ux = y by back substitution
    BMatrix x = new BMatrix(vector.getRowDim(), vector.getColDim());
    x.set(vector.getRowDim(), 0, x.get(0, 0));
      	
    for (int i = vector.getRowDim(); i &gt;= 0; i--) {
      for (parity = true, j = i + 1; j &lt; vector.getRowDim(); j++) {
      	if (luDecomp[1].get(i,j) &amp;&amp; x.get(j,0)) {
          parity = !parity;
        }
      }
      if (parity) {
        x.set(i, 0, y.get(i,0));
      } else {
        x.set(i, 0, !y.get(i,0));
      }
    }
    
    return x;
  }
    
  public BMatrix inverse() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }    	
    BMatrix[] luDecomp = this.LUDecomposition();
    BMatrix result = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix vector = new BMatrix(this.getRowDim(), 1);
    	
    for (int i = 0; i &lt; this.getColDim(); i++) {
      vector.set(i, 0, true);
      BMatrix column = backSub(luDecomp, vector);
      result.setMatrix(0, this.getRowDim(), i, i, column);
    		
      // For next pass
      vector.set(i, 0, false);
    }
    	
    return result; 
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>12837</id>
      <timestamp>2008-03-16T18:08:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/78.8.128.223|78.8.128.223]] ([[User_talk:78.8.128.223|78.8.128.223]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">{{develop}}
'''Binary matrix''' is a [http://en.wikipedia.org/wiki/Java_programming_language Java] class that deals with binary matrix operation. It implements basic matrix operations such as addition, subtraction, and multiplication. This package may be used later in many applications such as Hamming (7, 4) code.

For convenience, we assume that '''A''' denotes the given binary matrix. '''B''' denotes the operand matrix .

To do:
* getDeterminant: returns the determinant.
* inverse: matrix inversion
* random: generates a matrix with random elements

==Data==
Binary matrix is stored as a two-dimensional array of  ''boolean'' values, because binary matrix is composed of either 0 or 1. &lt;code&gt;false&lt;/code&gt; represents 0, and &lt;code&gt;true&lt;/code&gt; represents 1.
* &lt;code&gt;row&lt;/code&gt; is the number of rows.
* &lt;code&gt;col&lt;/code&gt; is the number of columns.
* &lt;code&gt;A&lt;/code&gt; is a two-dimensional array of boolean values.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private boolean A[][];
  private int row;
  private int col;
&lt;/codeblock&gt;

==Constructors==
* &lt;code&gt;BMatrix(int m, int n)&lt;/code&gt; initializes an m-by-n zero binary matrix.
* &lt;code&gt;BMatrix(int input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional integer array.
* &lt;code&gt;BMatrix(boolean input[][])&lt;/code&gt; initializes a binary matrix from a two-dimensional boolean array.
* &lt;code&gt;BMatrix(int n)&lt;/code&gt; initializes an n-by-n identity matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public BMatrix(int m, int n) {
    this.row = m;
    this.col = n;
    this.A = new boolean[m][n];
    for (int i = 0; i &lt; m; i++) {
      for (int j = 0; j &lt; n; j++) {
        A[i][j] = false;
      }
    }
  }

  public BMatrix(int input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (input[i][j] == 0) {
          A[i][j] = false;
        } else {
          A[i][j] = true;
        }
      }
    }
  }

  public BMatrix(boolean input[][]) {
    this.row = input.length;
    this.col = input[0].length;
    this.A = new boolean[this.row][this.col];
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        A[i][j] = input[i][j];
      }
    }
  }

  public BMatrix(int n) {
    this(n, n);
    for (int i = 0; i &lt; n; i++) {
      this.set(i, i, true);
    }
  }
&lt;/codeblock&gt;

==Getter==
* The &lt;code&gt;getRowDim&lt;/code&gt; method returns the row dimension.
* The &lt;code&gt;getColDim&lt;/code&gt; method returns the column dimension.
* The &lt;code&gt;getArray&lt;/code&gt; method returns the internal two-dimensional array.
* The &lt;code&gt;get(i, j)&lt;/code&gt; method returns a single element &lt;code&gt;A[i, j]&lt;/code&gt;.
* The &lt;code&gt;getMatrix(i0, j0, i1, j1)&lt;/code&gt; method returns a submatrix &lt;code&gt;A[i0:i1, j0:j1]&lt;/code&gt;. If the index is out of bound, we raise an &lt;code&gt;ArrayIndexOutOfBoundsException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public int getRowDim() {
    return this.row;
  }

  public int getColDim() {
    return this.col;
  }

  public boolean[][] getArray() {
    return this.A;
  }

  public boolean get(int i, int j) {
    return A[i][j];
  }

  public BMatrix getMatrix(int i0, int j0, int i1, int j1){
    int row = i1 - i0 + 1;
    int col = j1 - j0 + 1;
    BMatrix result = new BMatrix(row, col);
    try {
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          result.set(i, j, this.get(i + i0, j + j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Setter==
* The &lt;code&gt;set(i, j, value)&lt;/code&gt; method sets the value of &lt;code&gt;A[i, j]&lt;/code&gt; to &lt;code&gt;value&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void set(int i, int j, boolean value) {
    A[i][j] = value;
  }

  public void setMatrix(int i0, int j0, int i1, int j1, BMatrix X){
    try {
      for (int i = i0; i &lt;= i1; i++) {
        for (int j = j0; j &lt;= j1; j++) {
          this.set(i, j, this.get(i - i0, j - j0));
        }
      }
    } catch(ArrayIndexOutOfBoundsException e) {
      throw new ArrayIndexOutOfBoundsException(&quot;Submatrix indices.&quot;);
    }
    return result;
  }
&lt;/codeblock&gt;

==Equals==
The &lt;code&gt;equals&lt;/code&gt; method checks whether '''A''' = '''B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Equals&gt;&gt;=
  public boolean equals(BMatrix B) {
    if ((this.row != B.getRowDim()) ||(this.col != B.getColDim())) {
      return false;
    } else {
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          if (this.get(i, j) != B.get(i, j)) {
            return false;
          }
        }
      }
    }
    return true;
  }
&lt;/codeblock&gt;

==Negate==
The &lt;code&gt;negate&lt;/code&gt; method toggles every element in '''A'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Negate&gt;&gt;=
  public void negate() {
    for (int i = 0; i &lt; this.row; i++) {
      for (int j = 0; j &lt; this.col; j++) {
        if (this.get(i, j)) {
          this.set(i, j, false);
        } else {
          this.set(i, j, true);
        }
      }
    }
  }
&lt;/codeblock&gt;

==Add==
The &lt;code&gt;add&lt;/code&gt; method computes '''A''' + '''B'''. As the addition is defined on binary matrices, it can be simplified to bitwise operation.
* If &lt;code&gt;A[i,j]&lt;/code&gt; is &lt;code&gt;true&lt;/code&gt;. Then &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just inverting &lt;code&gt;B[i,j]&lt;/code&gt;. 
* Otherwise, &lt;code&gt;A[i,j] + B[i,j]&lt;/code&gt; is just same as &lt;code&gt;B[i,j]&lt;/code&gt;.
If the dimensions of '''A''' and '''B''' are different, we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Add&gt;&gt;=
  public BMatrix add(BMatrix B) {
    int bCol = B.getColDim();
    int bRow = B.getRowDim();
    if (bCol == this.col &amp;&amp; bRow == this.row) {
      BMatrix result = new BMatrix(B.getArray());
      for (int i = 0; i &lt; this.row; i++) {
        for (int j = 0; j &lt; this.col; j++) {
          // Invert the value when the operand is true.
	  if (B.get(i,j)) {
            result.set(i, j, !this.get(i,j));
          } else {
            result.set(i, j, this.get(i, j));
          }
        }
      }
      return result;
    } else {
      throw new IllegalArgumentException(&quot;Different dimensions.&quot;);
    }
  }
&lt;/codeblock&gt;

==Subtract==
The &lt;code&gt;sub&lt;/code&gt; method computes '''A''' - '''B'''. Internally, it runs &lt;code&gt;negate&lt;/code&gt; method to obtain '''-B'''.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Subtract&gt;&gt;=
  public BMatrix sub(BMatrix B) {
    B.negate();
    BMatrix Bminus = new BMatrix(B.getArray());
    BMatrix result = this.add(Bminus);
    return result;
  }
&lt;/codeblock&gt;

==Multiply==
The &lt;code&gt;mul&lt;/code&gt; method computes '''A''' * '''B'''. If '''A''' is an ''m''-by-''n'' matrix and '''B''' is an ''n''-by-''p'' matrix, then their product is an ''m''-by-''p'' matrix. The product is given by 
:&lt;math&gt; (AB)_{ij} = \sum_{r=1}^n a_{ir}b_{rj} = a_{i1}b_{1j} + a_{i2}b_{2j} + \cdots + a_{in}b_{nj}. &lt;/math&gt;
If the number of columns of '''A''' is different from the number of rows of '''B''', we raise an &lt;code&gt;IllegalArgumentException&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Multiply&gt;&gt;=
  public BMatrix mul(BMatrix B) {
    int bRow = B.getRowDim();
    int bCol = B.getColDim();
    if (bRow != this.col) {
      throw new IllegalArgumentException(this.row + &quot;-by-&quot; + this.col + &quot;, &quot; + bRow);
    } else {
      BMatrix result = new BMatrix(this.getRowDim(), bCol);
      for (int i = 0; i &lt; this.getRowDim(); i++) {
        for (int j = 0; j &lt; bCol; j++) {
          for (int k = 0; k &lt; bRow; k++) {
            // Toggle the output only when two inputs are 1.
            if (this.get(i, k) &amp;&amp; B.get(k, j)) {
              result.set(i, j, !result.get(i, j));
            }
          }
        }
      }
      return result;
    }
  }
&lt;/codeblock&gt;

==Inverse==
Calculating matrix inverses is difficult. An efficient method is to first calculate the LU decomposition and then use back-substitution to solve for the inverse. Thus we first require an implementation of an LU decomposition.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;LU decomposition&gt;&gt;=
  private BMatrix[] pivot() {
    BMatrix output = new BMatrix(A);
    BMatrix permutation = new BMatrix(this.getRowDim());
    boolean[][] parityInitializer = {{false}};
    BMatrix parity = new BMatrix(parityInitializer);
    	
    for (int j = 0; j &lt; this.getColDim(); j++) {
      if (!this.get(j, j)) {
        for (int i = j; i &lt; this.getRowDim(); i++) {
          if (this.get(i,j)) {
            output.swapRows(i,j);
            permutation.swapRows(i,j);
            parity.set(0, 0, !parity.get(0, 0));
	    break;
          }
        }    
      }
    }
	
    BMatrix[] result = new BMatrix[3];
    result[0] = output;
    result[1] = permutation;
    result[2] = parity;
	
    return result;
  }
    
  public BMatrix[] LUDecomposition() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }
    BMatrix lower = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix upper = new BMatrix(this.getRowDim());
    	
    BMatrix[] input = pivot();
    	
    // Initialise first column of lower, and first row of upper
    for (int i = 0; i &lt; this.getRowDim(); i++) {
      lower.set(i, 0, input[0].get(i, 0));
      upper.set(0, i, input[0].get(0, i));
    }
    	
    int n;
    boolean parity;
    for (int i = 0; i &lt; this.getRowDim(); i ++) {
      // Determine column i of lower
      for (int j = i; j &lt; this.getColDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(j, n) &amp;&amp; upper.get(n, i)) {
    	    parity = !parity;
    	  }
    	}
    	if (parity) {
    	  lower.set(j, i, input[0].get(j, i));
    	} else {
    	  lower.set(j, i, !input[0].get(j, i));
    	}
      }
      // Determine row i of upper
      for (int j = i + 1; j &lt; this.getRowDim(); j++) {
    	for (n = 0, parity = true; n &lt; i; n++) {
    	  if (lower.get(i, n) &amp;&amp; upper.get(n, j)) {
    	    parity = !parity;
          }
    	}
    	if (parity) {
    	  lower.set(i, j, input[0].get(i, j));
    	} else {
    	  lower.set(i, j, !input[0].get(i, j));
    	}    			
      }
    }
    	
    BMatrix[] result = new BMatrix[4];
    result[0] = lower;
    result[1] = upper;
    result[2] = input[1];
    result[3] = input[2];
    	
    return result;
  }
&lt;/codeblock&gt;


The &lt;code&gt;inverse&lt;/code&gt; method returns '''A'''&lt;sup&gt;-1&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Inverse&gt;&gt;=
&lt;&lt;LU decomposition&gt;&gt;
  private BMatrix backSub(BMatrix[] luDecomp, BMatrix vector) {
    // Correct vector for permutation in LU decomp:
    BMatrix b = luDecomp[2].mul(vector);
      	
    // Solve Ly = b by forward substitition
    BMatrix y = new BMatrix(vector.getRowDim(), vector.getColDim());
    y.set(0, 0, b.get(0, 0));
      	
    boolean parity;
    int j;
    for (int i = 1; i &lt; vector.getRowDim(); i++) {
      for (parity = true, j = 0; j &lt; i; j++) {
        if (luDecomp[0].get(i,j) &amp;&amp; y.get(j,0)) {
      	  parity = !parity;
        }    
      } 
      if (parity) {
        y.set(i, 0, b.get(i,0));
      } else {
        y.set(i, 0, !b.get(i,0));
      }
    }
    // Solve Ux = y by back substitution
    BMatrix x = new BMatrix(vector.getRowDim(), vector.getColDim());
    x.set(vector.getRowDim(), 0, x.get(0, 0));
      	
    for (int i = vector.getRowDim(); i &gt;= 0; i--) {
      for (parity = true, j = i + 1; j &lt; vector.getRowDim(); j++) {
      	if (luDecomp[1].get(i,j) &amp;&amp; x.get(j,0)) {
          parity = !parity;
        }
      }
      if (parity) {
        x.set(i, 0, y.get(i,0));
      } else {
        x.set(i, 0, !y.get(i,0));
      }
    }
    
    return x;
  }
    
  public BMatrix inverse() {
    if (this.getRowDim() != this.getColDim()) {
      throw new UnsupportedOperationException(&quot;Matrix is not square&quot;);
    }    	
    BMatrix[] luDecomp = this.LUDecomposition();
    BMatrix result = new BMatrix(this.getRowDim(), this.getColDim());
    BMatrix vector = new BMatrix(this.getRowDim(), 1);
    	
    for (int i = 0; i &lt; this.getColDim(); i++) {
      vector.set(i, 0, true);
      BMatrix column = backSub(luDecomp, vector);
      result.setMatrix(0, this.getRowDim(), i, i, column);
    		
      // For next pass
      vector.set(i, 0, false);
    }
    	
    return result; 
  }
&lt;/codeblock&gt;

==Transpose==
The &lt;code&gt;transpose&lt;/code&gt; method returns the transpose matrix '''A'''&lt;sup&gt;T&lt;/sup&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Transpose&gt;&gt;=
  public BMatrix transpose() {
    BMatrix X = new BMatrix(this.col, this.row);
    for (int i = 0; i &lt; this.col; i++) {
      for (int j = 0; j &lt; this.row; j++) {
        X.A[i][j] = this.A[j][i];
      }
    }
    return X;
  }
&lt;/codeblock&gt;

==String representation==
We override the &lt;code&gt;toString&lt;/code&gt; method for string representation of a binary matrix.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_representation&gt;&gt;=
  public String toString() {
    String result = new String();
      for (int i = 0; i &lt; row; i++) {
        for (int j = 0; j &lt; col; j++) {
          if (this.get(i, j)) {
            result += &quot;1 &quot;;
          } else {
            result += &quot;0 &quot;;
          }
        }
       result += &quot;\n&quot;;
      }
    return result;
  }
&lt;/codeblock&gt;

==Test==
This chunk is used to test the whole class.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    int a[][] = {{1, 0, 0}, {1, 1, 1}, {0, 1, 0}};
    BMatrix A = new BMatrix(a);
  }
&lt;/codeblock&gt;

==The Whole Class==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BMatrix.java&gt;&gt;=
public class BMatrix {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Equals&gt;&gt;
  &lt;&lt;Negate&gt;&gt;
  &lt;&lt;Add&gt;&gt;
  &lt;&lt;Subtract&gt;&gt;
  &lt;&lt;Multiply&gt;&gt;
  &lt;&lt;Inverse&gt;&gt;
  &lt;&lt;Transpose&gt;&gt;
  &lt;&lt;String_representation&gt;&gt;
  &lt;&lt;Test&gt;&gt;
  &lt;&lt;Data&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Matrix algebra]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
  </page>
  <page>
    <title>Binary numeral conversion (Python)</title>
    <id>1985</id>
    <revision>
      <id>4612</id>
      <timestamp>2006-05-12T23:52:27Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>commonly implemented function in Python. this version should be faster than most</comment>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python has no built-in support for going the other way: displaying an integer in binary.

Python does have the ability to display an integer in hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the hexadecimal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
hex2bin = {'0': '0000', '1': '0001', '2': '0010', '3': '0011', '4': '0100',
 '5': '0101', '6': '0110', '7': '0111', '8': '1000', '9': '1001', 'a': '1010',
 'b': '1011', 'c': '1100', 'd': '1101', 'e': '1110', 'f': '1111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of four binary digits
    s = [hex2bin[hexdigit] for hexdigit in (&quot;%x&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7078</id>
      <timestamp>2006-07-27T00:10:47Z</timestamp>
      <contributor>
        <ip>68.40.206.30</ip>
      </contributor>
      <comment>added alternate method</comment>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python has no built-in support for going the other way: displaying an integer in binary.

Python does have the ability to display an integer in hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the hexadecimal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
hex2bin = {'0': '0000', '1': '0001', '2': '0010', '3': '0011', '4': '0100',
 '5': '0101', '6': '0110', '7': '0111', '8': '1000', '9': '1001', 'a': '1010',
 'b': '1011', 'c': '1100', 'd': '1101', 'e': '1110', 'f': '1111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of four binary digits
    s = [hex2bin[hexdigit] for hexdigit in (&quot;%x&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10700</id>
      <timestamp>2007-07-17T19:09:02Z</timestamp>
      <contributor>
        <ip>207.108.42.8</ip>
      </contributor>
      <comment>in alt_bin() corrected call to bin() to call alt_bin()</comment>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python has no built-in support for going the other way: displaying an integer in binary.

Python does have the ability to display an integer in hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the hexadecimal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
hex2bin = {'0': '0000', '1': '0001', '2': '0010', '3': '0011', '4': '0100',
 '5': '0101', '6': '0110', '7': '0111', '8': '1000', '9': '1001', 'a': '1010',
 'b': '1011', 'c': '1100', 'd': '1101', 'e': '1110', 'f': '1111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of four binary digits
    s = [hex2bin[hexdigit] for hexdigit in (&quot;%x&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + alt_bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14310</id>
      <timestamp>2008-08-17T03:23:24Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>octal would be shorter than hex</comment>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python has no built-in support for going the other way: displaying an integer in binary.

Python does have the ability to display an integer in octal (with &lt;tt&gt;&quot;%o&quot; % n&lt;/tt&gt;) or hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the octal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
oct2bin = {'0': '000', '1': '001', '2': '010', '3': '011', '4': '100',
 '5': '101', '6': '110', '7': '111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of three binary digits
    s = [oct2bin[octdigit] for octdigit in (&quot;%o&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + alt_bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15374</id>
      <timestamp>2008-10-31T03:44:39Z</timestamp>
      <contributor>
        <ip>24.130.24.6</ip>
      </contributor>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python has no built-in support for going the other way: displaying an integer in binary. Python 3.0 tenatively has '''bin''', '''oct''', and '''hex''' functions in the built-in namespace.

Python does have the ability to display an integer in octal (with &lt;tt&gt;&quot;%o&quot; % n&lt;/tt&gt;) or hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the octal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
oct2bin = {'0': '000', '1': '001', '2': '010', '3': '011', '4': '100',
 '5': '101', '6': '110', '7': '111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of three binary digits
    s = [oct2bin[octdigit] for octdigit in (&quot;%o&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + alt_bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15375</id>
      <timestamp>2008-10-31T04:24:45Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>tweak</comment>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python 2.0 and earlier has no built-in support for going the other way: displaying an integer in binary. Python 3.0 tentatively has '''bin''', '''oct''', and '''hex''' functions in the built-in namespace.

Python does have the ability to display an integer in octal (with &lt;tt&gt;&quot;%o&quot; % n&lt;/tt&gt;) or hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the octal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
oct2bin = {'0': '000', '1': '001', '2': '010', '3': '011', '4': '100',
 '5': '101', '6': '110', '7': '111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of three binary digits
    s = [oct2bin[octdigit] for octdigit in (&quot;%o&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + alt_bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15712</id>
      <timestamp>2008-12-30T03:50:23Z</timestamp>
      <contributor>
        <ip>71.141.116.30</ip>
      </contributor>
      <text xml:space="preserve">It is easy to create an integer from a binary numeral in Python. The expression

&lt;codeblock language=python&gt;
int(&quot;10111001&quot;, base=2)
&lt;/codeblock&gt;

evaluates to 185 as expected. However, Python 2.x and earlier has no built-in support for going the other way: displaying an integer in binary. Python 2.6 and above has '''bin''', '''oct''', and '''hex''' functions in the built-in namespace.

Python does have the ability to display an integer in octal (with &lt;tt&gt;&quot;%o&quot; % n&lt;/tt&gt;) or hexadecimal (with &lt;tt&gt;&quot;%x&quot; % n&lt;/tt&gt;). We can utilize this to produce the binary representation by translating the octal digits one by one. We create a lookup table:

&lt;codeblock language=python&gt;
&lt;&lt;lookup table&gt;&gt;=
oct2bin = {'0': '000', '1': '001', '2': '010', '3': '011', '4': '100',
 '5': '101', '6': '110', '7': '111'}
&lt;/codeblock&gt;

The implementation is straightforward:

&lt;codeblock language=python&gt;
&lt;&lt;main function&gt;&gt;=
def bin(n):
    if n &lt; 0:
        return &quot;-&quot; + bin(-n)
    # Build list of groups of three binary digits
    s = [oct2bin[octdigit] for octdigit in (&quot;%o&quot; % n)]
    # Merge list to single string and remove leading zeros
    s = &quot;&quot;.join(s).lstrip(&quot;0&quot;)
    return s or &quot;0&quot;
&lt;/codeblock&gt;

A more canonical version that does not utilize a lookup table is also simple to implement. This method goes through the bits of the integer from least significant bit to most significant bit by examining whether the number is even or odd, then bit-shifting right one position. As we step through the bits by doing this, we also prepend a '1' or '0' to a string based on whether the number is even or odd.

&lt;codeblock language=python&gt;
&lt;&lt;alternate function&gt;&gt;=
def alt_bin(n):
    if n &lt; 0:
        return &quot;-&quot; + alt_bin(-n)
    s = ''
    while n != 0:
        if n % 2 == 0: bit = '0'
        else: bit = '1'
        s = bit + s
        n &gt;&gt;= 1
    return s or '0'
&lt;/codeblock&gt;

A simple test driver:

&lt;codeblock language=python&gt;
&lt;&lt;test&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    for i in range(-50, 50):
        assert i == int(bin(i), 2)
        assert i == int(alt_bin(i), 2)
&lt;/codeblock&gt;

&lt;codeblock language=python&gt;
&lt;&lt;binary.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;main function&gt;&gt;
&lt;&lt;alternate function&gt;&gt;
&lt;&lt;test&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search (C Plus Plus)</title>
    <id>2273</id>
    <revision>
      <id>5953</id>
      <timestamp>2006-06-05T21:56:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial implementation for generic arrays, generic random access containers, simple test code for int arrays and vectors</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator. Our comparison operator defaults to &quot;std::less&lt;T&gt;&quot;, which is just the ordinary &quot;&lt;&quot; operator as applied to objects of type T.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less = std::less&lt;T&gt; &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

We need the algorithm header for &lt;code&gt;std::less&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less = std::less&lt;T&gt; &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != a + num_elements ||
        binary_search(v.begin(), v.end(), num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5954</id>
      <timestamp>2006-06-05T21:57:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix extension</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator. Our comparison operator defaults to &quot;std::less&lt;T&gt;&quot;, which is just the ordinary &quot;&lt;&quot; operator as applied to objects of type T.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less = std::less&lt;T&gt; &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

We need the algorithm header for &lt;code&gt;std::less&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less = std::less&lt;T&gt; &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != a + num_elements ||
        binary_search(v.begin(), v.end(), num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5955</id>
      <timestamp>2006-06-05T22:01:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add brace, can't use default template parameters</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != a + num_elements ||
        binary_search(v.begin(), v.end(), num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5956</id>
      <timestamp>2006-06-05T22:01:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Header files</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val)
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != a + num_elements ||
        binary_search(v.begin(), v.end(), num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5957</id>
      <timestamp>2006-06-05T22:04:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>{</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != a + num_elements ||
        binary_search(v.begin(), v.end(), num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5958</id>
      <timestamp>2006-06-05T22:05:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fixes</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;binary search&gt;&gt;
&lt;&lt;generic binary search&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        general_binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    if (general_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        general_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5959</id>
      <timestamp>2006-06-05T22:07:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Avoid name conflict with std::binary_search</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;generic binary search&gt;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    int present_val = a[rand() % num_elements];
    int* found_at = binary_search(a, a + num_elements, present_val);
    if (found_at == a + num_elements || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    present_val = v[rand() % num_elements];
    std::vector&lt;int&gt;::iterator found_at =
        generic_binary_search(v.begin(), v.end(), present_val);
    if (found_at == v.end() || *found_at != present_val) {
        puts(&quot;ERROR&quot;);
    }
    if (generic_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        generic_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5960</id>
      <timestamp>2006-06-05T22:09:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Prevent redecl error</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;generic binary search&gt;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    {
        int present_val = a[rand() % num_elements];
        int* found_at = generic_binary_search(a, a + num_elements, present_val);
        if (found_at == a + num_elements || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    {
        int present_val = v[rand() % num_elements];
        std::vector&lt;int&gt;::iterator found_at =
            generic_binary_search(v.begin(), v.end(), present_val);
        if (found_at == v.end() || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    if (generic_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        generic_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5961</id>
      <timestamp>2006-06-05T22:11:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Binary Search (C Plus Plus)]] moved to [[Binary search (C Plus Plus)]]: Capitalization convention</comment>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;stdlib.h&gt;  // atoi

&lt;&lt;generic binary search&gt;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    {
        int present_val = a[rand() % num_elements];
        int* found_at = generic_binary_search(a, a + num_elements, present_val);
        if (found_at == a + num_elements || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    {
        int present_val = v[rand() % num_elements];
        std::vector&lt;int&gt;::iterator found_at =
            generic_binary_search(v.begin(), v.end(), present_val);
        if (found_at == v.end() || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    if (generic_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        generic_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14959</id>
      <timestamp>2008-10-12T04:34:12Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename compare_less &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

For convenience, we supply an overload that doesn't take a comparison operator, just using &quot;&lt;&quot;. We can't use &lt;code&gt;std::less&lt;/code&gt; because C++ doesn't support default template parameters on functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;=
template&lt; typename T, typename IterT &gt;
IterT generic_binary_search(IterT begin, IterT end, T target) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (target &lt; *middle)
            end = middle;
        else if (*middle &lt; target)
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;cstdlib&gt;  // atoi

&lt;&lt;generic binary search&gt;&gt;
&lt;&lt;generic binary search with two template arguments&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = std::atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    {
        int present_val = a[rand() % num_elements];
        int* found_at = generic_binary_search(a, a + num_elements, present_val);
        if (found_at == a + num_elements || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    {
        int present_val = v[rand() % num_elements];
        std::vector&lt;int&gt;::iterator found_at =
            generic_binary_search(v.begin(), v.end(), present_val);
        if (found_at == v.end() || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    if (generic_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        generic_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17116</id>
      <timestamp>2011-05-04T15:50:52Z</timestamp>
      <contributor>
        <username>Dleinhaeuser</username>
        <id>2271</id>
      </contributor>
      <text xml:space="preserve">{{Category:Binary search}}
C++ has a template-based [http://www.sgi.com/tech/stl/binary_search.html binary_search()] in its standard library, which is what should normally be used, as well as the function pointer based [http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch] inherited from C. A number of simple C implementations that also compile as C++ are described at [[Binary search (C)]].

In C++, we can take advantage of templates to easily generalize the C implementation described at [[Binary search (C)]] to arrays of any type. We simply replace the element type everywhere by a template parameter &quot;T&quot; and replace &quot;&lt;&quot; by a user-supplied less-than comparison operator.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;array binary search&gt;&gt;=
template&lt; typename T, typename compare_less &gt;
int array_binary_search(T a[], int low, int high, T target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (compare_less(target, a[middle]))
            high = middle - 1;
        else if (compare_less(a[middle], target))
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

But we need not stop at arrays &amp;mdash; we can generalize the implementation even further to any container permitting random access, such as &lt;code&gt;std::vector&lt;/code&gt;.  The conventional way of doing this, as done by the standard library's &lt;code&gt;binary_search&lt;/code&gt;, is to pass in a begin and end iterator specifying the range. This is very similar to the above implementation, but with the indexes low and high and the return value replaced by iterators. Also, by convention, we make &quot;end&quot; point one past the last element to be searched instead of using an inclusive range, resulting in each instance of &quot;end&quot; being adjusted by 1; if the element is not found we can return the initial value of end, since this is outside the range being searched and so not a normal return value.
The optional &lt;code&gt;compare_less&lt;/code&gt; parameter can be used to specifiy a custom comparison operation.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;generic binary search&gt;&gt;=
template&lt; typename T, typename IterT, typename CmpT &gt;
IterT generic_binary_search(IterT begin, IterT end, T target, CmpT compare_less = std::less&lt; T &gt;()) {
    IterT initial_end = end;
    while (begin &lt; end) {
        IterT middle = begin + (end - begin - 1)/2;
        if (compare_less(target, *middle))
            end = middle;
        else if (compare_less(*middle, target))
            begin = middle + 1;
        else
            return middle;
    }
    return initial_end;
}
&lt;/codeblock&gt;

This simple test code tries out the final binary search on an array and a vector, using &lt;code&gt;std::sort&lt;/code&gt; to sort them first:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;binary_search.cpp&gt;&gt;=
#include &lt;algorithm&gt;
#include &lt;functional&gt; // std::less
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;cstdlib&gt;  // atoi

&lt;&lt;generic binary search&gt;&gt;

int main(int argc, char* argv[]) {
    int num_elements = std::atoi(argv[1]);
    int* a = new int[num_elements];
    std::vector&lt;int&gt; v;
    for(int i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
        v.push_back(a[i]);
    }
    std::sort(a, a + num_elements);
    std::sort(v.begin(), v.end());

    {
        int present_val = a[rand() % num_elements];
        int* found_at = generic_binary_search(a, a + num_elements, present_val);
        if (found_at == a + num_elements || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    {
        int present_val = v[rand() % num_elements];
        std::vector&lt;int&gt;::iterator found_at =
            generic_binary_search(v.begin(), v.end(), present_val);
        if (found_at == v.end() || *found_at != present_val) {
            puts(&quot;ERROR&quot;);
        }
    }
    if (generic_binary_search(a, a + num_elements, num_elements/7) != a + num_elements ||
        generic_binary_search(v.begin(), v.end(),  num_elements/7) != v.end())
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

[[Category:Binary search]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search (C)</title>
    <id>3803</id>
    <revision>
      <id>5939</id>
      <timestamp>2006-06-05T19:32:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial recursive implementation, iterative implementation, test code, description, cats, link bsearch</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int[] a, int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int[] a, int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(void* left, void* right) {
    return *((int*)left) - *((int*)right);
}

int main() {
    int* a = (int*)malloc(100000*sizeof(int));
    int i;
    for(i=0; i&lt;100000; i++) {
        do {
            a[i] = rand() % 10000;
        } while(a[i] == 2000);
    }
    qsort(a, 100000, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % 100000];
        int found_at = binary_search(a, 0, 99999, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, 99999, 2000)  != -1 ||
        binary_search(a, 0, 99999, -1)    != -1 ||
        binary_search(a, 0, 99999, 10001) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5940</id>
      <timestamp>2006-06-05T19:34:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Mixing up my languages again</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int[] a, int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(void* left, void* right) {
    return *((int*)left) - *((int*)right);
}

int main() {
    int* a = (int*)malloc(100000*sizeof(int));
    int i;
    for(i=0; i&lt;100000; i++) {
        do {
            a[i] = rand() % 10000;
        } while(a[i] == 2000);
    }
    qsort(a, 100000, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % 100000];
        int found_at = binary_search(a, 0, 99999, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, 99999, 2000)  != -1 ||
        binary_search(a, 0, 99999, -1)    != -1 ||
        binary_search(a, 0, 99999, 10001) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5941</id>
      <timestamp>2006-06-05T19:36:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix other too</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(void* left, void* right) {
    return *((int*)left) - *((int*)right);
}

int main() {
    int* a = (int*)malloc(100000*sizeof(int));
    int i;
    for(i=0; i&lt;100000; i++) {
        do {
            a[i] = rand() % 10000;
        } while(a[i] == 2000);
    }
    qsort(a, 100000, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % 100000];
        int found_at = binary_search(a, 0, 99999, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, 99999, 2000)  != -1 ||
        binary_search(a, 0, 99999, -1)    != -1 ||
        binary_search(a, 0, 99999, 10001) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5942</id>
      <timestamp>2006-06-05T19:37:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+#include &lt;stdlib.h&gt;</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(void* left, void* right) {
    return *((int*)left) - *((int*)right);
}

int main() {
    int* a = (int*)malloc(100000*sizeof(int));
    int i;
    for(i=0; i&lt;100000; i++) {
        do {
            a[i] = rand() % 10000;
        } while(a[i] == 2000);
    }
    qsort(a, 100000, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % 100000];
        int found_at = binary_search(a, 0, 99999, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, 99999, 2000)  != -1 ||
        binary_search(a, 0, 99999, -1)    != -1 ||
        binary_search(a, 0, 99999, 10001) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5943</id>
      <timestamp>2006-06-05T19:37:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>consts</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main() {
    int* a = (int*)malloc(100000*sizeof(int));
    int i;
    for(i=0; i&lt;100000; i++) {
        do {
            a[i] = rand() % 10000;
        } while(a[i] == 2000);
    }
    qsort(a, 100000, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % 100000];
        int found_at = binary_search(a, 0, 99999, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, 99999, 2000)  != -1 ||
        binary_search(a, 0, 99999, -1)    != -1 ||
        binary_search(a, 0, 99999, 10001) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5944</id>
      <timestamp>2006-06-05T19:41:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Generalize</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);
    for(i=0; i&lt;10; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    ;
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5945</id>
      <timestamp>2006-06-05T19:44:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Timing</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);
    clock_t start = clock();
    for(i=0; i&lt;100; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;, (clock() - start)/(CLOCKS_PER_SEC)/100);
    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5946</id>
      <timestamp>2006-06-05T19:45:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Header</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;100; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;, (clock() - start)/(CLOCKS_PER_SEC)/100);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5947</id>
      <timestamp>2006-06-05T19:46:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, cast</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;100; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/100);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5948</id>
      <timestamp>2006-06-05T19:48:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>More iterations</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;50000; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/50000);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation. Because binary search is very fast, we must repeat the test many times to get useful measurements with the resolution of the typical &lt;code&gt;clock()&lt;/code&gt; timer.

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5949</id>
      <timestamp>2006-06-05T19:52:58Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Performance</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;50000; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/50000);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation. Because binary search is very fast, we must repeat the test many times to get useful measurements with the resolution of the typical &lt;code&gt;clock()&lt;/code&gt; timer.

== Performance ==

We measured the performance of binary search using the above test code on lists of a number of sizes. The code was compiled using gcc with the &quot;-O3&quot; flag and run on a Pentium 2.8 GhZ with 1GB of RAM under Gentoo Linux. The results show that binary search is extremely fast, even for the largest lists that could be allocated (notice that the time is measured in microseconds, &amp;mu;s).

{|
|'''List size'''                    || 1,000 || 10,000 || 100,000 || 1M || 10M || 100M
|-
|'''Binary search''' (microseconds) || 0     || 0      || 0       ||  1 ||   1 || 2
|}

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5950</id>
      <timestamp>2006-06-05T19:53:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Performance */ Border</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays (&gt;2&lt;sup&gt;30&lt;/sup&gt; elements) due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;50000; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/50000);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation. Because binary search is very fast, we must repeat the test many times to get useful measurements with the resolution of the typical &lt;code&gt;clock()&lt;/code&gt; timer.

== Performance ==

We measured the performance of binary search using the above test code on lists of a number of sizes. The code was compiled using gcc with the &quot;-O3&quot; flag and run on a Pentium 2.8 GhZ with 1GB of RAM under Gentoo Linux. The results show that binary search is extremely fast, even for the largest lists that could be allocated (notice that the time is measured in microseconds, &amp;mu;s).

{|border=&quot;1&quot;
|'''List size'''                    || 1,000 || 10,000 || 100,000 || 1M || 10M || 100M
|-
|'''Binary search''' (microseconds) || 0     || 0      || 0       ||  1 ||   1 || 2
|}

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5952</id>
      <timestamp>2006-06-05T21:07:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Remove platform specific comment</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;50000; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/50000);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation. Because binary search is very fast, we must repeat the test many times to get useful measurements with the resolution of the typical &lt;code&gt;clock()&lt;/code&gt; timer.

== Performance ==

We measured the performance of binary search using the above test code on lists of a number of sizes. The code was compiled using gcc with the &quot;-O3&quot; flag and run on a Pentium 2.8 GhZ with 1GB of RAM under Gentoo Linux. The results show that binary search is extremely fast, even for the largest lists that could be allocated (notice that the time is measured in microseconds, &amp;mu;s).

{|border=&quot;1&quot;
|'''List size'''                    || 1,000 || 10,000 || 100,000 || 1M || 10M || 100M
|-
|'''Binary search''' (microseconds) || 0     || 0      || 0       ||  1 ||   1 || 2
|}

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16429</id>
      <timestamp>2009-05-09T13:43:50Z</timestamp>
      <contributor>
        <username>Totoro</username>
        <id>1819</id>
      </contributor>
      <minor/>
      <comment>/* Performance */</comment>
      <text xml:space="preserve">{{Category:Binary search}}

C has built-in support in its library for a generic form of binary search based on function pointers ([http://www.cplusplus.com/ref/cstdlib/bsearch.html bsearch()]). Here, we describe a straightforward implementation on integer arrays. We begin with a simple recursive implementation. The search receives four arguments:
* The array
* Lower and upper bound indexes indicating the inclusive range of elements to search
* The value to search for

We then compare the desired value to the value in the center of the range and use this to narrow the range passed to the next recursive call. If the range ever becomes empty (upper &amp;lt; lower) then the element is not present and we return &amp;minus;1 to indicate this.

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm (recursive)&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    if (high &lt; low)
        return -1;
    int middle = (low + high)/2;
    if (target &lt; a[middle])
        return binary_search(a, low, middle-1, target);
    else if (target &gt; a[middle])
        return binary_search(a, middle+1, high, target);
    else if (target == a[middle])
        return middle;
}
&lt;/codeblock&gt;

While effective and clear, this implementation has a few practical problems:

* The recursive calls are all ''tail calls'', and so can be rewritten as a loop to save stack space and call overhead. Many C compilers will not perform this rewriting automatically.
* The computation &lt;code&gt;(low + high)/2&lt;/code&gt; may return incorrect results for very large arrays due to overflow; see [http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html Joshua Bloch's article].
* The last comparison (==) is not needed, since it is implied by the failure of the first two and the [http://mathworld.wolfram.com/TrichotomyLaw.html trichotomy law].

Taking these into account, we rewrite it as:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main algorithm&gt;&gt;=
int binary_search(int a[], int low, int high, int target) {
    while (low &lt;= high) {
        int middle = low + (high - low)/2;
        if (target &lt; a[middle])
            high = middle - 1;
        else if (target &gt; a[middle])
            low = middle + 1;
        else
            return middle;
    }
    return -1;
}
&lt;/codeblock&gt;

To test it, we generate a list of random numbers, sort it, and then search for some values known to be in the list. We allow the number of items in the list to be specified for performance testing. We deliberately exclude one value from the list to test the &quot;not found&quot; case:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;binary_search.c&gt;&gt;=
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;time.h&gt;

&lt;&lt;main algorithm&gt;&gt;

/* For qsort */
int less_int(const void* left, const void* right) {
    return *((const int*)left) - *((const int*)right);
}

int main(int argc, char* argv[]) {
    clock_t start;
    int num_elements = atoi(argv[1]);
    int* a = (int*)malloc(num_elements*sizeof(int));
    int i;
    for(i=0; i&lt;num_elements; i++) {
        do {
            a[i] = rand() % num_elements;
        } while(a[i] == num_elements/7);
    }
    qsort(a, num_elements, sizeof(int), less_int);

    start = clock();
    for(i=0; i&lt;50000; i++) {
        int present_val = a[rand() % num_elements];
        int found_at = binary_search(a, 0, num_elements - 1, present_val);
        if (found_at == -1 || a[found_at] != present_val)
            puts(&quot;ERROR&quot;);
    }
    printf(&quot;Average search time: %f sec\n&quot;,
           ((double)(clock() - start))/(CLOCKS_PER_SEC)/50000);

    if (binary_search(a, 0, num_elements - 1, num_elements/7)   != -1 ||
        binary_search(a, 0, num_elements - 1, -1)               != -1 ||
        binary_search(a, 0, num_elements - 1, num_elements + 1) != -1)
    {
        puts(&quot;ERROR&quot;);
    }
    return 0;
}
&lt;/codeblock&gt;

The cast to &lt;code&gt;int*&lt;/code&gt; enables this code to compile as C++. It's necessary to add timing code to this example for performance testing because the binary search itself is much faster than the array generation. Because binary search is very fast, we must repeat the test many times to get useful measurements with the resolution of the typical &lt;code&gt;clock()&lt;/code&gt; timer.

== Performance ==

We measured the performance of binary search using the above test code on lists of a number of sizes. The code was compiled using gcc with the &quot;-O3&quot; flag and run on a Pentium 2.8 GHz with 1GB of RAM under Gentoo Linux. The results show that binary search is extremely fast, even for the largest lists that could be allocated (notice that the time is measured in microseconds, &amp;mu;s).

{|border=&quot;1&quot;
|'''List size'''                    || 1,000 || 10,000 || 100,000 || 1M || 10M || 100M
|-
|'''Binary search''' (microseconds) || 0     || 0      || 0       ||  1 ||   1 || 2
|}

[[Category:Binary search]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search (Java)</title>
    <id>2819</id>
    <revision>
      <id>8187</id>
      <timestamp>2006-11-27T02:08:59Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Binary search (Java)</comment>
      <text xml:space="preserve">==Overview==

An implementation of [http://en.wikipedia.org/wiki/Binary_search binary search] in Java. This implementation is of illustrative purpose as Java provides static binary search methods in the Arrays and Collections classes. Searches for an element in a sorted list of elements. Returns the index of the element if found or the negative index where the element should be inserted to maintain ascending ordering. Therefore this is an implementation of binary search as an insertion search, not a pure exsistence search, which would only return if the element was found or not.

==Implementation==

The method takes two arguments: The value to search and the list of values to search in. The input list must be sorted in ascending order prior to searching, else the result of this method is undefined. It must also contain at least one element. Through Java generics, the method can be used with any elements that extend Comparable, like Java number objects or strings, making Java 5 a requirement.

While we are searching, the interval [0, left] is empty or contains only list values &lt; value. The interval [right, n-1] is empty or contains only list values &gt; value. The remaining search interval is [left, right]. The parts left and right of that interval have been searched.

&lt;codeblock language=java&gt;
&lt;&lt;search&gt;&gt;=

do {
    mid = (left + right) / 2;
    midVal = values.get(mid);
    if (value.compareTo(values.get(mid)) &lt; 0)
        right = mid - 1;
    else if (value.compareTo(values.get(mid)) &gt; 0)
        left = mid + 1;
    else
        return mid;
} while (left &lt;= right);
&lt;/codeblock&gt;

Now left &gt; right and the value was not found in the list. We now want to determine the index at which the element should be inserted to maintain the ordering. As the remaining searching interval is empty now, there is an interval ''i'' [0, n-1] with two disjunct intervals ''i1'' [0, left] and ''i2'' [right, n-1] with the following attributes: all indices in ''i1'' have list values &lt; value, all indices in ''i2'' have list values &gt; value and ''i1'' merged with ''i2'' equals ''i''. We now have two possible cases:

Case a) ''value &lt; midVal &amp; right = mid-1''. From the first part follows that ''mid'' is in interval [right, n-1] and from the second part follows that ''mid'' is at the left edge of the interval, so ''mid'' is the smallest index with list value &gt; value. So in case a) an insertion must happen on index ''mid''.

Case b) ''value &gt; midVal &amp; left = mid+1''. From the first part follows that ''mid'' is in interval [0, left]. From the second part follows that ''mid'' is at the right edge of the interval. This means ''mid'' is the largest index with a list value &lt; value, so in case b) we need to insert at ''mid'' + 1.

&lt;codeblock language=java&gt;
&lt;&lt;return&gt;&gt;=

return (value.compareTo(midVal) &lt; 0) ? -mid : -(mid + 1);
&lt;/codeblock&gt;

==Usage==
Illustration of the functionality using JUnit 4 unit tests for strings and integers:

&lt;codeblock language=java&gt;
&lt;&lt;test_strings&gt;&gt;=

assertEquals(-1, BinarySearch.search(&quot;Billy&quot;, Arrays.asList(&quot;Anny&quot;,&quot;Emmy&quot;,&quot;Grammy&quot;)));
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;test_integers&gt;&gt;=

assertEquals(-1, BinarySearch.search(2, Arrays.asList(1, 3, 4)));
&lt;/codeblock&gt;
The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinarySearch.java&gt;&gt;=

import static org.junit.Assert.assertEquals;
import org.junit.Test;

import java.util.Arrays;
import java.util.List;

public class BinarySearch {
	static &lt;T extends Comparable&lt;? super T&gt;&gt; int search(T value, List&lt;T&gt; values) {
		int n = values.size();
		int mid, left, right;
		T midVal;
		left = 0;
		right = n - 1;
		&lt;&lt;search&gt;&gt;
		&lt;&lt;return&gt;&gt;
	}
	@Test
	public void testStringSearch() {
		&lt;&lt;test_strings&gt;&gt;
	}
	
	@Test
	public void testIntegerSearch() {
		&lt;&lt;test_integers&gt;&gt;
	}
}
&lt;/codeblock&gt;
[[Category:Binary search|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11427</id>
      <timestamp>2007-10-30T20:32:32Z</timestamp>
      <contributor>
        <ip>24.68.79.41</ip>
      </contributor>
      <text xml:space="preserve">==Overview==

An implementation of [http://en.wikipedia.org/wiki/Binary_search binary search] in Java. This implementation is of illustrative purpose as Java provides static binary search methods in the Arrays and Collections classes. Searches for an element in a sorted list of elements. Returns the index of the element if found or the negative index where the element should be inserted to maintain ascending ordering. Therefore this is an implementation of binary search as an insertion search, not a pure existence search, which would only return if the element was found or not.

==Implementation==

The method takes two arguments: The value to search and the list of values to search in. The input list must be sorted in ascending order prior to searching, else the result of this method is undefined. It must also contain at least one element. Through Java generics, the method can be used with any elements that extend Comparable, like Java number objects or strings, making Java 5 a requirement.

While we are searching, the interval [0, left] is empty or contains only list values &lt; value. The interval [right, n-1] is empty or contains only list values &gt; value. The remaining search interval is [left, right]. The parts left and right of that interval have been searched.

&lt;codeblock language=java&gt;
&lt;&lt;search&gt;&gt;=

do {
    mid = (left + right) / 2;
    midVal = values.get(mid);
    if (value.compareTo(values.get(mid)) &lt; 0)
        right = mid - 1;
    else if (value.compareTo(values.get(mid)) &gt; 0)
        left = mid + 1;
    else
        return mid;
} while (left &lt;= right);
&lt;/codeblock&gt;

Now left &gt; right and the value was not found in the list. We now want to determine the index at which the element should be inserted to maintain the ordering. As the remaining searching interval is empty now, there is an interval ''i'' [0, n-1] with two disjunct intervals ''i1'' [0, left] and ''i2'' [right, n-1] with the following attributes: all indices in ''i1'' have list values &lt; value, all indices in ''i2'' have list values &gt; value and ''i1'' merged with ''i2'' equals ''i''. We now have two possible cases:

Case a) ''value &lt; midVal &amp; right = mid-1''. From the first part follows that ''mid'' is in interval [right, n-1] and from the second part follows that ''mid'' is at the left edge of the interval, so ''mid'' is the smallest index with list value &gt; value. So in case a) an insertion must happen on index ''mid''.

Case b) ''value &gt; midVal &amp; left = mid+1''. From the first part follows that ''mid'' is in interval [0, left]. From the second part follows that ''mid'' is at the right edge of the interval. This means ''mid'' is the largest index with a list value &lt; value, so in case b) we need to insert at ''mid'' + 1.

&lt;codeblock language=java&gt;
&lt;&lt;return&gt;&gt;=

return (value.compareTo(midVal) &lt; 0) ? -mid : -(mid + 1);
&lt;/codeblock&gt;

==Usage==
Illustration of the functionality using JUnit 4 unit tests for strings and integers:

&lt;codeblock language=java&gt;
&lt;&lt;test_strings&gt;&gt;=

assertEquals(-1, BinarySearch.search(&quot;Billy&quot;, Arrays.asList(&quot;Anny&quot;,&quot;Emmy&quot;,&quot;Grammy&quot;)));
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;test_integers&gt;&gt;=

assertEquals(-1, BinarySearch.search(2, Arrays.asList(1, 3, 4)));
&lt;/codeblock&gt;
The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinarySearch.java&gt;&gt;=

import static org.junit.Assert.assertEquals;
import org.junit.Test;

import java.util.Arrays;
import java.util.List;

public class BinarySearch {
	static &lt;T extends Comparable&lt;? super T&gt;&gt; int search(T value, List&lt;T&gt; values) {
		int n = values.size();
		int mid, left, right;
		T midVal;
		left = 0;
		right = n - 1;
		&lt;&lt;search&gt;&gt;
		&lt;&lt;return&gt;&gt;
	}
	@Test
	public void testStringSearch() {
		&lt;&lt;test_strings&gt;&gt;
	}
	
	@Test
	public void testIntegerSearch() {
		&lt;&lt;test_integers&gt;&gt;
	}
}
&lt;/codeblock&gt;
[[Category:Binary search|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14958</id>
      <timestamp>2008-10-12T04:31:03Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">==Overview==

An implementation of [http://en.wikipedia.org/wiki/Binary_search binary search] in Java. This implementation is of illustrative purpose as Java provides static binary search methods in the Arrays and Collections classes. Searches for an element in a sorted list of elements. Returns the index of the element if found or the negative index where the element should be inserted to maintain ascending ordering. Therefore this is an implementation of binary search as an insertion search, not a pure existence search, which would only return if the element was found or not.

==Implementation==

The method takes two arguments: The value to search and the list of values to search in. The input list must be sorted in ascending order prior to searching, else the result of this method is undefined. It must also contain at least one element. Through Java generics, the method can be used with any elements that extend Comparable, like Java number objects or strings, making Java 5 a requirement.

While we are searching, the interval [0, left] is empty or contains only list values &lt; value. The interval [right, n-1] is empty or contains only list values &gt; value. The remaining search interval is [left, right]. The parts left and right of that interval have been searched.

&lt;codeblock language=java&gt;
&lt;&lt;search&gt;&gt;=

do {
    int mid = (left + right) / 2;
    T midVal = values.get(mid);
    if (value.compareTo(midVal) &lt; 0)
        right = mid - 1;
    else if (value.compareTo(midVal) &gt; 0)
        left = mid + 1;
    else
        return mid;
} while (left &lt;= right);
&lt;/codeblock&gt;

Now left &gt; right and the value was not found in the list. We now want to determine the index at which the element should be inserted to maintain the ordering. As the remaining searching interval is empty now, there is an interval ''i'' [0, n-1] with two disjunct intervals ''i1'' [0, left] and ''i2'' [right, n-1] with the following attributes: all indices in ''i1'' have list values &lt; value, all indices in ''i2'' have list values &gt; value and ''i1'' merged with ''i2'' equals ''i''. We now have two possible cases:

Case a) ''value &lt; midVal &amp; right = mid-1''. From the first part follows that ''mid'' is in interval [right, n-1] and from the second part follows that ''mid'' is at the left edge of the interval, so ''mid'' is the smallest index with list value &gt; value. So in case a) an insertion must happen on index ''mid''.

Case b) ''value &gt; midVal &amp; left = mid+1''. From the first part follows that ''mid'' is in interval [0, left]. From the second part follows that ''mid'' is at the right edge of the interval. This means ''mid'' is the largest index with a list value &lt; value, so in case b) we need to insert at ''mid'' + 1.

&lt;codeblock language=java&gt;
&lt;&lt;return&gt;&gt;=

return (value.compareTo(midVal) &lt; 0) ? -mid : -(mid + 1);
&lt;/codeblock&gt;

==Usage==
Illustration of the functionality using JUnit 4 unit tests for strings and integers:

&lt;codeblock language=java&gt;
&lt;&lt;test_strings&gt;&gt;=

assertEquals(-1, BinarySearch.search(&quot;Billy&quot;, Arrays.asList(&quot;Anny&quot;,&quot;Emmy&quot;,&quot;Grammy&quot;)));
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;test_integers&gt;&gt;=

assertEquals(-1, BinarySearch.search(2, Arrays.asList(1, 3, 4)));
&lt;/codeblock&gt;
The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinarySearch.java&gt;&gt;=

import static org.junit.Assert.assertEquals;
import org.junit.Test;

import java.util.Arrays;
import java.util.List;

public class BinarySearch {
	static &lt;T extends Comparable&lt;? super T&gt;&gt; int search(T value, List&lt;T&gt; values) {
		int n = values.size();
		int left = 0, right = n - 1;
		&lt;&lt;search&gt;&gt;
		&lt;&lt;return&gt;&gt;
	}
	@Test
	public void testStringSearch() {
		&lt;&lt;test_strings&gt;&gt;
	}
	
	@Test
	public void testIntegerSearch() {
		&lt;&lt;test_integers&gt;&gt;
	}
}
&lt;/codeblock&gt;
[[Category:Binary search|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (C Plus Plus)</title>
    <id>1782</id>
    <revision>
      <id>3205</id>
      <timestamp>2006-03-11T23:33:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial C++ version</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode* left;
    BSTNode* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode** search(T data);
&lt;&lt;search operation&gt;&gt;=
BSTNode** search(T data);
BSTNode** BinarySearchTree::search(T data) {
    BSTNode** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
void BinarySearchTree::insert(T data) {
    BSTNode** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete(BSTNode** node);
&lt;&lt;delete operation&gt;&gt;=
void BinarySearchTree::delete(BSTNode** node) {
    BSTNode* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3206</id>
      <timestamp>2006-03-11T23:35:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix header file chunks</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode* left;
    BSTNode* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode** search(T data);
&lt;&lt;search operation&gt;&gt;=
BSTNode** search(T data);
BSTNode** BinarySearchTree::search(T data) {
    BSTNode** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
void BinarySearchTree::insert(T data) {
    BSTNode** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete(BSTNode** node);
&lt;&lt;delete operation&gt;&gt;=
void BinarySearchTree::delete(BSTNode** node) {
    BSTNode* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3207</id>
      <timestamp>2006-03-11T23:37:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix missing template parameters</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
BSTNode&lt;T&gt;** BinarySearchTree::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
void BinarySearchTree::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
void BinarySearchTree::delete(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3209</id>
      <timestamp>2006-03-11T23:46:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix keyword conflict</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
BSTNode&lt;T&gt;** BinarySearchTree::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
void BinarySearchTree::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
void BinarySearchTree::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3210</id>
      <timestamp>2006-03-11T23:48:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+template &lt;class T&gt;</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3211</id>
      <timestamp>2006-03-11T23:48:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>+&lt;T&gt; x3</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
std::swap((*pred)-&gt;data, (*node)-&gt;data);

delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3212</id>
      <timestamp>2006-03-11T23:49:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Remove now-obvious comment</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>4116</id>
      <timestamp>2006-04-13T14:16:25Z</timestamp>
      <contributor>
        <ip>62.214.235.197</ip>
      </contributor>
      <comment>/* Node structure */</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode&lt;T&gt;;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>4117</id>
      <timestamp>2006-04-13T14:17:17Z</timestamp>
      <contributor>
        <ip>62.214.235.197</ip>
      </contributor>
      <comment>/* Files */</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode&lt;T&gt;;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_
#define _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>13424</id>
      <timestamp>2008-05-21T00:59:10Z</timestamp>
      <contributor>
        <ip>205.155.154.3</ip>
      </contributor>
      <comment>/* Search */</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode&lt;T&gt;;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
          if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_
#define _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>14052</id>
      <timestamp>2008-07-21T19:03:37Z</timestamp>
      <contributor>
        <ip>128.114.69.94</ip>
      </contributor>
      <comment>/* Insert */</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode&lt;T&gt;;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
          if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

(Warning: This section contains errors!)
Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_
#define _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>14977</id>
      <timestamp>2008-10-12T20:28:02Z</timestamp>
      <contributor>
        <ip>83.144.87.140</ip>
      </contributor>
      <comment>delete(pred) -&gt; delete_node(pred)</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C++ with search, insert, and delete operations.

== Node structure ==

We begin by defining a templated node class, which contains left and right child pointers and the node's data. The data is publically accessible but read-only to preserve the order property:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;node class&gt;&gt;=
template &lt;class T&gt;
class BSTNode {
public:
    &lt;&lt;BSTNode method declarations&gt;&gt;
    T getData() { return data; }
private:
    T data;
    BSTNode&lt;T&gt;* left;
    BSTNode&lt;T&gt;* right;
};
&lt;/codeblock&gt;

We assume that &lt;code&gt;T&lt;/code&gt; implements &lt;code&gt;operator&amp;lt;&lt;/code&gt;, which we will need to order the nodes. Constructing nodes is straightforward:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BSTNode method declarations&gt;&gt;=
BSTNode(T data);
&lt;&lt;node constructor&gt;&gt;=
template &lt;class T&gt;
BSTNode::BSTNode(T data) {
    this-&gt;data = data;
    this-&gt;left = this-&gt;right = NULL;
}
&lt;/codeblock&gt;

We represent a whole tree with a class that just contains a pointer to the root node, which can be NULL for an empty tree. We make &lt;code&gt;BSTNode&lt;/code&gt; a friend class so that the tree can access its internal child pointers but no one else can:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;tree class&gt;&gt;=
template &lt;class T&gt;
class BinarySearchTree {
public:
    &lt;&lt;BinarySearchTree method declarations&gt;&gt;
private:
    BSTNode&lt;T&gt;* root;
    friend class BSTNode&lt;T&gt;;
};
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
BSTNode&lt;T&gt;** search(T data);
&lt;&lt;search operation&gt;&gt;=
template &lt;class T&gt;
BSTNode&lt;T&gt;** BinarySearchTree&lt;T&gt;::search(T data) {
    BSTNode&lt;T&gt;** node = &amp;root;
    while (*node != NULL) {
          if (data &lt; (*node)-&gt;data)
            node = &amp;(*node)-&gt;left;
        else if ((*node)-&gt;data &lt; data)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

(Warning: This section contains errors!)
Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void insert(T data);
&lt;&lt;insert operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::insert(T data) {
    BSTNode&lt;T&gt;** node = search(data);
    if (*node == NULL) {
        *node = new BSTNode&lt;T&gt;(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;BinarySearchTree method declarations&gt;&gt;=
void delete_node(BSTNode&lt;T&gt;** node);
&lt;&lt;delete operation&gt;&gt;=
template &lt;class T&gt;
void BinarySearchTree&lt;T&gt;::delete_node(BSTNode&lt;T&gt;** node) {
    BSTNode&lt;T&gt;* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        delete old_node;
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        delete old_node;
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
BSTNode&lt;T&gt;** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;
std::swap((*pred)-&gt;data, (*node)-&gt;data);
delete_node(pred);
&lt;/codeblock&gt;

We need a header for &lt;code&gt;std::swap&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;algorithm&gt;
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_
#define _BST_H_

&lt;&lt;node class&gt;&gt;
&lt;&lt;tree class&gt;&gt;

#endif

&lt;&lt;bst.cpp&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (C)</title>
    <id>1779</id>
    <revision>
      <id>3190</id>
      <timestamp>2006-03-11T22:24:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Write complete article with node structure, search, insert, delete</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left, right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;node-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;node-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;value;
(*pred)-&gt;value = (*node)-&gt;value;
(*node)-&gt;value = temp;

delete(pred);
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3192</id>
      <timestamp>2006-03-11T22:28:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Files</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left, right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;node-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;node-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;value;
(*pred)-&gt;value = (*node)-&gt;value;
(*node)-&gt;value = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3193</id>
      <timestamp>2006-03-11T22:29:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix pointer notation (grr C decls)</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;node-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;node-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;value;
(*pred)-&gt;value = (*node)-&gt;value;
(*node)-&gt;value = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3194</id>
      <timestamp>2006-03-11T22:32:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add header, other fixes</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;node-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;node-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3195</id>
      <timestamp>2006-03-11T22:33:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Add missing dereferences</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>4244</id>
      <timestamp>2006-04-22T15:23:05Z</timestamp>
      <contributor>
        <ip>202.38.56.22</ip>
      </contributor>
      <comment>/* Insert */</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }pppppppppppppppppppppppp
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>4245</id>
      <timestamp>2006-04-22T15:31:34Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert, change didn't make any sense</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>6758</id>
      <timestamp>2006-07-11T12:44:38Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Binary search tree (C)]] moved to [[Binary search tree (C) on Wheels]]</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>6932</id>
      <timestamp>2006-07-11T14:24:36Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Binary search tree (C) on Wheels]] moved to [[Binary search tree (C)]]: revert</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a void pointer referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}

&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>9770</id>
      <timestamp>2007-04-14T18:42:40Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>Improved description</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11060</id>
      <timestamp>2007-10-05T19:07:34Z</timestamp>
      <contributor>
        <ip>66.249.2.50</ip>
      </contributor>
      <text xml:space="preserve">varrollae
This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11061</id>
      <timestamp>2007-10-05T22:51:12Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/66.249.2.50|66.249.2.50]] ([[User_talk:66.249.2.50|66.249.2.50]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11200</id>
      <timestamp>2007-10-13T06:12:27Z</timestamp>
      <contributor>
        <ip>208.109.123.121</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11214</id>
      <timestamp>2007-10-13T07:57:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11227</id>
      <timestamp>2007-10-18T01:36:48Z</timestamp>
      <contributor>
        <ip>201.12.178.33</ip>
      </contributor>
      <text xml:space="preserve">zelacvar
This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11232</id>
      <timestamp>2007-10-18T05:10:48Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11415</id>
      <timestamp>2007-10-30T04:56:18Z</timestamp>
      <contributor>
        <ip>87.51.32.30</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11419</id>
      <timestamp>2007-10-30T08:18:44Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11434</id>
      <timestamp>2007-10-31T15:33:21Z</timestamp>
      <contributor>
        <ip>192.18.100.50</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11435</id>
      <timestamp>2007-10-31T15:35:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11560</id>
      <timestamp>2007-11-12T23:25:07Z</timestamp>
      <contributor>
        <ip>61.235.241.69</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11562</id>
      <timestamp>2007-11-13T00:47:38Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.235.241.69|61.235.241.69]] ([[User_talk:61.235.241.69|61.235.241.69]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11770</id>
      <timestamp>2007-12-04T23:47:36Z</timestamp>
      <contributor>
        <ip>89.35.105.14</ip>
      </contributor>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
}
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11771</id>
      <timestamp>2007-12-04T23:48:11Z</timestamp>
      <contributor>
        <ip>89.35.105.14</ip>
      </contributor>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11807</id>
      <timestamp>2007-12-08T17:16:20Z</timestamp>
      <contributor>
        <ip>222.63.132.15</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>11808</id>
      <timestamp>2007-12-08T17:53:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>12322</id>
      <timestamp>2008-01-27T13:58:00Z</timestamp>
      <contributor>
        <ip>141.223.149.36</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>12324</id>
      <timestamp>2008-01-27T15:54:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>15077</id>
      <timestamp>2008-10-17T15:36:54Z</timestamp>
      <contributor>
        <ip>203.121.145.53</ip>
      </contributor>
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This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.%0</text>
    </revision>
    <revision>
      <id>15081</id>
      <timestamp>2008-10-17T16:07:00Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/203.121.145.53|203.121.145.53]] ([[User_talk:203.121.145.53|203.121.145.53]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>15726</id>
      <timestamp>2009-01-03T10:10:36Z</timestamp>
      <contributor>
        <ip>87.118.125.129</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_acelallita.com/</text>
    </revision>
    <revision>
      <id>15737</id>
      <timestamp>2009-01-03T19:25:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/87.118.125.129|87.118.125.129]] ([[User_talk:87.118.125.129|87.118.125.129]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in C with search, insert, and delete operations. A binary search tree is a tree where each node contains a value, and for each node, the left subtree only contains values less than the value of the node, and the right subtree only contains greater values. This allows to find the node for any value in &lt;math&gt;O(\log N)&lt;/math&gt; average time.

The binary search tree shall work with any data type, therefore the code takes pointers to void for the data, and relies on an user-supplied comparison function for sorting.

== Node structure ==

We begin by defining a node structure, which contains left and right child pointers and a pointer to void referring to the node's data:

&lt;codeblock language=c&gt;
&lt;&lt;node structure&gt;&gt;=
struct bst_node {
    void* data;
    struct bst_node* left;
    struct bst_node* right;
};
&lt;/codeblock&gt;

We represent an entire tree using a pointer to its root node; thus this structure doubles as a tree representation. Constructing and destroying nodes is straightforward. Newly constructed nodes initially are leaf nodes, i.e. they have no left or right child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node* new_node(void* data);
&lt;&lt;node constructor&gt;&gt;=
struct bst_node* new_node(void* data) {
    struct bst_node* result = malloc(sizeof(struct bst_node));
    result-&gt;data = data;
    result-&gt;left = result-&gt;right = NULL;
    return result;
}
&lt;/codeblock&gt;

NULL requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

On destroying nodes, it is assumed that the node has already been removed from the tree. Especially there are no subtrees to destroy. Moreover, this search tree implementation doesn't take over ownership of the data values, therefore the data pointer doesn't have to be destroyed either.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void free_node(struct bst_node* node);
&lt;&lt;node destructor&gt;&gt;=
void free_node(struct bst_node* node) {
    free(node);
}
&lt;/codeblock&gt;

Since our data is generic, the comparison function is supplied by the user via a function pointer and must be the same for all operations. We choose to use a three-way comparator:

&lt;codeblock language=c&gt;
&lt;&lt;type definitions&gt;&gt;=
/* Returns negative (left&lt;right), zero (left==right), or positive (left&gt;right). */
typedef int comparator(void* left, void* right);
&lt;/codeblock&gt;

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node or prove that it is not in the tree, in which case it returns a pointer to NULL. We return the address of the node pointer instead of just the node pointer to facilitate in-place updates.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data);
&lt;&lt;search operation&gt;&gt;=
struct bst_node** search(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = root;
    while (*node != NULL) {
        int compare_result = compare(data, (*node)-&gt;data);
        if (compare_result &lt; 0)
            node = &amp;(*node)-&gt;left;
        else if (compare_result &gt; 0)
            node = &amp;(*node)-&gt;right;
        else
            break;
    }
    return node;
}
&lt;/codeblock&gt;

== Insert ==

Inserting is now simple. We search for the node, and if it is not found, we create a new node and put it in the place the search function expected to find it, which is where it belongs in the tree. This particular insertion function does not allow duplicate values in the tree (set semantics), but one that does would be similar.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data);
&lt;&lt;insert operation&gt;&gt;=
void insert(struct bst_node** root, comparator compare, void* data) {
    struct bst_node** node = search(root, compare, data);
    if (*node == NULL) {
        *node = new_node(data);
    }
}
&lt;/codeblock&gt;

== Deletion ==

Deletion is the most complicated operation. We focus on deleting nodes rather than values, since &lt;code&gt;search()&lt;/code&gt; can be used to find a node based on a value if necessary. Deleting a node with one child or less is simple; we just replace it with its child:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void delete(struct bst_node** node);
&lt;&lt;delete operation&gt;&gt;=
void delete(struct bst_node** node) {
    struct bst_node* old_node = *node;
    if ((*node)-&gt;left == NULL) {
        *node = (*node)-&gt;right;
        free_node(old_node);
    } else if ((*node)-&gt;right == NULL) {
        *node = (*node)-&gt;left;
        free_node(old_node);
    } else {
        &lt;&lt;delete node with two children&gt;&gt;
    }
}
&lt;/codeblock&gt;

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by following right child pointers repeatedly starting at the node's left child. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by following left child pointers starting at the node's right child.

&lt;codeblock language=c&gt;
&lt;&lt;find inorder predecessor&gt;&gt;=
struct bst_node** pred = &amp;(*node)-&gt;left;
while ((*pred)-&gt;right != NULL) {
    pred = &amp;(*pred)-&gt;right;
}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply exchange the value of the node with either its inorder predecessor or successor, then delete the node that we exchanged with. This preserves the order properties of the tree, and the predecessor/successor nodes always have at most one child, so we already know how to delete them. In this implementation, we choose to consistently use the predecessor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=c&gt;
&lt;&lt;delete node with two children&gt;&gt;=
&lt;&lt;find inorder predecessor&gt;&gt;

/* Swap values */
void* temp = (*pred)-&gt;data;
(*pred)-&gt;data = (*node)-&gt;data;
(*node)-&gt;data = temp;

delete(pred);
&lt;/codeblock&gt;

== Files ==

We can place this implementation in a source and header file for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;bst.h&gt;&gt;=
#ifndef _BST_H_

&lt;&lt;type definitions&gt;&gt;
&lt;&lt;node structure&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif

&lt;&lt;bst.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;bst.h&quot;

&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (Haskell)</title>
    <id>3329</id>
    <revision>
      <id>12695</id>
      <timestamp>2008-03-04T23:31:35Z</timestamp>
      <contributor>
        <ip>158.104.165.201</ip>
      </contributor>
      <comment>Article Creation</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- The natural way to insert into a tree
insertAsc itm tre = insert itm tre (&lt;=)

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree lst f = foldr insert Tip (reverse lst) f
listToTreeAsc lst = foldr insertAsc Tip (reverse lst)

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary Search Tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12704</id>
      <timestamp>2008-03-06T09:14:20Z</timestamp>
      <contributor>
        <username>Dimo414</username>
        <id>1621</id>
      </contributor>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- The natural way to insert into a tree
insertAsc itm tre = insert itm tre (&lt;=)

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree lst f = foldr insert Tip (reverse lst) f
listToTreeAsc lst = foldr insertAsc Tip (reverse lst)

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTreeAsc ls)

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary Search Tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12707</id>
      <timestamp>2008-03-06T10:31:29Z</timestamp>
      <contributor>
        <username>Dimo414</username>
        <id>1621</id>
      </contributor>
      <comment>Code Restructured</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

The Two files are Numeric and General Binary Search Tree definitions.  BinarySearchNum.hs is simpler and easier to follow, but is limited to working with primitive types such as numbers and strings, whereas the general case allows the user to pass their own comparator function.

&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = 1 + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds farthest left item.  In a BST this is the smallest value
-- This function does not deal with a tree which is just a tip
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
-- This function does not deal with a tree which is just a tip
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = 1 + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary Search Tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12708</id>
      <timestamp>2008-03-06T10:52:38Z</timestamp>
      <contributor>
        <username>Dimo414</username>
        <id>1621</id>
      </contributor>
      <comment>Code Rewrite</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary Search Tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12830</id>
      <timestamp>2008-03-16T03:57:04Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>[[Binary Search Tree (Haskell)]] moved to [[Binary search tree (Haskell)]]: consistency with other languages</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary Search Tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12834</id>
      <timestamp>2008-03-16T03:58:14Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manor which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary search tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12985</id>
      <timestamp>2008-04-06T15:52:01Z</timestamp>
      <contributor>
        <ip>220.233.205.122</ip>
      </contributor>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manner which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater than.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary search tree|Haskell]]</text>
    </revision>
    <revision>
      <id>12986</id>
      <timestamp>2008-04-06T15:52:42Z</timestamp>
      <contributor>
        <ip>220.233.205.122</ip>
      </contributor>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manner which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = (Node x (mirror xr) (mirror xl))
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) = if (a &lt;= x) then (Node x (insert a xl) xr) else (Node x xl (insert a xr))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls = listToTreeHelp ls Tip
                where listToTreeHelp [] tre = tre
                      listToTreeHelp (x:xs) tre = listToTreeHelp xs (insert x tre)

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls = treeToListOrd (listToTree ls)

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = if (x &lt;= xlSm) then x else xlSm
                        where xlSm = mint xl
mint (Node x Tip xr)  = if (x &lt;= xrSm) then x else xrSm
                        where xrSm = mint xr
mint (Node x xl xr)   = if (x &lt;= xlSm &amp;&amp; x &lt;= xrSm) then x
                        else if (xlSm &lt;= xrSm) then xlSm else xrSm
                        where xlSm = mint xl
                              xrSm = mint xr

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = if (x &gt; xlSm) then x else xlSm
                        where xlSm = maxt xl
maxt (Node x Tip xr)  = if (x &gt; xrSm) then x else xrSm
                        where xrSm = maxt xr
maxt (Node x xl xr)   = if (x &gt; xlSm &amp;&amp; x &gt; xrSm) then x
                        else if (xlSm &gt; xrSm) then xlSm else xrSm
                        where xlSm = maxt xl
                              xrSm = maxt xr

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f = if (f a x) then (Node x (insert a xl f) xr) else (Node x xl (insert a xr f))

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = listToTreeHelp ls Tip f
                where listToTreeHelp [] tre _ = tre
                      listToTreeHelp (x:xs) tre f = listToTreeHelp xs (insert x tre f) f

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  = if (f x xlSm) then x else xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  = if (f x xrSm) then x else xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   = if (f x xlSm &amp;&amp; f x xrSm) then x
                        else if (f xlSm xrSm) then xlSm else xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  = if ((flip f) x xlSm) then x else xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  = if ((flip f) x xrSm) then x else xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   = if ((flip f) x xlSm &amp;&amp; (flip f) x xrSm) then x
                        else if ((flip f) xlSm xrSm) then xlSm else xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node x xl xr) = 1 + if (xlSz &gt;= xrSz) then xlSz else xrSz
                        where xlSz = height xl
                              xrSz = height xr
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary search tree|Haskell]]</text>
    </revision>
    <revision>
      <id>15677</id>
      <timestamp>2008-12-24T12:07:38Z</timestamp>
      <contributor>
        <ip>71.141.107.171</ip>
      </contributor>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_search_tree Binary Search Tree] is a tree, where each node has two children, and the children are related in a manner which allows them to be compared.  The generic example is that all items to the left of a given node are less than that node, and all items to the right are greater.  How equality is treated is ambiguous, and depends on the specific application of the tree.

This file contains basic Binary Search Tree functions (including the data type definition) which operate unrelated to the actual contents of the BST.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearch.hs&gt;&gt;=
-- This file contains functions to work with Binary Search Trees unrelated to their contents.

module BinarySearch where

-- The data type definition.  A tree can consist of either a Tip or a node with a value and two tree.
data Tree a = Tip | Node a (Tree a) (Tree a) deriving (Show,Eq)

-- Returns a leaf node, makes writing leafs easier
leaf x = Node x Tip Tip

-- Some examples of structure in code
t1 = Node 10 Tip Tip
t2 = Node 17 (Node 12 (Node 5 Tip (leaf 8)) (leaf 15))
             (Node 115
                   (Node 32 (leaf 30) (Node 46 Tip (leaf 57)))
                   (leaf 163))

-- The size of the tree - the number of items in the tree
size Tip = 0
size (Node _ tl tr) = 1 + size tl + size tr

-- Converts a tree into a list.  This list, if converted back into a tree, will return the same tree
treeToList Tip = []
treeToList (Node x xl xr) = x : treeToList xl ++ treeToList xr

-- Converts a tree into a sorted list.  This list will not convert back into the same tree.
treeToListOrd Tip = []
treeToListOrd (Node x xl xr) = treeToListOrd xl ++ x : treeToListOrd xr

-- Visually outputs a tree (sideways) by indenting each next node and additional tab in, outputs the right side, then the node, then the left side
pict t = putStr (pic &quot;&quot; t)
         where pic ind Tip = ind ++ &quot;.&quot;
               pic ind (Node x tl tr) = pic ('\t':ind) tr ++ &quot;\n&quot; ++
                                        ind ++ show x     ++ &quot;\n&quot; ++
                                        pic ('\t':ind) tl ++ &quot;\n&quot;

-- Finds farthest left item.  In a BST this is the smallest value
farLft (Node x Tip _) = x
farLft (Node x xl _) = farLft xl

-- Finds farthest right item.  In a BST this is the largest value
farRt (Node x _ Tip) = x
farRt (Node x _ xr) = farRt xr

-- Mirrors a tree, so every right and left node switch
mirror Tip = Tip
mirror (Node x xl xr) = Node x (mirror xr) (mirror xl)
&lt;/codeblock&gt;

This file contains functions which work with BSTs of naturally comparable items, such as numbers and strings.  The comparison function is (&lt;=)
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchNum.hs&gt;&gt;=
-- This file contains functions to work with Numeric (and string, since Haskell can use the &lt; operator on strings) Binary Search Trees.

module BinarySearchNum where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip = leaf a
insert a (Node x xl xr) | a &lt;= x    = Node x (insert a xl) xr
                        | otherwise = Node x xl (insert a xr)

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree = foldl (flip insert) Tip

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort = treeToListOrd . listToTree

-- Adds up all items in a numerical Binary Tree
sumt Tip = 0
sumt (Node x xl xr) = x + sumt xl + sumt xr

-- Finds smalles item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) = x
mint (Node x xl Tip)  = min x (mint xl)
mint (Node x Tip xr)  = min x (mint xr)
mint (Node x xl xr)   = min x (min (mint xl) (mint xr))

-- Finds largest item in a tree (not necessarily ordered)
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) = x
maxt (Node x xl Tip)  = max x (maxt xl)
maxt (Node x Tip xr)  = max x (maxt xr)
maxt (Node x xl xr)   = max x (max (maxt xl) (maxt xr))

-- Finds height of tree
height Tip = 0
height (Node _ xl xr) = 1 + max (height xl) (height xr)
&lt;/codeblock&gt;

This file contains functions which work with any binary search tree.  The comparison function must be specified via the f parameter.
&lt;codeblock language=haskell&gt;
&lt;&lt;BinarySearchAll.hs&gt;&gt;=
-- This file contains functions to work with any kind of Binary Search Tree - the comparison operator is passed as needed by the f parameter

module BinarySearchAll where

import BinarySearch

-- Insert into a tree
-- The third parameter is a comparator function, if the contents of the tree are not numbers or strings, you can pass a different function to this third parameter to properly define how to compare, and therefore sort, the tree.
insert a Tip _ = leaf a
insert a (Node x xl xr) f | f a x     = Node x (insert a xl f) xr
                          | otherwise = Node x xl (insert a xr f)

-- Converts a list to a tree, using either comparator function f, or the natural (&lt;=) function
listToTree ls f = foldl (\tre x -&gt; insert x tre f) Tip ls

-- Tree Sort - takes a list, and sorts it by converting to a tree and then back to a list
tsort ls f = treeToListOrd (listToTree ls f)

-- Adds up all items in a numerical Binary Tree
-- h is a function which combines two items - default would be (+)
sumt Tip h = 0
sumt (Node x xl xr) h = h (h x (sumt xl h)) (sumt xr h)

-- Finds smalles item in a tree (not necessarily ordered) using comparator f
-- This function does not deal with a tree which is just a tip
mint (Node x Tip Tip) f = x
mint (Node x xl Tip) f  | f x xlSm  = x
                        | otherwise = xlSm
                        where xlSm = mint xl f
mint (Node x Tip xr) f  | f x xrSm  = x
                        | otherwise = xrSm
                        where xrSm = mint xr f
mint (Node x xl xr) f   | f x xlSm &amp;&amp; f x xrSm = x
                        | f xlSm xrSm          = xlSm
                        | otherwise            = xrSm
                        where xlSm = mint xl f
                              xrSm = mint xr f

-- Finds largest item in a tree (not necessarily ordered) using comparator f
-- flips the parameters of f in order to find the largest using a smaller-than comparator
-- This function does not deal with a tree which is just a tip
maxt (Node x Tip Tip) f = x
maxt (Node x xl Tip) f  | (flip f) x xlSm = x
                        | otherwise       = xlSm
                        where xlSm = maxt xl f
maxt (Node x Tip xr) f  | (flip f) x xrSm = x
                        | otherwise       = xrSm
                        where xrSm = maxt xr f
maxt (Node x xl xr) f   | (flip f) x xlSm &amp;&amp; (flip f) x xrSm = x
                        | (flip f) xlSm xrSm                 = xlSm
                        | otherwise                          = xrSm
                        where xlSm = maxt xl f
                              xrSm = maxt xr f

-- Finds height of tree
height Tip = 0
height (Node _ xl xr) = 1 + max (height xl) (height xr)
&lt;/codeblock&gt;

[[Category:Programming language:Haskell]]
[[Category:Binary search tree|Haskell]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (Java)</title>
    <id>2834</id>
    <revision>
      <id>8209</id>
      <timestamp>2006-11-28T05:53:38Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Simple binary search tree.</comment>
      <text xml:space="preserve">=Overview=

A simple [http://en.wikipedia.org/wiki/Binary_search_tree binary search tree], implemented as an object-oriented, recursive data structure in Java, for objects that extend Comparable. Note that Java already provides efficient tree-based data structures, e.g. TreeSet.

=Implementation=

A node in a binary tree has three attributes: the left and the right child nodes and a value. The tree has one root node. This is the structure of the binary tree, as represented in the UML class diagram below.

[[Image:Binary-tree-class-diagram.png|UML class diagram for the binary search tree implementation]]

==Construction==

When adding an element to the tree, if the element is in the tree already, it is not added. The proper place to insert at is searched recursivley by calling the insert method.

&lt;codeblock language=java&gt;
&lt;&lt;add&gt;&gt;=

public void add(Comparable element) {
    if (this.root == null &amp;&amp; element != null) {
        this.root = new Node(element);
        this.size++;
    } else if (element != null) {
        this.root = insert(this.root, element);
    }
}
&lt;/codeblock&gt;

The recursive insertion method takes two parameters: the node to search from and the element to add. It returns the node including the inserted new element. When the value is already in the tree, nothing is done. For a more sophisticated tree, we could add the new element, count frequencies, etc.

&lt;codeblock language=java&gt;
&lt;&lt;equal&gt;&gt;=

if (compare == 0) {
    return result;
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the left subtree:
&lt;codeblock language=java&gt;
&lt;&lt;left&gt;&gt;=

if (compare &gt; 0) {
    if (result.left != null) {
        result.left = insert(result.left, value);
    } else {
        result.left = new Node(value);
        this.size++;
    }
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the right subtree:
&lt;codeblock language=java&gt;
&lt;&lt;right&gt;&gt;=

else if (compare &lt; 0) {
    if (result.right != null) {
        result.right = insert(result.right, value);
    } else {
        result.right = new Node(value);
        this.size++;
    }
}
&lt;/codeblock&gt;

* Search for a value in the tree, return the element if found or null if the element is not in the tree:

&lt;codeblock language=java&gt;
&lt;&lt;get&gt;&gt;=

public Comparable get(Comparable key) {
    if (this.root == null)
        return null;
    else
        return find(this.root, key);
}
&lt;/codeblock&gt;

* Recursively search a value in the tree, starting from a given node, continuing either in the left or in the right subtree. Return the element, if found:
&lt;codeblock language=java&gt;
&lt;&lt;find&gt;&gt;=

private Comparable find(Node node, Comparable searchValue) {
    int compareResult;
    Comparable result = null;
    if ((compareResult = node.value.compareTo(searchValue)) == 0) {
        return node.value;
    } else if (compareResult &gt; 0) {
        if (node.left != null)
            return find(node.left, searchValue);
    } else {
        if (node.right != null)
            return find(node.right, searchValue);
    }
    return result;
}
&lt;/codeblock&gt;
==Traversal==
* Create an array from the tree and return it:
&lt;codeblock language=java&gt;
&lt;&lt;array&gt;&gt;=

public Comparable[] toArray() {
    i = 0;
    Comparable[] result = new Comparable[this.size];
    if (this.root != null)
        treeToArray(this.root, result);
    return result;
}
&lt;/codeblock&gt;

* Recursive preorder traversal of the tree, saving the values to the array:
&lt;codeblock language=java&gt;
&lt;&lt;traversal&gt;&gt;=

private void treeToArray(Node node, Comparable[] goal) {
    if (node.left != null)
        treeToArray(node.left, goal);
    goal[i] = node.value;
    if (i == goal.length - 1)
        return;
    i++;
    if (node.right != null)
        treeToArray(node.right, goal);
    return;
}
&lt;/codeblock&gt;

=Usage=

* Sample usage: we create a tree and add a few strings. We check if it's sorted and if searching works (uses JUnit 4, requiring Java 5):

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=

BinaryTree tree = new BinaryTree();
tree.add(&quot;Hanno&quot;);
tree.add(&quot;Zacharias&quot;);
tree.add(&quot;Berhard&quot;);
assertEquals(new Comparable[] { &quot;Berhard&quot;, &quot;Hanno&quot;, &quot;Zacharias&quot; }, tree.toArray());
assertEquals(null, tree.get(&quot;Otto&quot;));
assertEquals(&quot;Hanno&quot;, tree.get(&quot;Hanno&quot;));
&lt;/codeblock&gt;

* The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinaryTree.java&gt;&gt;=

class Node {
    public Node left;
    public Node right;
    public Comparable value;
    Node(Comparable value) {
        this.value = value;
    }
    Node(Node node) {
        this.left = node.left;
        this.right = node.right;
        this.value = node.value;
    }
}
    
public class BinaryTree {
	Node root;
    int size = 0;
    int i;
	@Test
    public void testTree() {
    	&lt;&lt;usage&gt;&gt;
    }
    &lt;&lt;add&gt;&gt;
    private Node insert(Node node, Comparable value) {
        Node result = new Node(node);
        int compare = result.value.compareTo(value);
        &lt;&lt;equal&gt;&gt;
        &lt;&lt;left&gt;&gt;
        &lt;&lt;right&gt;&gt;
        return result;
    }
    &lt;&lt;get&gt;&gt;
    &lt;&lt;find&gt;&gt;
    &lt;&lt;array&gt;&gt;
    &lt;&lt;traversal&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Binary search tree|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8210</id>
      <timestamp>2006-11-28T05:57:17Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Added missing imports.</comment>
      <text xml:space="preserve">=Overview=

A simple [http://en.wikipedia.org/wiki/Binary_search_tree binary search tree], implemented as an object-oriented, recursive data structure in Java, for objects that extend Comparable. Note that Java already provides efficient tree-based data structures, e.g. TreeSet.

=Implementation=

A node in a binary tree has three attributes: the left and the right child nodes and a value. The tree has one root node. This is the structure of the binary tree, as represented in the UML class diagram below.

[[Image:Binary-tree-class-diagram.png|UML class diagram for the binary search tree implementation]]

==Construction==

When adding an element to the tree, if the element is in the tree already, it is not added. The proper place to insert at is searched recursivley by calling the insert method.

&lt;codeblock language=java&gt;
&lt;&lt;add&gt;&gt;=

public void add(Comparable element) {
    if (this.root == null &amp;&amp; element != null) {
        this.root = new Node(element);
        this.size++;
    } else if (element != null) {
        this.root = insert(this.root, element);
    }
}
&lt;/codeblock&gt;

The recursive insertion method takes two parameters: the node to search from and the element to add. It returns the node including the inserted new element. When the value is already in the tree, nothing is done. For a more sophisticated tree, we could add the new element, count frequencies, etc.

&lt;codeblock language=java&gt;
&lt;&lt;equal&gt;&gt;=

if (compare == 0) {
    return result;
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the left subtree:
&lt;codeblock language=java&gt;
&lt;&lt;left&gt;&gt;=

if (compare &gt; 0) {
    if (result.left != null) {
        result.left = insert(result.left, value);
    } else {
        result.left = new Node(value);
        this.size++;
    }
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the right subtree:
&lt;codeblock language=java&gt;
&lt;&lt;right&gt;&gt;=

else if (compare &lt; 0) {
    if (result.right != null) {
        result.right = insert(result.right, value);
    } else {
        result.right = new Node(value);
        this.size++;
    }
}
&lt;/codeblock&gt;

* Search for a value in the tree, return the element if found or null if the element is not in the tree:

&lt;codeblock language=java&gt;
&lt;&lt;get&gt;&gt;=

public Comparable get(Comparable key) {
    if (this.root == null)
        return null;
    else
        return find(this.root, key);
}
&lt;/codeblock&gt;

* Recursively search a value in the tree, starting from a given node, continuing either in the left or in the right subtree. Return the element, if found:
&lt;codeblock language=java&gt;
&lt;&lt;find&gt;&gt;=

private Comparable find(Node node, Comparable searchValue) {
    int compareResult;
    Comparable result = null;
    if ((compareResult = node.value.compareTo(searchValue)) == 0) {
        return node.value;
    } else if (compareResult &gt; 0) {
        if (node.left != null)
            return find(node.left, searchValue);
    } else {
        if (node.right != null)
            return find(node.right, searchValue);
    }
    return result;
}
&lt;/codeblock&gt;
==Traversal==
* Create an array from the tree and return it:
&lt;codeblock language=java&gt;
&lt;&lt;array&gt;&gt;=

public Comparable[] toArray() {
    i = 0;
    Comparable[] result = new Comparable[this.size];
    if (this.root != null)
        treeToArray(this.root, result);
    return result;
}
&lt;/codeblock&gt;

* Recursive preorder traversal of the tree, saving the values to the array:
&lt;codeblock language=java&gt;
&lt;&lt;traversal&gt;&gt;=

private void treeToArray(Node node, Comparable[] goal) {
    if (node.left != null)
        treeToArray(node.left, goal);
    goal[i] = node.value;
    if (i == goal.length - 1)
        return;
    i++;
    if (node.right != null)
        treeToArray(node.right, goal);
    return;
}
&lt;/codeblock&gt;

=Usage=

* Sample usage: we create a tree and add a few strings. We check if it's sorted and if searching works (uses JUnit 4, requiring Java 5):

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=

BinaryTree tree = new BinaryTree();
tree.add(&quot;Hanno&quot;);
tree.add(&quot;Zacharias&quot;);
tree.add(&quot;Berhard&quot;);
assertEquals(new Comparable[] { &quot;Berhard&quot;, &quot;Hanno&quot;, &quot;Zacharias&quot; }, tree.toArray());
assertEquals(null, tree.get(&quot;Otto&quot;));
assertEquals(&quot;Hanno&quot;, tree.get(&quot;Hanno&quot;));
&lt;/codeblock&gt;

* The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinaryTree.java&gt;&gt;=
import static org.junit.Assert.*;
import org.junit.Test;

class Node {
	public Node left;
	public Node right;
	public Comparable value;
	Node(Comparable value) {
		this.value = value;
	}
	Node(Node node) {
		this.left = node.left;
		this.right = node.right;
		this.value = node.value;
	}
}
    
public class BinaryTree {
	Node root;
	int size = 0;
	int i;
	@Test
	public void testTree() {
		&lt;&lt;usage&gt;&gt;
	}
	&lt;&lt;add&gt;&gt;
	private Node insert(Node node, Comparable value) {
		Node result = new Node(node);
		int compare = result.value.compareTo(value);
		&lt;&lt;equal&gt;&gt;
		&lt;&lt;left&gt;&gt;
		&lt;&lt;right&gt;&gt;
		return result;
	}
	&lt;&lt;get&gt;&gt;
	&lt;&lt;find&gt;&gt;
	&lt;&lt;array&gt;&gt;
	&lt;&lt;traversal&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Binary search tree|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11974</id>
      <timestamp>2008-01-09T05:09:55Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>added generics and other things</comment>
      <text xml:space="preserve">=Overview=

A simple [http://en.wikipedia.org/wiki/Binary_search_tree binary search tree], implemented as an object-oriented, recursive data structure in Java, for objects that extend Comparable. Note that Java already provides efficient tree-based data structures, e.g. TreeSet and TreeMap.

=Implementation=

A node in a binary tree has three attributes: the left and the right child nodes and a value. The tree has one root node. This is the structure of the binary tree, as represented in the UML class diagram below.

[[Image:Binary-tree-class-diagram.png|UML class diagram for the binary search tree implementation]]

==Construction==

When adding an element to the tree, if the element is in the tree already, it is not added. The proper place to insert at is searched recursivley by calling the insert method.

&lt;codeblock language=java&gt;
&lt;&lt;add&gt;&gt;=

public void add(E element) {
    if (root == null &amp;&amp; element != null) {
        root = new Node&lt;E&gt;(element);
        size++;
    } else if (element != null) {
        root = insert(root, element);
    }
}
&lt;/codeblock&gt;

The recursive insertion method takes two parameters: the node to search from and the element to add. It returns the node including the inserted new element. When the value is already in the tree, nothing is done. For a more sophisticated tree, we could add the new element, count frequencies, etc.

&lt;codeblock language=java&gt;
&lt;&lt;equal&gt;&gt;=

if (compare == 0) {
    return result;
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the left subtree:
&lt;codeblock language=java&gt;
&lt;&lt;left&gt;&gt;=

if (compare &gt; 0) {
    if (result.left != null) {
        result.left = insert(result.left, value);
    } else {
        result.left = new Node&lt;E&gt;(value);
        size++;
    }
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the right subtree:
&lt;codeblock language=java&gt;
&lt;&lt;right&gt;&gt;=

else if (compare &lt; 0) {
    if (result.right != null) {
        result.right = insert(result.right, value);
    } else {
        result.right = new Node&lt;E&gt;(value);
        size++;
    }
}
&lt;/codeblock&gt;

* Search for a value in the tree, return the element if found or null if the element is not in the tree. Iteratively search a value in the tree, starting from the root, continuing either in the left or in the right subtree. Return the element, if found:

&lt;codeblock language=java&gt;
&lt;&lt;get&gt;&gt;=

public E get(E key) {
    if (root == null)
        return null;

    Node&lt;E&gt; node = root;
    int compareResult;
    while ((compareResult = node.value.compareTo(key)) != 0) {
        if (compareResult &gt; 0) {
            if (node.left != null)
                node = node.left;
            else
                return null;
        } else {
            if (node.right != null)
                node = node.right;
            else
                return null;
        }
    }
    return node.value;
}
&lt;/codeblock&gt;

==Traversal==
* Create a List from the tree and return it:
&lt;codeblock language=java&gt;
&lt;&lt;array&gt;&gt;=

public List&lt;E&gt; toArray() {
    List&lt;E&gt; result = new ArrayList&lt;E&gt;();
    treeToArray(root, result);
    return result;
}
&lt;/codeblock&gt;

* Recursive preorder traversal of the tree, saving the values to the array:
&lt;codeblock language=java&gt;
&lt;&lt;traversal&gt;&gt;=

private void treeToArray(Node&lt;E&gt; node, List&lt;E&gt; goal) {
    if (node != null) {
        treeToArray(node.left, goal);
        goal.add(node.value);
        treeToArray(node.right, goal);
    }
}
&lt;/codeblock&gt;

=Usage=

* Sample usage: we create a tree and add a few strings. We check if it's sorted and if searching works (uses JUnit 4, requiring Java 5):

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=

BinaryTree&lt;String&gt; tree = new BinaryTree&lt;String&gt;();
tree.add(&quot;Hanno&quot;);
tree.add(&quot;Zacharias&quot;);
tree.add(&quot;Berhard&quot;);
assertEquals(new String[]{ &quot;Berhard&quot;, &quot;Hanno&quot;, &quot;Zacharias&quot; }, tree.toArray().toArray(new String[3]));
assertEquals(null, tree.get(&quot;Otto&quot;));
assertEquals(&quot;Hanno&quot;, tree.get(&quot;Hanno&quot;));
&lt;/codeblock&gt;

* The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinaryTree.java&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import static org.junit.Assert.*;
import org.junit.Test;

class Node&lt;E extends Comparable&lt;? super E&gt;&gt; {
	public Node&lt;E&gt; left;
	public Node&lt;E&gt; right;
	public final E value;
	Node(E value) {
		this.value = value;
	}
	Node(Node&lt;E&gt; node) {
		left = node.left;
		right = node.right;
		value = node.value;
	}
}
    
public class BinaryTree&lt;E extends Comparable&lt;? super E&gt;&gt; {
	Node&lt;E&gt; root;
	int size = 0;
	int i;
	@Test
	public void testTree() {
		&lt;&lt;usage&gt;&gt;
	}
	&lt;&lt;add&gt;&gt;
	private Node&lt;E&gt; insert(Node&lt;E&gt; node, E value) {
		Node&lt;E&gt; result = new Node&lt;E&gt;(node);
		int compare = result.value.compareTo(value);
		&lt;&lt;equal&gt;&gt;
		&lt;&lt;left&gt;&gt;
		&lt;&lt;right&gt;&gt;
		return result;
	}
	&lt;&lt;get&gt;&gt;
	&lt;&lt;find&gt;&gt;
	&lt;&lt;array&gt;&gt;
	&lt;&lt;traversal&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Binary search tree|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11975</id>
      <timestamp>2008-01-09T05:11:39Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">=Overview=

A simple [http://en.wikipedia.org/wiki/Binary_search_tree binary search tree], implemented as an object-oriented, recursive data structure in Java, for objects that extend Comparable. Note that Java already provides efficient tree-based data structures, e.g. TreeSet and TreeMap.

=Implementation=

A node in a binary tree has three attributes: the left and the right child nodes and a value. The tree has one root node. This is the structure of the binary tree, as represented in the UML class diagram below.

[[Image:Binary-tree-class-diagram.png|UML class diagram for the binary search tree implementation]]

==Construction==

When adding an element to the tree, if the element is in the tree already, it is not added. The proper place to insert at is searched recursivley by calling the insert method.

&lt;codeblock language=java&gt;
&lt;&lt;add&gt;&gt;=

public void add(E element) {
    if (root == null &amp;&amp; element != null) {
        root = new Node&lt;E&gt;(element);
        size++;
    } else if (element != null) {
        root = insert(root, element);
    }
}
&lt;/codeblock&gt;

The recursive insertion method takes two parameters: the node to search from and the element to add. It returns the node including the inserted new element. When the value is already in the tree, nothing is done. For a more sophisticated tree, we could add the new element, count frequencies, etc.

&lt;codeblock language=java&gt;
&lt;&lt;equal&gt;&gt;=

if (compare == 0) {
    return result;
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the left subtree:
&lt;codeblock language=java&gt;
&lt;&lt;left&gt;&gt;=

if (compare &gt; 0) {
    if (result.left != null) {
        result.left = insert(result.left, value);
    } else {
        result.left = new Node&lt;E&gt;(value);
        size++;
    }
}
&lt;/codeblock&gt;
* In case the new value needs to be inserted in the right subtree:
&lt;codeblock language=java&gt;
&lt;&lt;right&gt;&gt;=

else if (compare &lt; 0) {
    if (result.right != null) {
        result.right = insert(result.right, value);
    } else {
        result.right = new Node&lt;E&gt;(value);
        size++;
    }
}
&lt;/codeblock&gt;

* Search for a value in the tree, return the element if found or null if the element is not in the tree. Iteratively search a value in the tree, starting from the root, continuing either in the left or in the right subtree. Return the element, if found:

&lt;codeblock language=java&gt;
&lt;&lt;get&gt;&gt;=

public E get(E key) {
    if (root == null)
        return null;

    Node&lt;E&gt; node = root;
    int compareResult;
    while ((compareResult = node.value.compareTo(key)) != 0) {
        if (compareResult &gt; 0) {
            if (node.left != null)
                node = node.left;
            else
                return null;
        } else {
            if (node.right != null)
                node = node.right;
            else
                return null;
        }
    }
    return node.value;
}
&lt;/codeblock&gt;

==Traversal==
* Create a List from the tree and return it:
&lt;codeblock language=java&gt;
&lt;&lt;array&gt;&gt;=

public List&lt;E&gt; toList() {
    List&lt;E&gt; result = new ArrayList&lt;E&gt;();
    treeToList(root, result);
    return result;
}
&lt;/codeblock&gt;

* Recursive preorder traversal of the tree, saving the values to the array:
&lt;codeblock language=java&gt;
&lt;&lt;traversal&gt;&gt;=

private void treeToList(Node&lt;E&gt; node, List&lt;E&gt; goal) {
    if (node != null) {
        treeToList(node.left, goal);
        goal.add(node.value);
        treeToList(node.right, goal);
    }
}
&lt;/codeblock&gt;

=Usage=

* Sample usage: we create a tree and add a few strings. We check if it's sorted and if searching works (uses JUnit 4, requiring Java 5):

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=

BinaryTree&lt;String&gt; tree = new BinaryTree&lt;String&gt;();
tree.add(&quot;Hanno&quot;);
tree.add(&quot;Zacharias&quot;);
tree.add(&quot;Berhard&quot;);
assertEquals(new String[]{ &quot;Berhard&quot;, &quot;Hanno&quot;, &quot;Zacharias&quot; }, tree.toList().toArray(new String[3]));
assertEquals(null, tree.get(&quot;Otto&quot;));
assertEquals(&quot;Hanno&quot;, tree.get(&quot;Hanno&quot;));
&lt;/codeblock&gt;

* The complete program:
&lt;codeblock language=java&gt;
&lt;&lt;BinaryTree.java&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import static org.junit.Assert.*;
import org.junit.Test;

class Node&lt;E extends Comparable&lt;? super E&gt;&gt; {
	public Node&lt;E&gt; left;
	public Node&lt;E&gt; right;
	public final E value;
	Node(E value) {
		this.value = value;
	}
	Node(Node&lt;E&gt; node) {
		left = node.left;
		right = node.right;
		value = node.value;
	}
}
    
public class BinaryTree&lt;E extends Comparable&lt;? super E&gt;&gt; {
	Node&lt;E&gt; root;
	int size = 0;
	int i;
	@Test
	public void testTree() {
		&lt;&lt;usage&gt;&gt;
	}
	&lt;&lt;add&gt;&gt;
	private Node&lt;E&gt; insert(Node&lt;E&gt; node, E value) {
		Node&lt;E&gt; result = new Node&lt;E&gt;(node);
		int compare = result.value.compareTo(value);
		&lt;&lt;equal&gt;&gt;
		&lt;&lt;left&gt;&gt;
		&lt;&lt;right&gt;&gt;
		return result;
	}
	&lt;&lt;get&gt;&gt;
	&lt;&lt;array&gt;&gt;
	&lt;&lt;traversal&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Binary search tree|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (Scheme)</title>
    <id>2682</id>
    <revision>
      <id>7564</id>
      <timestamp>2006-09-03T11:25:22Z</timestamp>
      <contributor>
        <username>S. Carton</username>
        <id>82</id>
      </contributor>
      <comment>A persistent binary tree</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are notdestructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (cons value (del-rightmost tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predeccessor tree))
                  (new-value (car value-subtree))
                  (new-left-subtree (cdr value-subtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>7565</id>
      <timestamp>2006-09-03T15:20:08Z</timestamp>
      <contributor>
        <username>S. Carton</username>
        <id>82</id>
      </contributor>
      <comment>fixed subtle undefined behaviour in replace-in-order-predecessor</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predeccessor tree))
                  (new-value (car value-subtree))
                  (new-left-subtree (cdr value-subtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>7571</id>
      <timestamp>2006-09-04T09:27:29Z</timestamp>
      <contributor>
        <username>S. Carton</username>
        <id>82</id>
      </contributor>
      <comment>fixed bug in tree-delete-node</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predecessor lchild))
                  (new-value (car value-lsubtree))
                  (new-left-subtree (cdr value-lsubtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14799</id>
      <timestamp>2008-10-01T06:06:57Z</timestamp>
      <contributor>
        <ip>141.154.216.20</ip>
      </contributor>
      <comment>add Scheme category</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predecessor lchild))
                  (new-value (car value-lsubtree))
                  (new-left-subtree (cdr value-lsubtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;

[[Category:Programming language:Scheme]]</text>
    </revision>
    <revision>
      <id>14800</id>
      <timestamp>2008-10-01T06:12:13Z</timestamp>
      <contributor>
        <ip>141.154.216.20</ip>
      </contributor>
      <comment>add binary search tree category</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predecessor lchild))
                  (new-value (car value-lsubtree))
                  (new-left-subtree (cdr value-lsubtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>14803</id>
      <timestamp>2008-10-01T13:11:39Z</timestamp>
      <contributor>
        <ip>141.154.216.20</ip>
      </contributor>
      <minor/>
      <comment>[[Binary tree (Scheme)]] moved to [[Binary search tree (Scheme)]]: consistency with other binary tree articles</comment>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let* ((value-lsubtree (replace-in-order-predecessor lchild))
                  (new-value (car value-lsubtree))
                  (new-left-subtree (cdr value-lsubtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>16558</id>
      <timestamp>2009-11-17T18:10:09Z</timestamp>
      <contributor>
        <username>Llama</username>
        <id>1925</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

This is an implementation of a [http://en.wikipedia.org/wiki/Binary_tree persistent binary tree]. Its persistence is a desirable property: updates are not destructive, and earlier versions of the tree are preserved. 

Our binary tree will use a comparison predicate provided by us, so as to be generic in the elements it can contain.

We will represent a binary tree as a three-element list: the node's value, its left child and its right child.The empty list represents a null pointer (an empty child).

First, binary search. We check to see if the current subtree:

1) Is empty, which means the value we are searching for is not in the subtree;

2)The node value in the current subtree is equal to what we're searching for, in which case we return true;

3) The node value is greater than or equal to what we're searching for, so we recursively search its left child;

4) The value can only be in the right child, so we recursively search that.

&lt;codeblock language=scheme&gt;
(define (tree-search tree value tree-&lt;=)
  (cond ((null? tree)
	 #f)
	((equal? value (car tree))
	 #t)
	((tree-&lt;= value (car tree))
	 (tree-search (cadr tree) value tree-&lt;=))
	(else
	 (tree-search (caddr tree) value tree-&lt;=))))
&lt;/codeblock&gt;

Now, insertion. It is very easy: we just move down the tree using our comparison predicate and insert a new node when we find an empty child.

&lt;codeblock language=scheme&gt;
(define (tree-insert tree value tree-&lt;=)
  (cond ((null? tree)
	 (list value '() '()))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-insert (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-insert (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

Now node deletion, which is not as trivial as insertion or search.

1) Deleting a node that has no children is simple: replace it with the null list. 

2) Deleting a node with one child is simple also: replace the node with its only child.

3) Deleting a node with two children is more involved: we have to find either the node's in-order predecessor (the rightmost node of the left subtree) or the in-order successor (the leftmost node of the right subtree). We replace the node's value with the in-order predecessor's value and delete the in-order predecessor (which can only have at most 1 child, as its right child is empty by definition).

So the first problem we have to solve is, given a subtree, find its rightmost node, delete it, and return both its value and the new subtree (with the rightmost node deleted). We will return these (the value and the modified tree) in a cons pair.

Deletion of the rightmost node is simple: given that it has no right child, the node is simply substituted for the node's left child.

We use a bit of imperative code to be able to return both the node's value AND the modified subtree in only 1 tree traversal (we might use a functional zipper datastructure too). This is the only thorny part of the problem: how to access a value found at the end of a recursion without destroying the structure the recursion builds. This is the only use of imperative code in this program.

Notice we have to evaluate updated-tree before consing it with value to avoid undefined behaviour. We use the last let to ensure that value has been set before it is consed with updated-tree.

&lt;codeblock language=scheme&gt;
(define (replace-in-order-predecessor tree)
  (let ((value '()))
    (define (del-rightmost atree)
      (cond ((null? (caddr atree))
	     (begin
	       (set! value (car atree))
	       (cadr atree)))
	    (else
	     (list (car atree) (cadr atree) (del-rightmost (caddr atree))))))
    (let ((updated-tree (del-rightmost tree)))
      (cons value updated-tree))))
&lt;/codeblock&gt;

Now we make a function that, given a subtree, deletes its root node. It takes into account the three cases we described: no children, one child and two children:

&lt;codeblock language=scheme&gt;
(define (tree-delete-node tree)
  (let ((lchild (cadr tree)) (rchild (caddr tree)))
    (cond ((and (null? lchild) (null? rchild)) '())
          ((null? lchild) rchild)
          ((null? rchild) lchild)
          (else
           (let ((value-lsubtree (replace-in-order-predecessor lchild))
                  (new-value (car value-lsubtree))
                  (new-left-subtree (cdr value-lsubtree)))
             (list new-value new-left-subtree rchild))))))
&lt;/codeblock&gt;

Now comes the main delete procedure: it is given a value, and it finds and deletes the first node it finds with that value, using the tree-delete-node function. It gives an error if it can't find the value it's supposed to delete.

&lt;codeblock language=scheme&gt;

(define (tree-delete tree value tree-&lt;=)
  (cond ((null? tree)
	 (error &quot;tree-delete: value not in tree&quot;))
	((equal? (car tree) value)
	 (tree-delete-node tree))
	((tree-&lt;= value (car tree))
	 (list (car tree) (tree-delete (cadr tree) value tree-&lt;=) (caddr tree)))
	(else
	 (list (car tree) (cadr tree) (tree-delete (caddr tree) value tree-&lt;=)))))
&lt;/codeblock&gt;

And that's it. Now, let's build a list-&gt;tree function and a tree-flattening function in order to implement binary tree sort for testing our tree implementation:

&lt;codeblock language=scheme&gt;
(define (list-&gt;tree alist lt-pred)
  (define (helper blist tree)
    (if (null? blist)
        tree
        (helper (cdr blist) (tree-insert tree (car blist) lt-pred))))
  (helper alist '()))

(define (tree-fringe tree)
  (if (null? tree) 
      '()
      (append (tree-fringe (cadr tree)) 
              (list (car tree)) 
              (tree-fringe (caddr tree)))))

(define (tree-sort alist tree-&lt;)
  (tree-fringe (list-&gt;tree alist tree-&lt;) tree-&lt;))
&lt;/codeblock&gt;

And let's hit the repl with a test case:

&lt;codeblock&gt;
&gt; (tree-sort '(2 43 7 8 5 4 23 4556 6 7 4 3 2) &lt;)
(2 2 3 4 4 5 6 7 7 8 23 43 4556)
&lt;/codeblock&gt;

To illustrate the persistence of the structure:

&lt;codeblock&gt;
&gt; (define tree1 (list-&gt;tree '(3 2 1 4 5) &lt;))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&gt; (tree-delete tree1 4 &lt;)
(3 (2 (1 () ()) ()) (5 () ()))
&gt; tree1
(3 (2 (1 () ()) ()) (4 () (5 () ())))
&lt;/codeblock&gt;

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>16559</id>
      <timestamp>2009-11-17T18:19:28Z</timestamp>
      <contributor>
        <username>Bob11213</username>
        <id>1926</id>
      </contributor>
      <comment>updated to be more comprehensive</comment>
      <text xml:space="preserve">{{develop}}

Binary Trees

Suppose we want to create a new kind of recursive data type, our familiar binary trees. The first thing we have to do is to define the data type in terms of its constructors, selectors and recognizers. In the case of binary trees, we have the following:

Constructors: We have two kinds of binary trees, leaves and nodes. Accordingly, we need a constructor for each kind:
(make-bin-tree-leaf E): A leaf is a composite object with one component, the element E.
(make-bin-tree-node E B1 B2): A node consists of three components, an element E, a left subtree B1 and a right subtree B2. Each of B1 and B2 is a binary tree.
Notice that the definition of binary tree is inherently recursive (as in the case of nodes). Larger binary trees can be composed from smaller ones.
Selectors: We need to define a selector for each component of each kind of binary tree.
(bin-tree-leaf-element L): Retrieve the element of a leaf L.
(bin-tree-node-element N): Retrieve the element of a node N.
(bin-tree-node-left N): Retrieve the left subtree of a node N.
(bin-tree-node-right N): Retrieve the right subtree of a node N.
Recognizers: We define one recognizer for each kind of binary tree.
(bin-tree-leaf-p B): Test if a given binary tree B is a leaf.
(bin-tree-node-p B): Test if a given binary tree B is a node.
Notice that we have not written a line of code yet, and still we are able to write down the function signature of all the constructors, selectors and recognizers. The process is more or less mechanical:

Define a constructor for each variant of the recursive data type. The parameters for a constructor defines the components of a composite object.
For each parameter of each constructor, define a selector to retrieve the corresponding component.
For each constructor, define a corresponding recognizer.
The next question is how we are to represent a binary tree as a LISP object. Of course, a list is the first thing that comes to our mind:

We represent an leaf with element E by a singleton list containing E (i.e. (list E)).
A node with element E, left subtree B1 and right subtree B2 is represented as a list containing the three components (i.e. (list E B1 B2)).
Fixing the representation, we can thus implement the recursive data type functions:
&lt;codeblock language=scheme&gt;
;;
;; Binary Trees
;;

;;
;; Constructors for binary trees
;;

(defun make-bin-tree-leaf (E)
  &quot;Create a leaf.&quot;
  (list E))

(defun make-bin-tree-node (E B1 B2)
  &quot;Create a node with element K, left subtree B1 and right subtree B2.&quot;
  (list E B1 B2))

;;
;; Selectors for binary trees
;;

(defun bin-tree-leaf-element (L)
  &quot;Retrieve the element of a leaf L.&quot;
  (first L))

(defun bin-tree-node-element (N)
  &quot;Retrieve the element of a node N.&quot;
  (first N))

(defun bin-tree-node-left (N)
  &quot;Retrieve the left subtree of a node N.&quot;
  (second N))

(defun bin-tree-node-right (N)
  &quot;Retrieve the right subtree of a node N.&quot;
  (third N))

;;
;; Recognizers for binary trees
;;

(defun bin-tree-leaf-p (B)
  &quot;Test if binary tree B is a leaf.&quot;
  (and (listp B) (= (list-length B) 1)))

(defun bin-tree-node-p (B)
  &quot;Test if binary tree B is a node.&quot;
  (and (listp B) (= (list-length B) 3)))
The representation scheme works out like the following:

USER(5): (make-bin-tree-node '*
                             (make-bin-tree-node '+
                                                 (make-bin-tree-leaf 2)
                                                 (make-bin-tree-leaf 3))
                             (make-bin-tree-node '-
                                                 (make-bin-tree-leaf 7)
                                                 (make-bin-tree-leaf 8)))
&lt;/codeblock&gt;

(* (+ (2) (3)) (- (7) (8)))
The expression above is a binary tree node with element * and two subtrees. The left subtree is itself a binary tree node with + as its element and leaves as its subtress. The right subtree is also a binary tree node with - as its element and leaves as its subtrees. All the leaves are decorated by numeric components.
            *
           / \
          /   \
         /     \
        +       -
       / \     / \
      2   3   7   8
Searching Binary Trees

As discussed in previous tutorials, having recursive data structures defined in the way we did streamlines the process of formulating structural recursions. We review this concept in the following examples.

Suppose we treat binary trees as containers. An expression E is a member of a binary tree B if:

B is a leaf and its element is E.
B is a node and either its element is E or E is a member of one of its subtrees.
For example, the definition asserts that the members of (* (+ (2) (3)) (- (7) (8))) are *, +, 2, 3, -, 7 and 8. Such a definition can be directly implemented by our recursive data type functions:

&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (or (equal E (bin-tree-node-element B))
        (bin-tree-member-p (bin-tree-node-left B) E)
	(bin-tree-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

The function can be made more readable by using the let form:
&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (or (equal E elmt)
	  (bin-tree-member-p left E)
	  (bin-tree-member-p right E)))))
&lt;/codeblock&gt;
Tracing the execution of bin-tree-member-p, we get:

USER(14): (trace bin-tree-member-p)
(BIN-TREE-MEMBER-P)
USER(15): (bin-tree-member-p '(+ (* (2) (3)) (- (7) (8))) 7) 
 0: (BIN-TREE-MEMBER-P (+ (* (2) (3)) (- (7) (8))) 7)
   1: (BIN-TREE-MEMBER-P (* (2) (3)) 7)
     2: (BIN-TREE-MEMBER-P (2) 7)
     2: returned NIL
     2: (BIN-TREE-MEMBER-P (3) 7)
     2: returned NIL
   1: returned NIL
   1: (BIN-TREE-MEMBER-P (- (7) (8)) 7)
     2: (BIN-TREE-MEMBER-P (7) 7)
     2: returned T
   1: returned T
 0: returned T
T
Exercise: Let size(B) be the number of members in a binary tree B. Give a recursive definition of size(B), and then implement a LISP function (bin-tree-size B) that returns size(B).
Traversing Binary Trees

Let us write a function that will reverse a tree in the sense that the left and right subtrees of every node are swapped:

&lt;codeblock&gt;
(defun binary-tree-reverse (B)
  &quot;Reverse binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      B
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (make-bin-tree-node elmt
		          (binary-tree-reverse right)
		          (binary-tree-reverse left)))))
&lt;/codeblock&gt;

The correctness of the above implementation can be articulated as follows. Given a binary tree B and an object E, either the binary tree is a leaf or it is a node:

Case 1: B is a leaf.
Then the reversal of B is simply B itself.
Case 2: B is a node.
Then B has three components, namely, an element elmt, a left subtree left and a right subtree right. The reversal of B is a node with element elmt, left subtree the reversal of right, and right subtree the reversal of left.
The following shows us how the recursion unfolds:

USER(21): (trace bin-tree-reverse)
(BIN-TREE-REVERSE)
USER(22): (bin-tree-reverse '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-REVERSE (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-REVERSE (- (7) (8)))
     2: (BIN-TREE-REVERSE (8))
     2: returned (8)
     2: (BIN-TREE-REVERSE (7))
     2: returned (7)
   1: returned (- (8) (7))
   1: (BIN-TREE-REVERSE (+ (2) (3)))
     2: (BIN-TREE-REVERSE (3))
     2: returned (3)
     2: (BIN-TREE-REVERSE (2))
     2: returned (2)
   1: returned (+ (3) (2))
 0: returned (* (- (8) (7)) (+ (3) (2)))
(* (- (8) (7)) (+ (3) (2)))
The resulting expression represents the following tree:
            *
           / \
          /   \
         /     \
        -       +
       / \     / \
      8   7   3   2
Let us implement a function that will extract the members of a given binary tree, and put them into a list in preorder.

&lt;codeblock&gt;
(defun bin-tree-preorder (B)
  &quot;Create a list containing keys of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (list (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (append (bin-tree-preorder left)
		    (bin-tree-preorder right))))))
&lt;/codeblock&gt;

Tracing the execution of the function, we obtain the following:
USER(13): (trace bin-tree-preorder)
(BIN-TREE-PREORDER)
USER(14): (bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-PREORDER (+ (2) (3)))
     2: (BIN-TREE-PREORDER (2))
     2: returned (2)
     2: (BIN-TREE-PREORDER (3))
     2: returned (3)
   1: returned (+ 2 3)
   1: (BIN-TREE-PREORDER (- (7) (8)))
     2: (BIN-TREE-PREORDER (7))
     2: returned (7)
     2: (BIN-TREE-PREORDER (8))
     2: returned (8)
   1: returned (- 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
As we have discussed before, the append call in the code above is a source of inefficiency that can be obtimized away:
&lt;codeblock&gt;
(defun fast-bin-tree-preorder (B)
  &quot;A tail-recursive version of bin-tree-preorder.&quot;
  (preorder-aux B nil))

(defun preorder-aux (B A)
  &quot;Append A to the end of the list containing elements of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (cons (bin-tree-leaf-element B) A)
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (preorder-aux left
			  (preorder-aux right A))))))
&lt;/codeblock&gt;
An execution trace of the implementation is the following:
USER(15): (trace fast-bin-tree-preorder preorder-aux)          
(PREORDER-AUX FAST-BIN-TREE-PREORDER)
USER(16): (fast-bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (FAST-BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (PREORDER-AUX (* (+ (2) (3)) (- (7) (8))) NIL)
     2: (PREORDER-AUX (- (7) (8)) NIL)
       3: (PREORDER-AUX (8) NIL)
       3: returned (8)
       3: (PREORDER-AUX (7) (8))
       3: returned (7 8)
     2: returned (- 7 8)
     2: (PREORDER-AUX (+ (2) (3)) (- 7 8))
       3: (PREORDER-AUX (3) (- 7 8))
       3: returned (3 - 7 8)
       3: (PREORDER-AUX (2) (3 - 7 8))
       3: returned (2 3 - 7 8)
     2: returned (+ 2 3 - 7 8)
   1: returned (* + 2 3 - 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
Exercise: Implement a function that will create a list containing members of a given binary tree in postorder. Implement also a tail-recursive version of the same function.

Exercise: Repeat the last exercise with inorder.

Abstract Data Types

Abstract data types are blackboxes. They are defined in terms of their external interfaces, and not their implementation. For example, a set abstraction offers the following operations:

(make-empty-set) creates an empty set.
(set-insert S E) returns a set containing all members of set S plus an additional member E.
(set-remove S E) returns a set containing all members of set S except for E.
(set-member-p S E) returns true if E is a member of set S.
(set-empty-p S) returns true if set S is empty.
To implement an abstract data type, we need to decide on a representation. Let us represent a set by a list with no repeated members.

&lt;codeblock&gt;
(defun make-empty-set ()
  &quot;Creates an empty set.&quot;
  nil)

(defun set-insert (S E)
  &quot;Return a set containing all the members of set S plus the element E.&quot;
  (adjoin E S :test #'equal))

(defun set-remove (S E)
  &quot;Return a set containing all the members of set S except for element E.&quot;
  (remove E S :test #'equal))

(defun set-member-p (S E)
  &quot;Return non-NIL if set S contains element E.&quot;
  (member E S :test #'equal))

(defun set-empty-p (S)
  &quot;Return true if set S is empty.&quot;
  (null S))
&lt;/codeblock&gt;

Exercise: Look up the definition of adjoin, remove and member from CLTL2. In particular, find out how the :test keyword is used to specify the equality test function to be used by the three functions. What will happen if we omit the :test keyword and the subsequent #'equal when invoking the three functions?
Notice that we have implemented an abstract data type (sets) using a more fundamental recursive data structure (lists) with additional computational constraints (no repetition) imposed by the interface functions.

Binary Search Trees

Another way of implementing the same set abstraction is to use the more efficient binary search tree (BST). Binary search trees are basically binary trees with the following additional computational constraints:

All the members in the left subtree of a tree node is no greater than the element of the node.
All the members in the right subtree of a tree node is greater than the element of the node.
All the leaf members are distinct.
Again, we are implementing an abstract data type (sets) by a more fundamental recursive data structure (binary trees) with additional computational constraints. In particular, we use the leaves of a binary tree to store the member of a set, and the tree nodes for providing indexing information that improves search performance. for example, a BST representing the set {1 2 3 4} would look like:
            2
           / \
          /   \
         /     \
        1       3
       / \     / \
      1   2   3   4
An empty BST is represented by NIL, while a nonempty BST is represented by a binary tree. We begin with the constructor and recognizer for empty BST.

&lt;codeblock&gt;
(defun make-empty-BST ()
  &quot;Create an empty BST.&quot;
  nil)

(defun BST-empty-p (B)
  &quot;Check if BST B is empty.&quot;
  (null B))
Given the additional computational constraints, membership test can be implemented as follows:

(defun BST-member-p (B E)
  &quot;Check if E is a member of BST B.&quot;
  (if (BST-empty-p B)
      nil
    (BST-nonempty-member-p B E)))

(defun BST-nonempty-member-p (B E)
  &quot;Check if E is a member of nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (= E (bin-tree-leaf-element B))
    (if (&lt;= E (bin-tree-node-element B))
	(BST-nonempty-member-p (bin-tree-node-left B) E)
      (BST-nonempty-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

Notice that we handle the degenerate case of searching an empty BST separately, and apply the well-known recursive search algorithm only on nonempty BST.
USER(16): (trace BST-member-p BST-nonempty-member-p)
(BST-NONEMPTY-MEMBER-P BST-MEMBER-P)
USER(17): (BST-member-p '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NONEMPTY-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NONEMPTY-MEMBER-P (3 (3) (4)) 3)
       3: (BST-NONEMPTY-MEMBER-P (3) 3)
       3: returned T
     2: returned T
   1: returned T
 0: returned T
T
Insertion is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-insert (B E)
  &quot;Insert E into BST B.&quot;
  (if (BST-empty-p B)
      (make-bin-tree-leaf E)
    (BST-nonempty-insert B E)))

(defun BST-nonempty-insert (B E)
  &quot;Insert E into nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (BST-leaf-insert B E)
    (let ((elmt  (bin-tree-node-element B))
	  (left  (bin-tree-node-left    B))
	  (right (bin-tree-node-right   B)))
      (if (&lt;= E (bin-tree-node-element B))
	  (make-bin-tree-node elmt
			      (BST-nonempty-insert (bin-tree-node-left B) E)
			      right)
	(make-bin-tree-node elmt
			    left
			    (BST-nonempty-insert (bin-tree-node-right B) E))))))

(defun BST-leaf-insert (L E)
  &quot;Insert element E to a BST with only one leaf.&quot;
  (let ((elmt (bin-tree-leaf-element L)))
    (if (= E elmt)
	L
      (if (&lt; E elmt)
	  (make-bin-tree-node E
			      (make-bin-tree-leaf E)
			      (make-bin-tree-leaf elmt))
	(make-bin-tree-node elmt
			    (make-bin-tree-leaf elmt)
			    (make-bin-tree-leaf E))))))
&lt;/codeblock&gt;

As before, recursive insertion to nonempty BST is handled outside of the general entry point of BST insertion. Traversing down the index nodes, the recursive algorithm eventually arrives at a leaf. In case the element is not already in the tree, the leaf is turned into a node with leaf subtrees holding the inserted element and the element of the original leaf. For example, if we insert 2.5 into the tree represented by (2 (1 (1) (2)) (3 (3) (4))), the effect is the following:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       3
       / \     / \            / \     / \
      1   2   3   4          1   2  2.5  4
                                    / \
                                  2.5  3
A trace of the insertion operation is given below:
USER(22): (trace BST-insert BST-nonempty-insert BST-leaf-insert)
(BST-LEAF-INSERT BST-NONEMPTY-INSERT BST-INSERT)
USER(23): (BST-insert '(2 (1 (1) (2)) (3 (3) (4))) 2.5)
 0: (BST-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
   1: (BST-NONEMPTY-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
     2: (BST-NONEMPTY-INSERT (3 (3) (4)) 2.5)
       3: (BST-NONEMPTY-INSERT (3) 2.5)
         4: (BST-LEAF-INSERT (3) 2.5)
         4: returned (2.5 (2.5) (3))
       3: returned (2.5 (2.5) (3))
     2: returned (3 (2.5 (2.5) (3)) (4))
   1: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
 0: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
(2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
Removal of elements is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-remove (B E)
  &quot;Remove E from BST B.&quot;
  (if (BST-empty-p B)
      B
    (if (bin-tree-leaf-p B)
	(BST-leaf-remove B E)
      (BST-node-remove B E))))

(defun BST-leaf-remove (L E)
  &quot;Remove E from BST leaf L.&quot;
  (if (= E (bin-tree-leaf-element L))
      (make-empty-BST)
    L))

(defun BST-node-remove (N E)
  &quot;Remove E from BST node N.&quot;
  (let
      ((elmt  (bin-tree-node-element N))
       (left  (bin-tree-node-left    N))
       (right (bin-tree-node-right   N)))
    (if (&lt;= E elmt)
	(if (bin-tree-leaf-p left)
	    (if (= E (bin-tree-leaf-element left))
		right
	      N)
	  (make-bin-tree-node elmt (BST-node-remove left E) right))
      (if (bin-tree-leaf-p right)
	  (if (= E (bin-tree-leaf-element right))
	      left
	    N)
	(make-bin-tree-node elmt left (BST-node-remove right E))))))
&lt;/codeblock&gt;

This time, removal from empty BST's and BST's with a single leaf are both degenerate cases. The recursive removal algorithm deals with BST nodes. Traversing down the index nodes, the recursive algorithm searches for the parent node of the leaf to be removed. In case it is found, the sibling of the leaf to be removed replaces its parent node. For example, the effect of removing 2 from the BST represented by (2 (1 (1) (2)) (3 (3) (4))) is depicted as follows:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       4
       / \     / \            / \     
      1   2   3   4          1   2  
A trace of the deletion operation is given below:
USER(4): (trace BST-remove BST-node-remove)
(BST-NODE-REMOVE BST-REMOVE)
USER(5): (BST-remove '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NODE-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NODE-REMOVE (3 (3) (4)) 3)
     2: returned (4)
   1: returned (2 (1 (1) (2)) (4))
 0: returned (2 (1 (1) (2)) (4))
(2 (1 (1) (2)) (4)))) ()) (4 () (5 () ())))

http://www.cs.sfu.ca/CC/310/pwfong/Lisp/3/tutorial3.html

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>16560</id>
      <timestamp>2009-11-17T18:20:44Z</timestamp>
      <contributor>
        <username>Bob11213</username>
        <id>1926</id>
      </contributor>
      <text xml:space="preserve">Binary Trees

Suppose we want to create a new kind of recursive data type, our familiar binary trees. The first thing we have to do is to define the data type in terms of its constructors, selectors and recognizers. In the case of binary trees, we have the following:

Constructors: We have two kinds of binary trees, leaves and nodes. Accordingly, we need a constructor for each kind:
(make-bin-tree-leaf E): A leaf is a composite object with one component, the element E.
(make-bin-tree-node E B1 B2): A node consists of three components, an element E, a left subtree B1 and a right subtree B2. Each of B1 and B2 is a binary tree.
Notice that the definition of binary tree is inherently recursive (as in the case of nodes). Larger binary trees can be composed from smaller ones.
Selectors: We need to define a selector for each component of each kind of binary tree.
(bin-tree-leaf-element L): Retrieve the element of a leaf L.
(bin-tree-node-element N): Retrieve the element of a node N.
(bin-tree-node-left N): Retrieve the left subtree of a node N.
(bin-tree-node-right N): Retrieve the right subtree of a node N.
Recognizers: We define one recognizer for each kind of binary tree.
(bin-tree-leaf-p B): Test if a given binary tree B is a leaf.
(bin-tree-node-p B): Test if a given binary tree B is a node.
Notice that we have not written a line of code yet, and still we are able to write down the function signature of all the constructors, selectors and recognizers. The process is more or less mechanical:

Define a constructor for each variant of the recursive data type. The parameters for a constructor defines the components of a composite object.
For each parameter of each constructor, define a selector to retrieve the corresponding component.
For each constructor, define a corresponding recognizer.
The next question is how we are to represent a binary tree as a LISP object. Of course, a list is the first thing that comes to our mind:

We represent an leaf with element E by a singleton list containing E (i.e. (list E)).
A node with element E, left subtree B1 and right subtree B2 is represented as a list containing the three components (i.e. (list E B1 B2)).
Fixing the representation, we can thus implement the recursive data type functions:
&lt;codeblock language=scheme&gt;
;;
;; Binary Trees
;;

;;
;; Constructors for binary trees
;;

(defun make-bin-tree-leaf (E)
  &quot;Create a leaf.&quot;
  (list E))

(defun make-bin-tree-node (E B1 B2)
  &quot;Create a node with element K, left subtree B1 and right subtree B2.&quot;
  (list E B1 B2))

;;
;; Selectors for binary trees
;;

(defun bin-tree-leaf-element (L)
  &quot;Retrieve the element of a leaf L.&quot;
  (first L))

(defun bin-tree-node-element (N)
  &quot;Retrieve the element of a node N.&quot;
  (first N))

(defun bin-tree-node-left (N)
  &quot;Retrieve the left subtree of a node N.&quot;
  (second N))

(defun bin-tree-node-right (N)
  &quot;Retrieve the right subtree of a node N.&quot;
  (third N))

;;
;; Recognizers for binary trees
;;

(defun bin-tree-leaf-p (B)
  &quot;Test if binary tree B is a leaf.&quot;
  (and (listp B) (= (list-length B) 1)))

(defun bin-tree-node-p (B)
  &quot;Test if binary tree B is a node.&quot;
  (and (listp B) (= (list-length B) 3)))
The representation scheme works out like the following:

USER(5): (make-bin-tree-node '*
                             (make-bin-tree-node '+
                                                 (make-bin-tree-leaf 2)
                                                 (make-bin-tree-leaf 3))
                             (make-bin-tree-node '-
                                                 (make-bin-tree-leaf 7)
                                                 (make-bin-tree-leaf 8)))
&lt;/codeblock&gt;

(* (+ (2) (3)) (- (7) (8)))
The expression above is a binary tree node with element * and two subtrees. The left subtree is itself a binary tree node with + as its element and leaves as its subtress. The right subtree is also a binary tree node with - as its element and leaves as its subtrees. All the leaves are decorated by numeric components.
            *
           / \
          /   \
         /     \
        +       -
       / \     / \
      2   3   7   8
Searching Binary Trees

As discussed in previous tutorials, having recursive data structures defined in the way we did streamlines the process of formulating structural recursions. We review this concept in the following examples.

Suppose we treat binary trees as containers. An expression E is a member of a binary tree B if:

B is a leaf and its element is E.
B is a node and either its element is E or E is a member of one of its subtrees.
For example, the definition asserts that the members of (* (+ (2) (3)) (- (7) (8))) are *, +, 2, 3, -, 7 and 8. Such a definition can be directly implemented by our recursive data type functions:

&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (or (equal E (bin-tree-node-element B))
        (bin-tree-member-p (bin-tree-node-left B) E)
	(bin-tree-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

The function can be made more readable by using the let form:
&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (or (equal E elmt)
	  (bin-tree-member-p left E)
	  (bin-tree-member-p right E)))))
&lt;/codeblock&gt;
Tracing the execution of bin-tree-member-p, we get:

USER(14): (trace bin-tree-member-p)
(BIN-TREE-MEMBER-P)
USER(15): (bin-tree-member-p '(+ (* (2) (3)) (- (7) (8))) 7) 
 0: (BIN-TREE-MEMBER-P (+ (* (2) (3)) (- (7) (8))) 7)
   1: (BIN-TREE-MEMBER-P (* (2) (3)) 7)
     2: (BIN-TREE-MEMBER-P (2) 7)
     2: returned NIL
     2: (BIN-TREE-MEMBER-P (3) 7)
     2: returned NIL
   1: returned NIL
   1: (BIN-TREE-MEMBER-P (- (7) (8)) 7)
     2: (BIN-TREE-MEMBER-P (7) 7)
     2: returned T
   1: returned T
 0: returned T
T
Exercise: Let size(B) be the number of members in a binary tree B. Give a recursive definition of size(B), and then implement a LISP function (bin-tree-size B) that returns size(B).
Traversing Binary Trees

Let us write a function that will reverse a tree in the sense that the left and right subtrees of every node are swapped:

&lt;codeblock&gt;
(defun binary-tree-reverse (B)
  &quot;Reverse binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      B
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (make-bin-tree-node elmt
		          (binary-tree-reverse right)
		          (binary-tree-reverse left)))))
&lt;/codeblock&gt;

The correctness of the above implementation can be articulated as follows. Given a binary tree B and an object E, either the binary tree is a leaf or it is a node:

Case 1: B is a leaf.
Then the reversal of B is simply B itself.
Case 2: B is a node.
Then B has three components, namely, an element elmt, a left subtree left and a right subtree right. The reversal of B is a node with element elmt, left subtree the reversal of right, and right subtree the reversal of left.
The following shows us how the recursion unfolds:

USER(21): (trace bin-tree-reverse)
(BIN-TREE-REVERSE)
USER(22): (bin-tree-reverse '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-REVERSE (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-REVERSE (- (7) (8)))
     2: (BIN-TREE-REVERSE (8))
     2: returned (8)
     2: (BIN-TREE-REVERSE (7))
     2: returned (7)
   1: returned (- (8) (7))
   1: (BIN-TREE-REVERSE (+ (2) (3)))
     2: (BIN-TREE-REVERSE (3))
     2: returned (3)
     2: (BIN-TREE-REVERSE (2))
     2: returned (2)
   1: returned (+ (3) (2))
 0: returned (* (- (8) (7)) (+ (3) (2)))
(* (- (8) (7)) (+ (3) (2)))
The resulting expression represents the following tree:
            *
           / \
          /   \
         /     \
        -       +
       / \     / \
      8   7   3   2
Let us implement a function that will extract the members of a given binary tree, and put them into a list in preorder.

&lt;codeblock&gt;
(defun bin-tree-preorder (B)
  &quot;Create a list containing keys of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (list (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (append (bin-tree-preorder left)
		    (bin-tree-preorder right))))))
&lt;/codeblock&gt;

Tracing the execution of the function, we obtain the following:
USER(13): (trace bin-tree-preorder)
(BIN-TREE-PREORDER)
USER(14): (bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-PREORDER (+ (2) (3)))
     2: (BIN-TREE-PREORDER (2))
     2: returned (2)
     2: (BIN-TREE-PREORDER (3))
     2: returned (3)
   1: returned (+ 2 3)
   1: (BIN-TREE-PREORDER (- (7) (8)))
     2: (BIN-TREE-PREORDER (7))
     2: returned (7)
     2: (BIN-TREE-PREORDER (8))
     2: returned (8)
   1: returned (- 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
As we have discussed before, the append call in the code above is a source of inefficiency that can be obtimized away:
&lt;codeblock&gt;
(defun fast-bin-tree-preorder (B)
  &quot;A tail-recursive version of bin-tree-preorder.&quot;
  (preorder-aux B nil))

(defun preorder-aux (B A)
  &quot;Append A to the end of the list containing elements of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (cons (bin-tree-leaf-element B) A)
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (preorder-aux left
			  (preorder-aux right A))))))
&lt;/codeblock&gt;
An execution trace of the implementation is the following:
USER(15): (trace fast-bin-tree-preorder preorder-aux)          
(PREORDER-AUX FAST-BIN-TREE-PREORDER)
USER(16): (fast-bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (FAST-BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (PREORDER-AUX (* (+ (2) (3)) (- (7) (8))) NIL)
     2: (PREORDER-AUX (- (7) (8)) NIL)
       3: (PREORDER-AUX (8) NIL)
       3: returned (8)
       3: (PREORDER-AUX (7) (8))
       3: returned (7 8)
     2: returned (- 7 8)
     2: (PREORDER-AUX (+ (2) (3)) (- 7 8))
       3: (PREORDER-AUX (3) (- 7 8))
       3: returned (3 - 7 8)
       3: (PREORDER-AUX (2) (3 - 7 8))
       3: returned (2 3 - 7 8)
     2: returned (+ 2 3 - 7 8)
   1: returned (* + 2 3 - 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
Exercise: Implement a function that will create a list containing members of a given binary tree in postorder. Implement also a tail-recursive version of the same function.

Exercise: Repeat the last exercise with inorder.

Abstract Data Types

Abstract data types are blackboxes. They are defined in terms of their external interfaces, and not their implementation. For example, a set abstraction offers the following operations:

(make-empty-set) creates an empty set.
(set-insert S E) returns a set containing all members of set S plus an additional member E.
(set-remove S E) returns a set containing all members of set S except for E.
(set-member-p S E) returns true if E is a member of set S.
(set-empty-p S) returns true if set S is empty.
To implement an abstract data type, we need to decide on a representation. Let us represent a set by a list with no repeated members.

&lt;codeblock&gt;
(defun make-empty-set ()
  &quot;Creates an empty set.&quot;
  nil)

(defun set-insert (S E)
  &quot;Return a set containing all the members of set S plus the element E.&quot;
  (adjoin E S :test #'equal))

(defun set-remove (S E)
  &quot;Return a set containing all the members of set S except for element E.&quot;
  (remove E S :test #'equal))

(defun set-member-p (S E)
  &quot;Return non-NIL if set S contains element E.&quot;
  (member E S :test #'equal))

(defun set-empty-p (S)
  &quot;Return true if set S is empty.&quot;
  (null S))
&lt;/codeblock&gt;

Exercise: Look up the definition of adjoin, remove and member from CLTL2. In particular, find out how the :test keyword is used to specify the equality test function to be used by the three functions. What will happen if we omit the :test keyword and the subsequent #'equal when invoking the three functions?
Notice that we have implemented an abstract data type (sets) using a more fundamental recursive data structure (lists) with additional computational constraints (no repetition) imposed by the interface functions.

Binary Search Trees

Another way of implementing the same set abstraction is to use the more efficient binary search tree (BST). Binary search trees are basically binary trees with the following additional computational constraints:

All the members in the left subtree of a tree node is no greater than the element of the node.
All the members in the right subtree of a tree node is greater than the element of the node.
All the leaf members are distinct.
Again, we are implementing an abstract data type (sets) by a more fundamental recursive data structure (binary trees) with additional computational constraints. In particular, we use the leaves of a binary tree to store the member of a set, and the tree nodes for providing indexing information that improves search performance. for example, a BST representing the set {1 2 3 4} would look like:
            2
           / \
          /   \
         /     \
        1       3
       / \     / \
      1   2   3   4
An empty BST is represented by NIL, while a nonempty BST is represented by a binary tree. We begin with the constructor and recognizer for empty BST.

&lt;codeblock&gt;
(defun make-empty-BST ()
  &quot;Create an empty BST.&quot;
  nil)

(defun BST-empty-p (B)
  &quot;Check if BST B is empty.&quot;
  (null B))
Given the additional computational constraints, membership test can be implemented as follows:

(defun BST-member-p (B E)
  &quot;Check if E is a member of BST B.&quot;
  (if (BST-empty-p B)
      nil
    (BST-nonempty-member-p B E)))

(defun BST-nonempty-member-p (B E)
  &quot;Check if E is a member of nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (= E (bin-tree-leaf-element B))
    (if (&lt;= E (bin-tree-node-element B))
	(BST-nonempty-member-p (bin-tree-node-left B) E)
      (BST-nonempty-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

Notice that we handle the degenerate case of searching an empty BST separately, and apply the well-known recursive search algorithm only on nonempty BST.
USER(16): (trace BST-member-p BST-nonempty-member-p)
(BST-NONEMPTY-MEMBER-P BST-MEMBER-P)
USER(17): (BST-member-p '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NONEMPTY-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NONEMPTY-MEMBER-P (3 (3) (4)) 3)
       3: (BST-NONEMPTY-MEMBER-P (3) 3)
       3: returned T
     2: returned T
   1: returned T
 0: returned T
T
Insertion is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-insert (B E)
  &quot;Insert E into BST B.&quot;
  (if (BST-empty-p B)
      (make-bin-tree-leaf E)
    (BST-nonempty-insert B E)))

(defun BST-nonempty-insert (B E)
  &quot;Insert E into nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (BST-leaf-insert B E)
    (let ((elmt  (bin-tree-node-element B))
	  (left  (bin-tree-node-left    B))
	  (right (bin-tree-node-right   B)))
      (if (&lt;= E (bin-tree-node-element B))
	  (make-bin-tree-node elmt
			      (BST-nonempty-insert (bin-tree-node-left B) E)
			      right)
	(make-bin-tree-node elmt
			    left
			    (BST-nonempty-insert (bin-tree-node-right B) E))))))

(defun BST-leaf-insert (L E)
  &quot;Insert element E to a BST with only one leaf.&quot;
  (let ((elmt (bin-tree-leaf-element L)))
    (if (= E elmt)
	L
      (if (&lt; E elmt)
	  (make-bin-tree-node E
			      (make-bin-tree-leaf E)
			      (make-bin-tree-leaf elmt))
	(make-bin-tree-node elmt
			    (make-bin-tree-leaf elmt)
			    (make-bin-tree-leaf E))))))
&lt;/codeblock&gt;

As before, recursive insertion to nonempty BST is handled outside of the general entry point of BST insertion. Traversing down the index nodes, the recursive algorithm eventually arrives at a leaf. In case the element is not already in the tree, the leaf is turned into a node with leaf subtrees holding the inserted element and the element of the original leaf. For example, if we insert 2.5 into the tree represented by (2 (1 (1) (2)) (3 (3) (4))), the effect is the following:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       3
       / \     / \            / \     / \
      1   2   3   4          1   2  2.5  4
                                    / \
                                  2.5  3
A trace of the insertion operation is given below:
USER(22): (trace BST-insert BST-nonempty-insert BST-leaf-insert)
(BST-LEAF-INSERT BST-NONEMPTY-INSERT BST-INSERT)
USER(23): (BST-insert '(2 (1 (1) (2)) (3 (3) (4))) 2.5)
 0: (BST-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
   1: (BST-NONEMPTY-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
     2: (BST-NONEMPTY-INSERT (3 (3) (4)) 2.5)
       3: (BST-NONEMPTY-INSERT (3) 2.5)
         4: (BST-LEAF-INSERT (3) 2.5)
         4: returned (2.5 (2.5) (3))
       3: returned (2.5 (2.5) (3))
     2: returned (3 (2.5 (2.5) (3)) (4))
   1: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
 0: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
(2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
Removal of elements is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-remove (B E)
  &quot;Remove E from BST B.&quot;
  (if (BST-empty-p B)
      B
    (if (bin-tree-leaf-p B)
	(BST-leaf-remove B E)
      (BST-node-remove B E))))

(defun BST-leaf-remove (L E)
  &quot;Remove E from BST leaf L.&quot;
  (if (= E (bin-tree-leaf-element L))
      (make-empty-BST)
    L))

(defun BST-node-remove (N E)
  &quot;Remove E from BST node N.&quot;
  (let
      ((elmt  (bin-tree-node-element N))
       (left  (bin-tree-node-left    N))
       (right (bin-tree-node-right   N)))
    (if (&lt;= E elmt)
	(if (bin-tree-leaf-p left)
	    (if (= E (bin-tree-leaf-element left))
		right
	      N)
	  (make-bin-tree-node elmt (BST-node-remove left E) right))
      (if (bin-tree-leaf-p right)
	  (if (= E (bin-tree-leaf-element right))
	      left
	    N)
	(make-bin-tree-node elmt left (BST-node-remove right E))))))
&lt;/codeblock&gt;

This time, removal from empty BST's and BST's with a single leaf are both degenerate cases. The recursive removal algorithm deals with BST nodes. Traversing down the index nodes, the recursive algorithm searches for the parent node of the leaf to be removed. In case it is found, the sibling of the leaf to be removed replaces its parent node. For example, the effect of removing 2 from the BST represented by (2 (1 (1) (2)) (3 (3) (4))) is depicted as follows:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       4
       / \     / \            / \     
      1   2   3   4          1   2  
A trace of the deletion operation is given below:
USER(4): (trace BST-remove BST-node-remove)
(BST-NODE-REMOVE BST-REMOVE)
USER(5): (BST-remove '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NODE-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NODE-REMOVE (3 (3) (4)) 3)
     2: returned (4)
   1: returned (2 (1 (1) (2)) (4))
 0: returned (2 (1 (1) (2)) (4))
(2 (1 (1) (2)) (4)))) ()) (4 () (5 () ())))

http://www.cs.sfu.ca/CC/310/pwfong/Lisp/3/tutorial3.html

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>16561</id>
      <timestamp>2009-11-17T18:24:18Z</timestamp>
      <contributor>
        <username>Llama</username>
        <id>1925</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Binary Trees

Suppose we want to create a new kind of recursive data type, our familiar binary trees. The first thing we have to do is to define the data type in terms of its constructors, selectors and recognizers. In the case of binary trees, we have the following:

Constructors: We have two kinds of binary trees, leaves and nodes. Accordingly, we need a constructor for each kind:
(make-bin-tree-leaf E): A leaf is a composite object with one component, the element E.
(make-bin-tree-node E B1 B2): A node consists of three components, an element E, a left subtree B1 and a right subtree B2. Each of B1 and B2 is a binary tree.
Notice that the definition of binary tree is inherently recursive (as in the case of nodes). Larger binary trees can be composed from smaller ones.
Selectors: We need to define a selector for each component of each kind of binary tree.
(bin-tree-leaf-element L): Retrieve the element of a leaf L.
(bin-tree-node-element N): Retrieve the element of a node N.
(bin-tree-node-left N): Retrieve the left subtree of a node N.
(bin-tree-node-right N): Retrieve the right subtree of a node N.
Recognizers: We define one recognizer for each kind of binary tree.
(bin-tree-leaf-p B): Test if a given binary tree B is a leaf.
(bin-tree-node-p B): Test if a given binary tree B is a node.
Notice that we have not written a line of code yet, and still we are able to write down the function signature of all the constructors, selectors and recognizers. The process is more or less mechanical:

Define a constructor for each variant of the recursive data type. The parameters for a constructor defines the components of a composite object.
For each parameter of each constructor, define a selector to retrieve the corresponding component.
For each constructor, define a corresponding recognizer.
The next question is how we are to represent a binary tree as a LISP object. Of course, a list is the first thing that comes to our mind:

We represent an leaf with element E by a singleton list containing E (i.e. (list E)).
A node with element E, left subtree B1 and right subtree B2 is represented as a list containing the three components (i.e. (list E B1 B2)).
Fixing the representation, we can thus implement the recursive data type functions:
&lt;codeblock language=scheme&gt;
;;
;; Binary Trees
;;

;;
;; Constructors for binary trees
;;

(defun make-bin-tree-leaf (E)
  &quot;Create a leaf.&quot;
  (list E))

(defun make-bin-tree-node (E B1 B2)
  &quot;Create a node with element K, left subtree B1 and right subtree B2.&quot;
  (list E B1 B2))

;;
;; Selectors for binary trees
;;

(defun bin-tree-leaf-element (L)
  &quot;Retrieve the element of a leaf L.&quot;
  (first L))

(defun bin-tree-node-element (N)
  &quot;Retrieve the element of a node N.&quot;
  (first N))

(defun bin-tree-node-left (N)
  &quot;Retrieve the left subtree of a node N.&quot;
  (second N))

(defun bin-tree-node-right (N)
  &quot;Retrieve the right subtree of a node N.&quot;
  (third N))

;;
;; Recognizers for binary trees
;;

(defun bin-tree-leaf-p (B)
  &quot;Test if binary tree B is a leaf.&quot;
  (and (listp B) (= (list-length B) 1)))

(defun bin-tree-node-p (B)
  &quot;Test if binary tree B is a node.&quot;
  (and (listp B) (= (list-length B) 3)))
The representation scheme works out like the following:

USER(5): (make-bin-tree-node '*
                             (make-bin-tree-node '+
                                                 (make-bin-tree-leaf 5)
                                                 (make-bin-tree-leaf 4))
                             (make-bin-tree-node '-
                                                 (make-bin-tree-leaf 7)
                                                 (make-bin-tree-leaf 8)))
&lt;/codeblock&gt;

(* (+ (2) (3)) (- (7) (8)))
The expression above is a binary tree node with element * and two subtrees. The left subtree is itself a binary tree node with + as its element and leaves as its subtress. The right subtree is also a binary tree node with - as its element and leaves as its subtrees. All the leaves are decorated by numeric components.
            *
           / \
          /   \
         /     \
        +       -
       / \     / \
      7   5   7   8
Searching Binary Trees

As discussed in previous tutorials, having recursive data structures defined in the way we did streamlines the process of formulating structural recursions. We review this concept in the following examples.

Suppose we treat binary trees as containers. An expression E is a member of a binary tree B if:

B is a leaf and its element is E.
B is a node and either its element is E or E is a member of one of its subtrees.
For example, the definition asserts that the members of (* (+ (2) (3)) (- (7) (8))) are *, +, 2, 3, -, 7 and 8. Such a definition can be directly implemented by our recursive data type functions:

&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (or (equal E (bin-tree-node-element B))
        (bin-tree-member-p (bin-tree-node-left B) E)
	(bin-tree-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

The function can be made more readable by using the let form:
&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (or (equal E elmt)
	  (bin-tree-member-p left E)
	  (bin-tree-member-p right E)))))
&lt;/codeblock&gt;
Tracing the execution of bin-tree-member-p, we get:

USER(14): (trace bin-tree-member-p)
(BIN-TREE-MEMBER-P)
USER(15): (bin-tree-member-p '(+ (* (2) (3)) (- (7) (8))) 7) 
 0: (BIN-TREE-MEMBER-P (+ (* (2) (3)) (- (7) (8))) 7)
   1: (BIN-TREE-MEMBER-P (* (2) (3)) 7)
     2: (BIN-TREE-MEMBER-P (2) 7)
     2: returned NIL
     2: (BIN-TREE-MEMBER-P (3) 7)
     2: returned NIL
   1: returned NIL
   1: (BIN-TREE-MEMBER-P (- (7) (8)) 7)
     2: (BIN-TREE-MEMBER-P (7) 7)
     2: returned T
   1: returned T
 0: returned T
T
Exercise: Let size(B) be the number of members in a binary tree B. Give a recursive definition of size(B), and then implement a LISP function (bin-tree-size B) that returns size(B).
Traversing Binary Trees

Let us write a function that will reverse a tree in the sense that the left and right subtrees of every node are swapped:

&lt;codeblock&gt;
(defun binary-tree-reverse (B)
  &quot;Reverse binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      B
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (make-bin-tree-node elmt
		          (binary-tree-reverse right)
		          (binary-tree-reverse left)))))
&lt;/codeblock&gt;

The correctness of the above implementation can be articulated as follows. Given a binary tree B and an object E, either the binary tree is a leaf or it is a node: These cases will change our approach entirely.

Case 1: B is a leaf.
Then the reversal of B is simply B itself.
Case 2: B is a node.
Then B has three components, namely, an element elmt, a left subtree left and a right subtree right. The reversal of B is a node with element elmt, left subtree the reversal of right, and right subtree the reversal of left.
The following shows us how the recursion unfolds:

USER(21): (trace bin-tree-reverse)
(BIN-TREE-REVERSE)
USER(22): (bin-tree-reverse '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-REVERSE (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-REVERSE (- (7) (8)))
     2: (BIN-TREE-REVERSE (8))
     2: returned (8)
     2: (BIN-TREE-REVERSE (7))
     2: returned (7)
   1: returned (- (8) (7))
   1: (BIN-TREE-REVERSE (+ (2) (3)))
     2: (BIN-TREE-REVERSE (3))
     2: returned (3)
     2: (BIN-TREE-REVERSE (2))
     2: returned (2)
   1: returned (+ (3) (2))
 0: returned (* (- (8) (7)) (+ (3) (2)))
(* (- (8) (7)) (+ (3) (2)))
The resulting expression represents the following tree:
            *
           / \
          /   \
         /     \
        -       +
       / \     / \
      8   7   3   2
Let us implement a function that will extract the members of a given binary tree, and put them into a list in preorder.

&lt;codeblock&gt;
(defun bin-tree-preorder (B)
  &quot;Create a list containing keys of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (list (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (append (bin-tree-preorder left)
		    (bin-tree-preorder right))))))
&lt;/codeblock&gt;

Tracing the execution of the function, we obtain the following:
USER(13): (trace bin-tree-preorder)
(BIN-TREE-PREORDER)
USER(14): (bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-PREORDER (+ (2) (3)))
     2: (BIN-TREE-PREORDER (2))
     2: returned (2)
     2: (BIN-TREE-PREORDER (3))
     2: returned (3)
   1: returned (+ 2 3)
   1: (BIN-TREE-PREORDER (- (7) (8)))
     2: (BIN-TREE-PREORDER (7))
     2: returned (7)
     2: (BIN-TREE-PREORDER (8))
     2: returned (8)
   1: returned (- 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
As we have discussed before, the append call in the code above is a source of inefficiency that can be obtimized away:
&lt;codeblock&gt;
(defun fast-bin-tree-preorder (B)
  &quot;A tail-recursive version of bin-tree-preorder.&quot;
  (preorder-aux B nil))

(defun preorder-aux (B A)
  &quot;Append A to the end of the list containing elements of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (cons (bin-tree-leaf-element B) A)
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (preorder-aux left
			  (preorder-aux right A))))))
&lt;/codeblock&gt;
An execution trace of the implementation is the following:
USER(15): (trace fast-bin-tree-preorder preorder-aux)          
(PREORDER-AUX FAST-BIN-TREE-PREORDER)
USER(16): (fast-bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (FAST-BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (PREORDER-AUX (* (+ (2) (3)) (- (7) (8))) NIL)
     2: (PREORDER-AUX (- (7) (8)) NIL)
       3: (PREORDER-AUX (8) NIL)
       3: returned (8)
       3: (PREORDER-AUX (7) (8))
       3: returned (7 8)
     2: returned (- 7 8)
     2: (PREORDER-AUX (+ (2) (3)) (- 7 8))
       3: (PREORDER-AUX (3) (- 7 8))
       3: returned (3 - 7 8)
       3: (PREORDER-AUX (2) (3 - 7 8))
       3: returned (2 3 - 7 8)
     2: returned (+ 2 3 - 7 8)
   1: returned (* + 2 3 - 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
Exercise: Implement a function that will create a list containing members of a given binary tree in postorder. Implement also a tail-recursive version of the same function.

Exercise: Repeat the last exercise with inorder.

Abstract Data Types

Abstract data types are blackboxes. They are defined in terms of their external interfaces, and not their implementation. For example, a set abstraction offers the following operations:

(make-empty-set) creates an empty set.
(set-insert S E) returns a set containing all members of set S plus an additional member E.
(set-remove S E) returns a set containing all members of set S except for E.
(set-member-p S E) returns true if E is a member of set S.
(set-empty-p S) returns true if set S is empty.
To implement an abstract data type, we need to decide on a representation. Let us represent a set by a list with no repeated members.

&lt;codeblock&gt;
(defun make-empty-set ()
  &quot;Creates an empty set.&quot;
  nil)

(defun set-insert (S E)
  &quot;Return a set containing all the members of set S plus the element E.&quot;
  (adjoin E S :test #'equal))

(defun set-remove (S E)
  &quot;Return a set containing all the members of set S except for element E.&quot;
  (remove E S :test #'equal))

(defun set-member-p (S E)
  &quot;Return non-NIL if set S contains element E.&quot;
  (member E S :test #'equal))

(defun set-empty-p (S)
  &quot;Return true if set S is empty.&quot;
  (null S))
&lt;/codeblock&gt;

Exercise: Look up the definition of adjoin, remove and member from CLTL2. In particular, find out how the :test keyword is used to specify the equality test function to be used by the three functions. What will happen if we omit the :test keyword and the subsequent #'equal when invoking the three functions?
Notice that we have implemented an abstract data type (sets) using a more fundamental recursive data structure (lists) with additional computational constraints (no repetition) imposed by the interface functions.

Binary Search Trees

Another way of implementing the same set abstraction is to use the more efficient binary search tree (BST). Binary search trees are basically binary trees with the following additional computational constraints:

All the members in the left subtree of a tree node is no greater than the element of the node.
All the members in the right subtree of a tree node is greater than the element of the node.
All the leaf members are distinct.
Again, we are implementing an abstract data type (sets) by a more fundamental recursive data structure (binary trees) with additional computational constraints. In particular, we use the leaves of a binary tree to store the member of a set, and the tree nodes for providing indexing information that improves search performance. for example, a BST representing the set {1 2 3 4} would look like:
            2
           / \
          /   \
         /     \
        1       3
       / \     / \
      1   2   3   4
An empty BST is represented by NIL, while a nonempty BST is represented by a binary tree. We begin with the constructor and recognizer for empty BST.

&lt;codeblock&gt;
(defun make-empty-BST ()
  &quot;Create an empty BST.&quot;
  nil)

(defun BST-empty-p (B)
  &quot;Check if BST B is empty.&quot;
  (null B))
Given the additional computational constraints, membership test can be implemented as follows:

(defun BST-member-p (B E)
  &quot;Check if E is a member of BST B.&quot;
  (if (BST-empty-p B)
      nil
    (BST-nonempty-member-p B E)))

(defun BST-nonempty-member-p (B E)
  &quot;Check if E is a member of nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (= E (bin-tree-leaf-element B))
    (if (&lt;= E (bin-tree-node-element B))
	(BST-nonempty-member-p (bin-tree-node-left B) E)
      (BST-nonempty-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

Notice that we handle the degenerate case of searching an empty BST separately, and apply the well-known recursive search algorithm only on nonempty BST.
USER(16): (trace BST-member-p BST-nonempty-member-p)
(BST-NONEMPTY-MEMBER-P BST-MEMBER-P)
USER(17): (BST-member-p '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NONEMPTY-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NONEMPTY-MEMBER-P (3 (3) (4)) 3)
       3: (BST-NONEMPTY-MEMBER-P (3) 3)
       3: returned T
     2: returned T
   1: returned T
 0: returned T
T
Insertion is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-insert (B E)
  &quot;Insert E into BST B.&quot;
  (if (BST-empty-p B)
      (make-bin-tree-leaf E)
    (BST-nonempty-insert B E)))

(defun BST-nonempty-insert (B E)
  &quot;Insert E into nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (BST-leaf-insert B E)
    (let ((elmt  (bin-tree-node-element B))
	  (left  (bin-tree-node-left    B))
	  (right (bin-tree-node-right   B)))
      (if (&lt;= E (bin-tree-node-element B))
	  (make-bin-tree-node elmt
			      (BST-nonempty-insert (bin-tree-node-left B) E)
			      right)
	(make-bin-tree-node elmt
			    left
			    (BST-nonempty-insert (bin-tree-node-right B) E))))))

(defun BST-leaf-insert (L E)
  &quot;Insert element E to a BST with only one leaf.&quot;
  (let ((elmt (bin-tree-leaf-element L)))
    (if (= E elmt)
	L
      (if (&lt; E elmt)
	  (make-bin-tree-node E
			      (make-bin-tree-leaf E)
			      (make-bin-tree-leaf elmt))
	(make-bin-tree-node elmt
			    (make-bin-tree-leaf elmt)
			    (make-bin-tree-leaf E))))))
&lt;/codeblock&gt;

As before, recursive insertion to nonempty BST is handled outside of the general entry point of BST insertion. Traversing down the index nodes, the recursive algorithm eventually arrives at a leaf. In case the element is not already in the tree, the leaf is turned into a node with leaf subtrees holding the inserted element and the element of the original leaf. For example, if we insert 2.5 into the tree represented by (2 (1 (1) (2)) (3 (3) (4))), the effect is the following:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       3
       / \     / \            / \     / \
      1   2   3   4          1   2  2.5  4
                                    / \
                                  2.5  3
A trace of the insertion operation is given below:
USER(22): (trace BST-insert BST-nonempty-insert BST-leaf-insert)
(BST-LEAF-INSERT BST-NONEMPTY-INSERT BST-INSERT)
USER(23): (BST-insert '(2 (1 (1) (2)) (3 (3) (4))) 2.5)
 0: (BST-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
   1: (BST-NONEMPTY-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
     2: (BST-NONEMPTY-INSERT (3 (3) (4)) 2.5)
       3: (BST-NONEMPTY-INSERT (3) 2.5)
         4: (BST-LEAF-INSERT (3) 2.5)
         4: returned (2.5 (2.5) (3))
       3: returned (2.5 (2.5) (3))
     2: returned (3 (2.5 (2.5) (3)) (4))
   1: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
 0: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
(2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
Removal of elements is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-remove (B E)
  &quot;Remove E from BST B.&quot;
  (if (BST-empty-p B)
      B
    (if (bin-tree-leaf-p B)
	(BST-leaf-remove B E)
      (BST-node-remove B E))))

(defun BST-leaf-remove (L E)
  &quot;Remove E from BST leaf L.&quot;
  (if (= E (bin-tree-leaf-element L))
      (make-empty-BST)
    L))

(defun BST-node-remove (N E)
  &quot;Remove E from BST node N.&quot;
  (let
      ((elmt  (bin-tree-node-element N))
       (left  (bin-tree-node-left    N))
       (right (bin-tree-node-right   N)))
    (if (&lt;= E elmt)
	(if (bin-tree-leaf-p left)
	    (if (= E (bin-tree-leaf-element left))
		right
	      N)
	  (make-bin-tree-node elmt (BST-node-remove left E) right))
      (if (bin-tree-leaf-p right)
	  (if (= E (bin-tree-leaf-element right))
	      left
	    N)
	(make-bin-tree-node elmt left (BST-node-remove right E))))))
&lt;/codeblock&gt;

This time, removal from empty BST's and BST's with a single leaf are both degenerate cases. The recursive removal algorithm deals with BST nodes. Traversing down the index nodes, the recursive algorithm searches for the parent node of the leaf to be removed. In case it is found, the sibling of the leaf to be removed replaces its parent node. For example, the effect of removing 2 from the BST represented by (2 (1 (1) (2)) (3 (3) (4))) is depicted as follows:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       4
       / \     / \            / \     
      1   2   3   4          1   2  
A trace of the deletion operation is given below:
USER(4): (trace BST-remove BST-node-remove)
(BST-NODE-REMOVE BST-REMOVE)
USER(5): (BST-remove '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NODE-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NODE-REMOVE (3 (3) (4)) 3)
     2: returned (4)
   1: returned (2 (1 (1) (2)) (4))
 0: returned (2 (1 (1) (2)) (4))
(2 (1 (1) (2)) (4)))) ()) (4 () (5 () ())))

http://www.cs.sfu.ca/CC/310/pwfong/Lisp/3/tutorial3.html

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
    <revision>
      <id>16562</id>
      <timestamp>2009-11-18T16:40:15Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>if you are going to change the numbers you need to change them all. They have to match.</comment>
      <text xml:space="preserve">Binary Trees

Suppose we want to create a new kind of recursive data type, our familiar binary trees. The first thing we have to do is to define the data type in terms of its constructors, selectors and recognizers. In the case of binary trees, we have the following:

Constructors: We have two kinds of binary trees, leaves and nodes. Accordingly, we need a constructor for each kind:
(make-bin-tree-leaf E): A leaf is a composite object with one component, the element E.
(make-bin-tree-node E B1 B2): A node consists of three components, an element E, a left subtree B1 and a right subtree B2. Each of B1 and B2 is a binary tree.
Notice that the definition of binary tree is inherently recursive (as in the case of nodes). Larger binary trees can be composed from smaller ones.
Selectors: We need to define a selector for each component of each kind of binary tree.
(bin-tree-leaf-element L): Retrieve the element of a leaf L.
(bin-tree-node-element N): Retrieve the element of a node N.
(bin-tree-node-left N): Retrieve the left subtree of a node N.
(bin-tree-node-right N): Retrieve the right subtree of a node N.
Recognizers: We define one recognizer for each kind of binary tree.
(bin-tree-leaf-p B): Test if a given binary tree B is a leaf.
(bin-tree-node-p B): Test if a given binary tree B is a node.
Notice that we have not written a line of code yet, and still we are able to write down the function signature of all the constructors, selectors and recognizers. The process is more or less mechanical:

Define a constructor for each variant of the recursive data type. The parameters for a constructor defines the components of a composite object.
For each parameter of each constructor, define a selector to retrieve the corresponding component.
For each constructor, define a corresponding recognizer.
The next question is how we are to represent a binary tree as a LISP object. Of course, a list is the first thing that comes to our mind:

We represent an leaf with element E by a singleton list containing E (i.e. (list E)).
A node with element E, left subtree B1 and right subtree B2 is represented as a list containing the three components (i.e. (list E B1 B2)).
Fixing the representation, we can thus implement the recursive data type functions:
&lt;codeblock language=scheme&gt;
;;
;; Binary Trees
;;

;;
;; Constructors for binary trees
;;

(defun make-bin-tree-leaf (E)
  &quot;Create a leaf.&quot;
  (list E))

(defun make-bin-tree-node (E B1 B2)
  &quot;Create a node with element K, left subtree B1 and right subtree B2.&quot;
  (list E B1 B2))

;;
;; Selectors for binary trees
;;

(defun bin-tree-leaf-element (L)
  &quot;Retrieve the element of a leaf L.&quot;
  (first L))

(defun bin-tree-node-element (N)
  &quot;Retrieve the element of a node N.&quot;
  (first N))

(defun bin-tree-node-left (N)
  &quot;Retrieve the left subtree of a node N.&quot;
  (second N))

(defun bin-tree-node-right (N)
  &quot;Retrieve the right subtree of a node N.&quot;
  (third N))

;;
;; Recognizers for binary trees
;;

(defun bin-tree-leaf-p (B)
  &quot;Test if binary tree B is a leaf.&quot;
  (and (listp B) (= (list-length B) 1)))

(defun bin-tree-node-p (B)
  &quot;Test if binary tree B is a node.&quot;
  (and (listp B) (= (list-length B) 3)))
The representation scheme works out like the following:

USER(5): (make-bin-tree-node '*
                             (make-bin-tree-node '+
                                                 (make-bin-tree-leaf 2)
                                                 (make-bin-tree-leaf 3))
                             (make-bin-tree-node '-
                                                 (make-bin-tree-leaf 7)
                                                 (make-bin-tree-leaf 8)))
&lt;/codeblock&gt;

(* (+ (2) (3)) (- (7) (8)))
The expression above is a binary tree node with element * and two subtrees. The left subtree is itself a binary tree node with + as its element and leaves as its subtress. The right subtree is also a binary tree node with - as its element and leaves as its subtrees. All the leaves are decorated by numeric components.
            *
           / \
          /   \
         /     \
        +       -
       / \     / \
      2   3   7   8
Searching Binary Trees

As discussed in previous tutorials, having recursive data structures defined in the way we did streamlines the process of formulating structural recursions. We review this concept in the following examples.

Suppose we treat binary trees as containers. An expression E is a member of a binary tree B if:

B is a leaf and its element is E.
B is a node and either its element is E or E is a member of one of its subtrees.
For example, the definition asserts that the members of (* (+ (2) (3)) (- (7) (8))) are *, +, 2, 3, -, 7 and 8. Such a definition can be directly implemented by our recursive data type functions:

&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (or (equal E (bin-tree-node-element B))
        (bin-tree-member-p (bin-tree-node-left B) E)
	(bin-tree-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

The function can be made more readable by using the let form:
&lt;codeblock&gt;
(defun bin-tree-member-p (B E)
  &quot;Test if E is an element in binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      (equal E (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (or (equal E elmt)
	  (bin-tree-member-p left E)
	  (bin-tree-member-p right E)))))
&lt;/codeblock&gt;
Tracing the execution of bin-tree-member-p, we get:

USER(14): (trace bin-tree-member-p)
(BIN-TREE-MEMBER-P)
USER(15): (bin-tree-member-p '(+ (* (2) (3)) (- (7) (8))) 7) 
 0: (BIN-TREE-MEMBER-P (+ (* (2) (3)) (- (7) (8))) 7)
   1: (BIN-TREE-MEMBER-P (* (2) (3)) 7)
     2: (BIN-TREE-MEMBER-P (2) 7)
     2: returned NIL
     2: (BIN-TREE-MEMBER-P (3) 7)
     2: returned NIL
   1: returned NIL
   1: (BIN-TREE-MEMBER-P (- (7) (8)) 7)
     2: (BIN-TREE-MEMBER-P (7) 7)
     2: returned T
   1: returned T
 0: returned T
T
Exercise: Let size(B) be the number of members in a binary tree B. Give a recursive definition of size(B), and then implement a LISP function (bin-tree-size B) that returns size(B).
Traversing Binary Trees

Let us write a function that will reverse a tree in the sense that the left and right subtrees of every node are swapped:

&lt;codeblock&gt;
(defun binary-tree-reverse (B)
  &quot;Reverse binary tree B.&quot;
  (if (bin-tree-leaf-p B)
      B
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (make-bin-tree-node elmt
		          (binary-tree-reverse right)
		          (binary-tree-reverse left)))))
&lt;/codeblock&gt;

The correctness of the above implementation can be articulated as follows. Given a binary tree B and an object E, either the binary tree is a leaf or it is a node: We have to approach each case differently.

Case 1: B is a leaf.
Then the reversal of B is simply B itself.
Case 2: B is a node.
Then B has three components, namely, an element elmt, a left subtree left and a right subtree right. The reversal of B is a node with element elmt, left subtree the reversal of right, and right subtree the reversal of left.
The following shows us how the recursion unfolds:

USER(21): (trace bin-tree-reverse)
(BIN-TREE-REVERSE)
USER(22): (bin-tree-reverse '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-REVERSE (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-REVERSE (- (7) (8)))
     2: (BIN-TREE-REVERSE (8))
     2: returned (8)
     2: (BIN-TREE-REVERSE (7))
     2: returned (7)
   1: returned (- (8) (7))
   1: (BIN-TREE-REVERSE (+ (2) (3)))
     2: (BIN-TREE-REVERSE (3))
     2: returned (3)
     2: (BIN-TREE-REVERSE (2))
     2: returned (2)
   1: returned (+ (3) (2))
 0: returned (* (- (8) (7)) (+ (3) (2)))
(* (- (8) (7)) (+ (3) (2)))
The resulting expression represents the following tree:
            *
           / \
          /   \
         /     \
        -       +
       / \     / \
      8   7   3   2
Let us implement a function that will extract the members of a given binary tree, and put them into a list in preorder.

&lt;codeblock&gt;
(defun bin-tree-preorder (B)
  &quot;Create a list containing keys of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (list (bin-tree-leaf-element B))
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (append (bin-tree-preorder left)
		    (bin-tree-preorder right))))))
&lt;/codeblock&gt;

Tracing the execution of the function, we obtain the following:
USER(13): (trace bin-tree-preorder)
(BIN-TREE-PREORDER)
USER(14): (bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (BIN-TREE-PREORDER (+ (2) (3)))
     2: (BIN-TREE-PREORDER (2))
     2: returned (2)
     2: (BIN-TREE-PREORDER (3))
     2: returned (3)
   1: returned (+ 2 3)
   1: (BIN-TREE-PREORDER (- (7) (8)))
     2: (BIN-TREE-PREORDER (7))
     2: returned (7)
     2: (BIN-TREE-PREORDER (8))
     2: returned (8)
   1: returned (- 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
As we have discussed before, the append call in the code above is a source of inefficiency that can be obtimized away:
&lt;codeblock&gt;
(defun fast-bin-tree-preorder (B)
  &quot;A tail-recursive version of bin-tree-preorder.&quot;
  (preorder-aux B nil))

(defun preorder-aux (B A)
  &quot;Append A to the end of the list containing elements of B in preorder.&quot;
  (if (bin-tree-leaf-p B)
      (cons (bin-tree-leaf-element B) A)
    (let
	((elmt  (bin-tree-node-element B))
	 (left  (bin-tree-node-left    B))
	 (right (bin-tree-node-right   B)))
      (cons elmt
	    (preorder-aux left
			  (preorder-aux right A))))))
&lt;/codeblock&gt;
An execution trace of the implementation is the following:
USER(15): (trace fast-bin-tree-preorder preorder-aux)          
(PREORDER-AUX FAST-BIN-TREE-PREORDER)
USER(16): (fast-bin-tree-preorder '(* (+ (2) (3)) (- (7) (8))))
 0: (FAST-BIN-TREE-PREORDER (* (+ (2) (3)) (- (7) (8))))
   1: (PREORDER-AUX (* (+ (2) (3)) (- (7) (8))) NIL)
     2: (PREORDER-AUX (- (7) (8)) NIL)
       3: (PREORDER-AUX (8) NIL)
       3: returned (8)
       3: (PREORDER-AUX (7) (8))
       3: returned (7 8)
     2: returned (- 7 8)
     2: (PREORDER-AUX (+ (2) (3)) (- 7 8))
       3: (PREORDER-AUX (3) (- 7 8))
       3: returned (3 - 7 8)
       3: (PREORDER-AUX (2) (3 - 7 8))
       3: returned (2 3 - 7 8)
     2: returned (+ 2 3 - 7 8)
   1: returned (* + 2 3 - 7 8)
 0: returned (* + 2 3 - 7 8)
(* + 2 3 - 7 8)
Exercise: Implement a function that will create a list containing members of a given binary tree in postorder. Implement also a tail-recursive version of the same function.

Exercise: Repeat the last exercise with inorder.

Abstract Data Types

Abstract data types are blackboxes. They are defined in terms of their external interfaces, and not their implementation. For example, a set abstraction offers the following operations:

(make-empty-set) creates an empty set.
(set-insert S E) returns a set containing all members of set S plus an additional member E.
(set-remove S E) returns a set containing all members of set S except for E.
(set-member-p S E) returns true if E is a member of set S.
(set-empty-p S) returns true if set S is empty.
To implement an abstract data type, we need to decide on a representation. Let us represent a set by a list with no repeated members.

&lt;codeblock&gt;
(defun make-empty-set ()
  &quot;Creates an empty set.&quot;
  nil)

(defun set-insert (S E)
  &quot;Return a set containing all the members of set S plus the element E.&quot;
  (adjoin E S :test #'equal))

(defun set-remove (S E)
  &quot;Return a set containing all the members of set S except for element E.&quot;
  (remove E S :test #'equal))

(defun set-member-p (S E)
  &quot;Return non-NIL if set S contains element E.&quot;
  (member E S :test #'equal))

(defun set-empty-p (S)
  &quot;Return true if set S is empty.&quot;
  (null S))
&lt;/codeblock&gt;

Exercise: Look up the definition of adjoin, remove and member from CLTL2. In particular, find out how the :test keyword is used to specify the equality test function to be used by the three functions. What will happen if we omit the :test keyword and the subsequent #'equal when invoking the three functions?
Notice that we have implemented an abstract data type (sets) using a more fundamental recursive data structure (lists) with additional computational constraints (no repetition) imposed by the interface functions.

Binary Search Trees

Another way of implementing the same set abstraction is to use the more efficient binary search tree (BST). Binary search trees are basically binary trees with the following additional computational constraints:

All the members in the left subtree of a tree node is no greater than the element of the node.
All the members in the right subtree of a tree node is greater than the element of the node.
All the leaf members are distinct.
Again, we are implementing an abstract data type (sets) by a more fundamental recursive data structure (binary trees) with additional computational constraints. In particular, we use the leaves of a binary tree to store the member of a set, and the tree nodes for providing indexing information that improves search performance. for example, a BST representing the set {1 2 3 4} would look like:
            2
           / \
          /   \
         /     \
        1       3
       / \     / \
      1   2   3   4
An empty BST is represented by NIL, while a nonempty BST is represented by a binary tree. We begin with the constructor and recognizer for empty BST.

&lt;codeblock&gt;
(defun make-empty-BST ()
  &quot;Create an empty BST.&quot;
  nil)

(defun BST-empty-p (B)
  &quot;Check if BST B is empty.&quot;
  (null B))
Given the additional computational constraints, membership test can be implemented as follows:

(defun BST-member-p (B E)
  &quot;Check if E is a member of BST B.&quot;
  (if (BST-empty-p B)
      nil
    (BST-nonempty-member-p B E)))

(defun BST-nonempty-member-p (B E)
  &quot;Check if E is a member of nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (= E (bin-tree-leaf-element B))
    (if (&lt;= E (bin-tree-node-element B))
	(BST-nonempty-member-p (bin-tree-node-left B) E)
      (BST-nonempty-member-p (bin-tree-node-right B) E))))
&lt;/codeblock&gt;

Notice that we handle the degenerate case of searching an empty BST separately, and apply the well-known recursive search algorithm only on nonempty BST.
USER(16): (trace BST-member-p BST-nonempty-member-p)
(BST-NONEMPTY-MEMBER-P BST-MEMBER-P)
USER(17): (BST-member-p '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NONEMPTY-MEMBER-P (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NONEMPTY-MEMBER-P (3 (3) (4)) 3)
       3: (BST-NONEMPTY-MEMBER-P (3) 3)
       3: returned T
     2: returned T
   1: returned T
 0: returned T
T
Insertion is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-insert (B E)
  &quot;Insert E into BST B.&quot;
  (if (BST-empty-p B)
      (make-bin-tree-leaf E)
    (BST-nonempty-insert B E)))

(defun BST-nonempty-insert (B E)
  &quot;Insert E into nonempty BST B.&quot;
  (if (bin-tree-leaf-p B)
      (BST-leaf-insert B E)
    (let ((elmt  (bin-tree-node-element B))
	  (left  (bin-tree-node-left    B))
	  (right (bin-tree-node-right   B)))
      (if (&lt;= E (bin-tree-node-element B))
	  (make-bin-tree-node elmt
			      (BST-nonempty-insert (bin-tree-node-left B) E)
			      right)
	(make-bin-tree-node elmt
			    left
			    (BST-nonempty-insert (bin-tree-node-right B) E))))))

(defun BST-leaf-insert (L E)
  &quot;Insert element E to a BST with only one leaf.&quot;
  (let ((elmt (bin-tree-leaf-element L)))
    (if (= E elmt)
	L
      (if (&lt; E elmt)
	  (make-bin-tree-node E
			      (make-bin-tree-leaf E)
			      (make-bin-tree-leaf elmt))
	(make-bin-tree-node elmt
			    (make-bin-tree-leaf elmt)
			    (make-bin-tree-leaf E))))))
&lt;/codeblock&gt;

As before, recursive insertion to nonempty BST is handled outside of the general entry point of BST insertion. Traversing down the index nodes, the recursive algorithm eventually arrives at a leaf. In case the element is not already in the tree, the leaf is turned into a node with leaf subtrees holding the inserted element and the element of the original leaf. For example, if we insert 2.5 into the tree represented by (2 (1 (1) (2)) (3 (3) (4))), the effect is the following:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       3
       / \     / \            / \     / \
      1   2   3   4          1   2  2.5  4
                                    / \
                                  2.5  3
A trace of the insertion operation is given below:
USER(22): (trace BST-insert BST-nonempty-insert BST-leaf-insert)
(BST-LEAF-INSERT BST-NONEMPTY-INSERT BST-INSERT)
USER(23): (BST-insert '(2 (1 (1) (2)) (3 (3) (4))) 2.5)
 0: (BST-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
   1: (BST-NONEMPTY-INSERT (2 (1 (1) (2)) (3 (3) (4))) 2.5)
     2: (BST-NONEMPTY-INSERT (3 (3) (4)) 2.5)
       3: (BST-NONEMPTY-INSERT (3) 2.5)
         4: (BST-LEAF-INSERT (3) 2.5)
         4: returned (2.5 (2.5) (3))
       3: returned (2.5 (2.5) (3))
     2: returned (3 (2.5 (2.5) (3)) (4))
   1: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
 0: returned (2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
(2 (1 (1) (2)) (3 (2.5 (2.5) (3)) (4)))
Removal of elements is handled by the following family of functions:

&lt;codeblock&gt;
(defun BST-remove (B E)
  &quot;Remove E from BST B.&quot;
  (if (BST-empty-p B)
      B
    (if (bin-tree-leaf-p B)
	(BST-leaf-remove B E)
      (BST-node-remove B E))))

(defun BST-leaf-remove (L E)
  &quot;Remove E from BST leaf L.&quot;
  (if (= E (bin-tree-leaf-element L))
      (make-empty-BST)
    L))

(defun BST-node-remove (N E)
  &quot;Remove E from BST node N.&quot;
  (let
      ((elmt  (bin-tree-node-element N))
       (left  (bin-tree-node-left    N))
       (right (bin-tree-node-right   N)))
    (if (&lt;= E elmt)
	(if (bin-tree-leaf-p left)
	    (if (= E (bin-tree-leaf-element left))
		right
	      N)
	  (make-bin-tree-node elmt (BST-node-remove left E) right))
      (if (bin-tree-leaf-p right)
	  (if (= E (bin-tree-leaf-element right))
	      left
	    N)
	(make-bin-tree-node elmt left (BST-node-remove right E))))))
&lt;/codeblock&gt;

This time, removal from empty BST's and BST's with a single leaf are both degenerate cases. The recursive removal algorithm deals with BST nodes. Traversing down the index nodes, the recursive algorithm searches for the parent node of the leaf to be removed. In case it is found, the sibling of the leaf to be removed replaces its parent node. For example, the effect of removing 2 from the BST represented by (2 (1 (1) (2)) (3 (3) (4))) is depicted as follows:
            2                      2
           / \                    / \
          /   \                  /   \
         /     \       ==&gt;      /     \
        1       3              1       4
       / \     / \            / \     
      1   2   3   4          1   2  
A trace of the deletion operation is given below:
USER(4): (trace BST-remove BST-node-remove)
(BST-NODE-REMOVE BST-REMOVE)
USER(5): (BST-remove '(2 (1 (1) (2)) (3 (3) (4))) 3)
 0: (BST-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
   1: (BST-NODE-REMOVE (2 (1 (1) (2)) (3 (3) (4))) 3)
     2: (BST-NODE-REMOVE (3 (3) (4)) 3)
     2: returned (4)
   1: returned (2 (1 (1) (2)) (4))
 0: returned (2 (1 (1) (2)) (4))
(2 (1 (1) (2)) (4)))) ()) (4 () (5 () ())))

http://www.cs.sfu.ca/CC/310/pwfong/Lisp/3/tutorial3.html

[[Category:Programming language:Scheme]]
[[Category:Binary search tree|Scheme]]</text>
    </revision>
  </page>
  <page>
    <title>Binary search tree (Standard ML)</title>
    <id>1783</id>
    <revision>
      <id>3217</id>
      <timestamp>2006-03-12T01:17:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Standard ML version of binary search tree</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in Standard ML with search, insert, and delete operations.

== Node structure ==

We begin by defining a polymorphic recursive datatype to represent a binary tree of any desired type:

&lt;codeblock language=sml&gt;
&lt;&lt;tree datatype&gt;&gt;=
datatype 'a tree = Node of {data:'a, left:'a tree, right:'a tree}
                 | Leaf
&lt;/codeblock&gt;

Here, &quot;Leaf&quot; nodes do not contain any data or references and merely serve to indicate where the tree ends. They function much like NULL values in a C implementation. An example instance is this ''int tree'' containing 1, 2, and 3 with 2 at the root:

&lt;codeblock language=sml&gt;
Node{data=2, left=Node{data=1,left=Leaf,right=Leaf},
             right=Node{data=3,left=Leaf,right=Leaf}};
&lt;/codeblock&gt;

For each operation, the user will have to supply a comparison function of type &lt;code&gt;'a * 'a -&gt; order&lt;/code&gt;, which takes two data elements and determines whether the first is less, greater, or equal to the second by returning &lt;code&gt;LESS&lt;/code&gt;, &lt;code&gt;GREATER&lt;/code&gt;, or &lt;code&gt;EQUAL&lt;/code&gt;. The built-in types already have functions like this, such as &lt;code&gt;Int.compare&lt;/code&gt; and &lt;code&gt;String.compare&lt;/code&gt;.

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node and return &lt;code&gt;SOME value&lt;/code&gt;, where ''value'' is the stored value, or prove that it is not in the tree, in which case it returns &lt;code&gt;NONE&lt;/code&gt;. These values have type ''&amp;alpha; option''. We will have a case for leaves and a case for internal nodes, and use a nested function to avoid unnecessary argument passing.

&lt;codeblock language=sml&gt;
&lt;&lt;search operation&gt;&gt;=
fun search(tree : 'a tree, compare, data : 'a) = 
    let fun s(Leaf) = NONE
          | s(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; s(left)
                    | GREATER =&gt; s(right)
                    | EQUAL   =&gt; SOME nodedata)
    in
        s(tree)
    end
&lt;/codeblock&gt;

This function is primarily useful in two cases: if you want to know if a value is in the tree, as when using it as a set data structure, or when using a comparator that only uses part of the value, such as the first index of a tuple. We specify some types above because otherwise the type assigned for this function by type inference would be slightly more general than we intended:

&lt;codeblock language=sml&gt;
val search = fn : 'a tree * ('b * 'a -&gt; order) * 'b -&gt; 'a option
&lt;/codeblock&gt;

== Insert ==

Inserting is very similar to searching. Unlike in a procedural language, we can't literally update a child pointer to insert the node, because these references are immutable. Instead, we will create a new version of its parent node which points to the new child. But then since we've modified the parent, we have to create a new version of its parent, and so on up to the root. The effect is that the insertion operation is ''persistent'', meaning that both the old and new state are available through two different root references (but these two versions share most of their state).

&lt;codeblock language=sml&gt;
&lt;&lt;insert operation&gt;&gt;=
fun insert(tree : 'a tree, compare, data : 'a) = 
    let fun i(Leaf) = Node{data=data, left=Leaf, right=Leaf}
          | i(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata, left=i(left), right=right}
                    | GREATER =&gt; Node{data=nodedata, left=left, right=i(right)}
                    | EQUAL   =&gt; Node{data=nodedata, left=left, right=right})
    in
        i(tree)
    end
&lt;/codeblock&gt;

This is easiest to understand in an inductive way: if we take a tree and add a new node to the correct child subtree, then build a new root node from the updated subtree and the old version of the other child subtree, the result will be a new tree with the node correctly inserted.

This particular implementation does not allow duplicate values in the tree, but simply modifying the &quot;EQUAL&quot; branch above to look like the &quot;LESS&quot; branch would allow this.

== Deletion ==

Deletion is the most complicated operation, and is also a persistent operation. We begin by locating the subtree rooted at the node we wish to delete, in a manner very similar to the preceding functions, then invoke a &lt;code&gt;deleteNode()&lt;/code&gt; helper function on it:

&lt;codeblock language=sml&gt;
&lt;&lt;delete operation&gt;&gt;=
fun delete(tree : 'a tree, compare, data : 'a) = 
    let &lt;&lt;maximum helpers&gt;&gt;
        &lt;&lt;deleteNode helper function&gt;&gt;
        fun d(Leaf) = Leaf (* data was not found *)
          | d(node as Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata,left=d(left),right=right}
                    | GREATER =&gt; Node{data=nodedata,left=left,right=d(right)}
                    | EQUAL   =&gt; deleteNode(node))
    in
        d(tree)
    end
&lt;/codeblock&gt;

Deleting a node with no children is easy: we just replace it with a leaf. If it has one child, we just replace it with its child:

&lt;codeblock language=sml&gt;
&lt;&lt;deleteNode helper function&gt;&gt;=
fun deleteNode(Node{data=nodedata,left=Leaf,right=Leaf})  = Leaf
  | deleteNode(Node{data=nodedata,left=Leaf,right=right}) = right
  | deleteNode(Node{data=nodedata,left=left,right=Leaf})  = left
  | &lt;&lt;two children case&gt;&gt;
&lt;/codeblock&gt;

We have no branch for the Leaf case, which should not occur. Most Standard ML compilers will warn about this.

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by simply finding the maximum node in the node's left subtree. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by finding the minimum node in the node's left subtree. We add two helper functions, one to get the data from the maximum node of a subtree, and one to remove the maximum node, which can safely invoke &lt;code&gt;deleteNode()&lt;/code&gt; because the maximum node always has at most one child:

&lt;codeblock language=sml&gt;
&lt;&lt;maximum helpers&gt;&gt;=
fun valueMax(Node{data=nodedata,right=Leaf,...}) = nodedata
  | valueMax(Node{right=right,...})              = valueMax(right)

fun removeMax(node as Node{data=nodedata,left=left,right=Leaf}) =
        removeNode(node)
  | removeMax(Node{data=nodedata,left=left,right=right}) =
        Node{data=nodedata,left=left,right=removeMax(right)}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply replace the value of the node with that of its inorder predecessor, simultaneously deleting the predecessor. This preserves the order properties of the tree. One can similarly use the successor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=sml&gt;
&lt;&lt;two children case&gt;&gt;=
deleteNode(Node{data=nodedata,left=left,right=right}) =
    Node{data=valueMax(left), left=removeMax(left), right=right}
&lt;/codeblock&gt;

== Files ==

We can simply place all this code into an .sml file, which when loaded will add the above declarations to the top-level (for now we won't bother with a module):

&lt;codeblock language=sml&gt;
&lt;&lt;bst.sml&gt;&gt;=
&lt;&lt;tree datatype&gt;&gt;
&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:Standard ML]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3219</id>
      <timestamp>2006-03-12T01:22:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>small fix</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in Standard ML with search, insert, and delete operations.

== Node structure ==

We begin by defining a polymorphic recursive datatype to represent a binary tree of any desired type:

&lt;codeblock language=sml&gt;
&lt;&lt;tree datatype&gt;&gt;=
datatype 'a tree = Node of {data:'a, left:'a tree, right:'a tree}
                 | Leaf
&lt;/codeblock&gt;

Here, &quot;Leaf&quot; nodes do not contain any data or references and merely serve to indicate where the tree ends. They function much like NULL values in a C implementation. An example instance is this ''int tree'' containing 1, 2, and 3 with 2 at the root:

&lt;codeblock language=sml&gt;
Node{data=2, left=Node{data=1,left=Leaf,right=Leaf},
             right=Node{data=3,left=Leaf,right=Leaf}};
&lt;/codeblock&gt;

For each operation, the user will have to supply a comparison function of type &lt;code&gt;'a * 'a -&gt; order&lt;/code&gt;, which takes two data elements and determines whether the first is less, greater, or equal to the second by returning &lt;code&gt;LESS&lt;/code&gt;, &lt;code&gt;GREATER&lt;/code&gt;, or &lt;code&gt;EQUAL&lt;/code&gt;. The built-in types already have functions like this, such as &lt;code&gt;Int.compare&lt;/code&gt; and &lt;code&gt;String.compare&lt;/code&gt;.

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node and return &lt;code&gt;SOME value&lt;/code&gt;, where ''value'' is the stored value, or prove that it is not in the tree, in which case it returns &lt;code&gt;NONE&lt;/code&gt;. These values have type ''&amp;alpha; option''. We will have a case for leaves and a case for internal nodes, and use a nested function to avoid unnecessary argument passing.

&lt;codeblock language=sml&gt;
&lt;&lt;search operation&gt;&gt;=
fun search(tree : 'a tree, compare, data : 'a) = 
    let fun s(Leaf) = NONE
          | s(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; s(left)
                    | GREATER =&gt; s(right)
                    | EQUAL   =&gt; SOME nodedata)
    in
        s(tree)
    end
&lt;/codeblock&gt;

This function is primarily useful in two cases: if you want to know if a value is in the tree, as when using it as a set data structure, or when using a comparator that only uses part of the value, such as the first index of a tuple. We specify some types above because otherwise the type assigned for this function by type inference would be slightly more general than we intended:

&lt;codeblock language=sml&gt;
val search = fn : 'a tree * ('b * 'a -&gt; order) * 'b -&gt; 'a option
&lt;/codeblock&gt;

== Insert ==

Inserting is very similar to searching. Unlike in a procedural language, we can't literally update a child pointer to insert the node, because these references are immutable. Instead, we will create a new version of its parent node which points to the new child. But then since we've modified the parent, we have to create a new version of its parent, and so on up to the root. The effect is that the insertion operation is ''persistent'', meaning that both the old and new state are available through two different root references (but these two versions share most of their state).

&lt;codeblock language=sml&gt;
&lt;&lt;insert operation&gt;&gt;=
fun insert(tree : 'a tree, compare, data : 'a) = 
    let fun i(Leaf) = Node{data=data, left=Leaf, right=Leaf}
          | i(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata, left=i(left), right=right}
                    | GREATER =&gt; Node{data=nodedata, left=left, right=i(right)}
                    | EQUAL   =&gt; Node{data=nodedata, left=left, right=right})
    in
        i(tree)
    end
&lt;/codeblock&gt;

This is easiest to understand in an inductive way: if we take a tree and add a new node to the correct child subtree, then build a new root node from the updated subtree and the old version of the other child subtree, the result will be a new tree with the node correctly inserted.

This particular implementation does not allow duplicate values in the tree, but simply modifying the &quot;EQUAL&quot; branch above to look like the &quot;LESS&quot; branch would allow this.

== Deletion ==

Deletion is the most complicated operation, and is also a persistent operation. We begin by locating the subtree rooted at the node we wish to delete, in a manner very similar to the preceding functions, then invoke a &lt;code&gt;deleteNode()&lt;/code&gt; helper function on it:

&lt;codeblock language=sml&gt;
&lt;&lt;delete operation&gt;&gt;=
fun delete(tree : 'a tree, compare, data : 'a) = 
    let &lt;&lt;maximum helpers&gt;&gt;
        &lt;&lt;deleteNode helper function&gt;&gt;
        fun d(Leaf) = Leaf (* data was not found *)
          | d(node as Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata,left=d(left),right=right}
                    | GREATER =&gt; Node{data=nodedata,left=left,right=d(right)}
                    | EQUAL   =&gt; deleteNode(node))
    in
        d(tree)
    end
&lt;/codeblock&gt;

Deleting a node with no children is easy: we just replace it with a leaf. If it has one child, we just replace it with its child:

&lt;codeblock language=sml&gt;
&lt;&lt;deleteNode helper function&gt;&gt;=
and deleteNode(Node{data=nodedata,left=Leaf,right=Leaf})  = Leaf
  | deleteNode(Node{data=nodedata,left=Leaf,right=right}) = right
  | deleteNode(Node{data=nodedata,left=left,right=Leaf})  = left
  | &lt;&lt;two children case&gt;&gt;
&lt;/codeblock&gt;

We have no branch for the Leaf case, which should not occur. Some Standard ML compilers will warn about this. We also use &quot;and&quot; instead of &quot;fun&quot; because it's mutually recursive with deleteMax, described later, which precedes it lexically.

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by simply finding the maximum node in the node's left subtree. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by finding the minimum node in the node's left subtree. We add two helper functions, one to get the data from the maximum node of a subtree, and one to remove the maximum node, which can safely invoke &lt;code&gt;deleteNode()&lt;/code&gt; because the maximum node always has at most one child:

&lt;codeblock language=sml&gt;
&lt;&lt;maximum helpers&gt;&gt;=
fun valueMax(Node{data=nodedata,right=Leaf,...}) = nodedata
  | valueMax(Node{right=right,...})              = valueMax(right)

fun removeMax(node as Node{data=nodedata,left=left,right=Leaf}) =
        removeNode(node)
  | removeMax(Node{data=nodedata,left=left,right=right}) =
        Node{data=nodedata,left=left,right=removeMax(right)}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply replace the value of the node with that of its inorder predecessor, simultaneously deleting the predecessor. This preserves the order properties of the tree. One can similarly use the successor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=sml&gt;
&lt;&lt;two children case&gt;&gt;=
deleteNode(Node{data=nodedata,left=left,right=right}) =
    Node{data=valueMax(left), left=removeMax(left), right=right}
&lt;/codeblock&gt;

== Files ==

We can simply place all this code into an .sml file, which when loaded will add the above declarations to the top-level (for now we won't bother with a module):

&lt;codeblock language=sml&gt;
&lt;&lt;bst.sml&gt;&gt;=
&lt;&lt;tree datatype&gt;&gt;
&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:Standard ML]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3220</id>
      <timestamp>2006-03-12T01:23:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Name change</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in Standard ML with search, insert, and delete operations.

== Node structure ==

We begin by defining a polymorphic recursive datatype to represent a binary tree of any desired type:

&lt;codeblock language=sml&gt;
&lt;&lt;tree datatype&gt;&gt;=
datatype 'a tree = Node of {data:'a, left:'a tree, right:'a tree}
                 | Leaf
&lt;/codeblock&gt;

Here, &quot;Leaf&quot; nodes do not contain any data or references and merely serve to indicate where the tree ends. They function much like NULL values in a C implementation. An example instance is this ''int tree'' containing 1, 2, and 3 with 2 at the root:

&lt;codeblock language=sml&gt;
Node{data=2, left=Node{data=1,left=Leaf,right=Leaf},
             right=Node{data=3,left=Leaf,right=Leaf}};
&lt;/codeblock&gt;

For each operation, the user will have to supply a comparison function of type &lt;code&gt;'a * 'a -&gt; order&lt;/code&gt;, which takes two data elements and determines whether the first is less, greater, or equal to the second by returning &lt;code&gt;LESS&lt;/code&gt;, &lt;code&gt;GREATER&lt;/code&gt;, or &lt;code&gt;EQUAL&lt;/code&gt;. The built-in types already have functions like this, such as &lt;code&gt;Int.compare&lt;/code&gt; and &lt;code&gt;String.compare&lt;/code&gt;.

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node and return &lt;code&gt;SOME value&lt;/code&gt;, where ''value'' is the stored value, or prove that it is not in the tree, in which case it returns &lt;code&gt;NONE&lt;/code&gt;. These values have type ''&amp;alpha; option''. We will have a case for leaves and a case for internal nodes, and use a nested function to avoid unnecessary argument passing.

&lt;codeblock language=sml&gt;
&lt;&lt;search operation&gt;&gt;=
fun search(tree : 'a tree, compare, data : 'a) = 
    let fun s(Leaf) = NONE
          | s(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; s(left)
                    | GREATER =&gt; s(right)
                    | EQUAL   =&gt; SOME nodedata)
    in
        s(tree)
    end
&lt;/codeblock&gt;

This function is primarily useful in two cases: if you want to know if a value is in the tree, as when using it as a set data structure, or when using a comparator that only uses part of the value, such as the first index of a tuple. We specify some types above because otherwise the type assigned for this function by type inference would be slightly more general than we intended:

&lt;codeblock language=sml&gt;
val search = fn : 'a tree * ('b * 'a -&gt; order) * 'b -&gt; 'a option
&lt;/codeblock&gt;

== Insert ==

Inserting is very similar to searching. Unlike in a procedural language, we can't literally update a child pointer to insert the node, because these references are immutable. Instead, we will create a new version of its parent node which points to the new child. But then since we've modified the parent, we have to create a new version of its parent, and so on up to the root. The effect is that the insertion operation is ''persistent'', meaning that both the old and new state are available through two different root references (but these two versions share most of their state).

&lt;codeblock language=sml&gt;
&lt;&lt;insert operation&gt;&gt;=
fun insert(tree : 'a tree, compare, data : 'a) = 
    let fun i(Leaf) = Node{data=data, left=Leaf, right=Leaf}
          | i(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata, left=i(left), right=right}
                    | GREATER =&gt; Node{data=nodedata, left=left, right=i(right)}
                    | EQUAL   =&gt; Node{data=nodedata, left=left, right=right})
    in
        i(tree)
    end
&lt;/codeblock&gt;

This is easiest to understand in an inductive way: if we take a tree and add a new node to the correct child subtree, then build a new root node from the updated subtree and the old version of the other child subtree, the result will be a new tree with the node correctly inserted.

This particular implementation does not allow duplicate values in the tree, but simply modifying the &quot;EQUAL&quot; branch above to look like the &quot;LESS&quot; branch would allow this.

== Deletion ==

Deletion is the most complicated operation, and is also a persistent operation. We begin by locating the subtree rooted at the node we wish to delete, in a manner very similar to the preceding functions, then invoke a &lt;code&gt;deleteNode()&lt;/code&gt; helper function on it:

&lt;codeblock language=sml&gt;
&lt;&lt;delete operation&gt;&gt;=
fun delete(tree : 'a tree, compare, data : 'a) = 
    let &lt;&lt;maximum helpers&gt;&gt;
        &lt;&lt;deleteNode helper function&gt;&gt;
        fun d(Leaf) = Leaf (* data was not found *)
          | d(node as Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata,left=d(left),right=right}
                    | GREATER =&gt; Node{data=nodedata,left=left,right=d(right)}
                    | EQUAL   =&gt; deleteNode(node))
    in
        d(tree)
    end
&lt;/codeblock&gt;

Deleting a node with no children is easy: we just replace it with a leaf. If it has one child, we just replace it with its child:

&lt;codeblock language=sml&gt;
&lt;&lt;deleteNode helper function&gt;&gt;=
and deleteNode(Node{data=nodedata,left=Leaf,right=Leaf})  = Leaf
  | deleteNode(Node{data=nodedata,left=Leaf,right=right}) = right
  | deleteNode(Node{data=nodedata,left=left,right=Leaf})  = left
  | &lt;&lt;two children case&gt;&gt;
&lt;/codeblock&gt;

We have no branch for the Leaf case, which should not occur. Some Standard ML compilers will warn about this. We also use &quot;and&quot; instead of &quot;fun&quot; because it's mutually recursive with deleteMax, described later, which precedes it lexically.

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by simply finding the maximum node in the node's left subtree. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by finding the minimum node in the node's left subtree. We add two helper functions, one to get the data from the maximum node of a subtree, and one to remove the maximum node, which can safely invoke &lt;code&gt;deleteNode()&lt;/code&gt; because the maximum node always has at most one child:

&lt;codeblock language=sml&gt;
&lt;&lt;maximum helpers&gt;&gt;=
fun valueMax(Node{data=nodedata,right=Leaf,...}) = nodedata
  | valueMax(Node{right=right,...})              = valueMax(right)

fun deleteMax(node as Node{data=nodedata,left=left,right=Leaf}) =
        deleteNode(node)
  | deleteMax(Node{data=nodedata,left=left,right=right}) =
        Node{data=nodedata,left=left,right=removeMax(right)}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply replace the value of the node with that of its inorder predecessor, simultaneously deleting the predecessor. This preserves the order properties of the tree. One can similarly use the successor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=sml&gt;
&lt;&lt;two children case&gt;&gt;=
deleteNode(Node{data=nodedata,left=left,right=right}) =
    Node{data=valueMax(left), left=deleteMax(left), right=right}
&lt;/codeblock&gt;

== Files ==

We can simply place all this code into an .sml file, which when loaded will add the above declarations to the top-level (for now we won't bother with a module):

&lt;codeblock language=sml&gt;
&lt;&lt;bst.sml&gt;&gt;=
&lt;&lt;tree datatype&gt;&gt;
&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:Standard ML]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>3221</id>
      <timestamp>2006-03-12T01:24:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Missed a name</comment>
      <text xml:space="preserve">This article implements a simple binary search tree data structure in Standard ML with search, insert, and delete operations.

== Node structure ==

We begin by defining a polymorphic recursive datatype to represent a binary tree of any desired type:

&lt;codeblock language=sml&gt;
&lt;&lt;tree datatype&gt;&gt;=
datatype 'a tree = Node of {data:'a, left:'a tree, right:'a tree}
                 | Leaf
&lt;/codeblock&gt;

Here, &quot;Leaf&quot; nodes do not contain any data or references and merely serve to indicate where the tree ends. They function much like NULL values in a C implementation. An example instance is this ''int tree'' containing 1, 2, and 3 with 2 at the root:

&lt;codeblock language=sml&gt;
Node{data=2, left=Node{data=1,left=Leaf,right=Leaf},
             right=Node{data=3,left=Leaf,right=Leaf}};
&lt;/codeblock&gt;

For each operation, the user will have to supply a comparison function of type &lt;code&gt;'a * 'a -&gt; order&lt;/code&gt;, which takes two data elements and determines whether the first is less, greater, or equal to the second by returning &lt;code&gt;LESS&lt;/code&gt;, &lt;code&gt;GREATER&lt;/code&gt;, or &lt;code&gt;EQUAL&lt;/code&gt;. The built-in types already have functions like this, such as &lt;code&gt;Int.compare&lt;/code&gt; and &lt;code&gt;String.compare&lt;/code&gt;.

== Search ==

The most important operation on the tree is searching, which uses the properties of the binary search tree to traverse from the root down towards a given node. In the end it will either find the requested node and return &lt;code&gt;SOME value&lt;/code&gt;, where ''value'' is the stored value, or prove that it is not in the tree, in which case it returns &lt;code&gt;NONE&lt;/code&gt;. These values have type ''&amp;alpha; option''. We will have a case for leaves and a case for internal nodes, and use a nested function to avoid unnecessary argument passing.

&lt;codeblock language=sml&gt;
&lt;&lt;search operation&gt;&gt;=
fun search(tree : 'a tree, compare, data : 'a) = 
    let fun s(Leaf) = NONE
          | s(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; s(left)
                    | GREATER =&gt; s(right)
                    | EQUAL   =&gt; SOME nodedata)
    in
        s(tree)
    end
&lt;/codeblock&gt;

This function is primarily useful in two cases: if you want to know if a value is in the tree, as when using it as a set data structure, or when using a comparator that only uses part of the value, such as the first index of a tuple. We specify some types above because otherwise the type assigned for this function by type inference would be slightly more general than we intended:

&lt;codeblock language=sml&gt;
val search = fn : 'a tree * ('b * 'a -&gt; order) * 'b -&gt; 'a option
&lt;/codeblock&gt;

== Insert ==

Inserting is very similar to searching. Unlike in a procedural language, we can't literally update a child pointer to insert the node, because these references are immutable. Instead, we will create a new version of its parent node which points to the new child. But then since we've modified the parent, we have to create a new version of its parent, and so on up to the root. The effect is that the insertion operation is ''persistent'', meaning that both the old and new state are available through two different root references (but these two versions share most of their state).

&lt;codeblock language=sml&gt;
&lt;&lt;insert operation&gt;&gt;=
fun insert(tree : 'a tree, compare, data : 'a) = 
    let fun i(Leaf) = Node{data=data, left=Leaf, right=Leaf}
          | i(Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata, left=i(left), right=right}
                    | GREATER =&gt; Node{data=nodedata, left=left, right=i(right)}
                    | EQUAL   =&gt; Node{data=nodedata, left=left, right=right})
    in
        i(tree)
    end
&lt;/codeblock&gt;

This is easiest to understand in an inductive way: if we take a tree and add a new node to the correct child subtree, then build a new root node from the updated subtree and the old version of the other child subtree, the result will be a new tree with the node correctly inserted.

This particular implementation does not allow duplicate values in the tree, but simply modifying the &quot;EQUAL&quot; branch above to look like the &quot;LESS&quot; branch would allow this.

== Deletion ==

Deletion is the most complicated operation, and is also a persistent operation. We begin by locating the subtree rooted at the node we wish to delete, in a manner very similar to the preceding functions, then invoke a &lt;code&gt;deleteNode()&lt;/code&gt; helper function on it:

&lt;codeblock language=sml&gt;
&lt;&lt;delete operation&gt;&gt;=
fun delete(tree : 'a tree, compare, data : 'a) = 
    let &lt;&lt;maximum helpers&gt;&gt;
        &lt;&lt;deleteNode helper function&gt;&gt;
        fun d(Leaf) = Leaf (* data was not found *)
          | d(node as Node{data=nodedata,left=left,right=right}) = 
                (case compare(data, nodedata) of
                      LESS    =&gt; Node{data=nodedata,left=d(left),right=right}
                    | GREATER =&gt; Node{data=nodedata,left=left,right=d(right)}
                    | EQUAL   =&gt; deleteNode(node))
    in
        d(tree)
    end
&lt;/codeblock&gt;

Deleting a node with no children is easy: we just replace it with a leaf. If it has one child, we just replace it with its child:

&lt;codeblock language=sml&gt;
&lt;&lt;deleteNode helper function&gt;&gt;=
and deleteNode(Node{data=nodedata,left=Leaf,right=Leaf})  = Leaf
  | deleteNode(Node{data=nodedata,left=Leaf,right=right}) = right
  | deleteNode(Node{data=nodedata,left=left,right=Leaf})  = left
  | &lt;&lt;two children case&gt;&gt;
&lt;/codeblock&gt;

We have no branch for the Leaf case, which should not occur. Some Standard ML compilers will warn about this. We also use &quot;and&quot; instead of &quot;fun&quot; because it's mutually recursive with deleteMax, described later, which precedes it lexically.

A node's ''inorder predecessor'' is the node whose value immediately precedes the node's value in sorted order. We can find this node by simply finding the maximum node in the node's left subtree. Similarly, the ''inorder successor'' immediately follows it in sorted order, and can be found by finding the minimum node in the node's left subtree. We add two helper functions, one to get the data from the maximum node of a subtree, and one to remove the maximum node, which can safely invoke &lt;code&gt;deleteNode()&lt;/code&gt; because the maximum node always has at most one child:

&lt;codeblock language=sml&gt;
&lt;&lt;maximum helpers&gt;&gt;=
fun valueMax(Node{data=nodedata,right=Leaf,...}) = nodedata
  | valueMax(Node{right=right,...})              = valueMax(right)

fun deleteMax(node as Node{data=nodedata,left=left,right=Leaf}) =
        deleteNode(node)
  | deleteMax(Node{data=nodedata,left=left,right=right}) =
        Node{data=nodedata,left=left,right=deleteMax(right)}
&lt;/codeblock&gt;

To delete a node with two children, as shown below, we simply replace the value of the node with that of its inorder predecessor, simultaneously deleting the predecessor. This preserves the order properties of the tree. One can similarly use the successor.

[[Image:Binary search tree delete.svg|400px]]

&lt;codeblock language=sml&gt;
&lt;&lt;two children case&gt;&gt;=
deleteNode(Node{data=nodedata,left=left,right=right}) =
    Node{data=valueMax(left), left=deleteMax(left), right=right}
&lt;/codeblock&gt;

== Files ==

We can simply place all this code into an .sml file, which when loaded will add the above declarations to the top-level (for now we won't bother with a module):

&lt;codeblock language=sml&gt;
&lt;&lt;bst.sml&gt;&gt;=
&lt;&lt;tree datatype&gt;&gt;
&lt;&lt;search operation&gt;&gt;
&lt;&lt;insert operation&gt;&gt;
&lt;&lt;delete operation&gt;&gt;
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:Standard ML]]
[[Category:Environment:Portable]]
[[Category:Binary search tree]]</text>
    </revision>
  </page>
  <page>
    <title>Binary tree (Scheme)</title>
    <id>3585</id>
    <revision>
      <id>14804</id>
      <timestamp>2008-10-01T13:11:39Z</timestamp>
      <contributor>
        <ip>141.154.216.20</ip>
      </contributor>
      <comment>[[Binary tree (Scheme)]] moved to [[Binary search tree (Scheme)]]: consistency with other binary tree articles</comment>
      <text xml:space="preserve">#REDIRECT [[Binary search tree (Scheme)]]</text>
    </revision>
  </page>
  <page>
    <title>Bloom filter (C)</title>
    <id>2792</id>
    <revision>
      <id>8138</id>
      <timestamp>2006-11-21T17:42:31Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created codedump</comment>
      <text xml:space="preserve">{{codedump}}

This is an implementation of a [http://en.wikipedia.org/wiki/Bloom_filter Bloom filter] in C.

&lt;codeblock language=c&gt;
&lt;&lt;bloom.h&gt;&gt;=
#ifndef __BLOOM_H__
#define __BLOOM_H__

#include&lt;stdlib.h&gt;

typedef unsigned int (*hashfunc_t)(const char *);
typedef struct {
	size_t asize;
	unsigned char *a;
	size_t nfuncs;
	hashfunc_t *funcs;
} BLOOM;

BLOOM *bloom_create(size_t size, size_t nfuncs, ...);
int bloom_destroy(BLOOM *bloom);
int bloom_add(BLOOM *bloom, const char *s);
int bloom_check(BLOOM *bloom, const char *s);

#endif
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;bloom.c&gt;&gt;=
#include&lt;limits.h&gt;
#include&lt;stdarg.h&gt;

#include&quot;bloom.h&quot;

#define SETBIT(a, n) (a[n/CHAR_BIT] |= (1&lt;&lt;(n%CHAR_BIT)))
#define GETBIT(a, n) (a[n/CHAR_BIT] &amp; (1&lt;&lt;(n%CHAR_BIT)))

BLOOM *bloom_create(size_t size, size_t nfuncs, ...)
{
	BLOOM *bloom;
	va_list l;
	int n;
	
	if(!(bloom=malloc(sizeof(BLOOM)))) return NULL;
	if(!(bloom-&gt;a=calloc((size+CHAR_BIT-1)/CHAR_BIT, sizeof(char)))) {
		free(bloom);
		return NULL;
	}
	if(!(bloom-&gt;funcs=(hashfunc_t*)malloc(nfuncs*sizeof(hashfunc_t)))) {
		free(bloom-&gt;a);
		free(bloom);
		return NULL;
	}

	va_start(l, nfuncs);
	for(n=0; n&lt;nfuncs; ++n) {
		bloom-&gt;funcs[n]=va_arg(l, hashfunc_t);
	}
	va_end(l);

	bloom-&gt;nfuncs=nfuncs;
	bloom-&gt;asize=size;

	return bloom;
}

int bloom_destroy(BLOOM *bloom)
{
	free(bloom-&gt;a);
	free(bloom-&gt;funcs);
	free(bloom);

	return 0;
}

int bloom_add(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		SETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize);
	}

	return 0;
}

int bloom_check(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		if(!(GETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize))) return 0;
	}

	return 1;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;test.c&gt;&gt;=

#include&lt;stdio.h&gt;
#include&lt;string.h&gt;

#include&quot;bloom.h&quot;

unsigned int sax_hash(const char *key)
{
	unsigned int h=0;

	while(*key) h^=(h&lt;&lt;5)+(h&gt;&gt;2)+(unsigned char)*key++;

	return h;
}

unsigned int sdbm_hash(const char *key)
{
	unsigned int h=0;
	while(*key) h=(unsigned char)*key++ + (h&lt;&lt;6) + (h&lt;&lt;16) - h;
	return h;
}

int main(int argc, char *argv[])
{
	FILE *fp;
	char line[1024];
	char *p;
	BLOOM *bloom;
	
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: No word file specified\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(bloom=bloom_create(2500000, 2, sax_hash, sdbm_hash))) {
		fprintf(stderr, &quot;ERROR: Could not create bloom filter\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(fp=fopen(argv[1], &quot;r&quot;))) {
		fprintf(stderr, &quot;ERROR: Could not open file %s\n&quot;, argv[1]);
		return EXIT_FAILURE;
	}

	while(fgets(line, 1024, fp)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		bloom_add(bloom, line);
	}

	fclose(fp);

	while(fgets(line, 1024, stdin)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		p=strtok(line, &quot; \t,.;:\r\n?!-/()&quot;);
		while(p) {
			if(!bloom_check(bloom, p)) {
				printf(&quot;No match for ford \&quot;%s\&quot;\n&quot;, p);
			}
			p=strtok(NULL, &quot; \t,.;:\r\n?!-/()&quot;);
		}
	}

	bloom_destroy(bloom);

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=Makefile&gt;
&lt;&lt;Makefile&gt;&gt;=
all: bloom

bloom: bloom.o test.o
	cc -o bloom -Wall -pedantic bloom.o test.o

bloom.o: bloom.c bloom.h
	cc -o bloom.o -Wall -pedantic -ansi -c bloom.c

test.o: test.c bloom.h
	cc -o test.o -Wall -pedantic -ansi -c test.c
&lt;/codeblock&gt;


[[Category:Bloom filter|C]]
[[Category:programming language:C]]</text>
    </revision>
    <revision>
      <id>8139</id>
      <timestamp>2006-11-21T17:44:17Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>noweb fix</comment>
      <text xml:space="preserve">{{codedump}}

This is an implementation of a [http://en.wikipedia.org/wiki/Bloom_filter Bloom filter] in C.

&lt;codeblock language=c&gt;
&lt;&lt;bloom.h&gt;&gt;=
#ifndef __BLOOM_H__
#define __BLOOM_H__

#include&lt;stdlib.h&gt;

typedef unsigned int (*hashfunc_t)(const char *);
typedef struct {
	size_t asize;
	unsigned char *a;
	size_t nfuncs;
	hashfunc_t *funcs;
} BLOOM;

BLOOM *bloom_create(size_t size, size_t nfuncs, ...);
int bloom_destroy(BLOOM *bloom);
int bloom_add(BLOOM *bloom, const char *s);
int bloom_check(BLOOM *bloom, const char *s);

#endif
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;bloom.c&gt;&gt;=
#include&lt;limits.h&gt;
#include&lt;stdarg.h&gt;

#include&quot;bloom.h&quot;

#define SETBIT(a, n) (a[n/CHAR_BIT] |= (1&lt;&lt;(n%CHAR_BIT)))
#define GETBIT(a, n) (a[n/CHAR_BIT] &amp; (1&lt;&lt;(n%CHAR_BIT)))

BLOOM *bloom_create(size_t size, size_t nfuncs, ...)
{
	BLOOM *bloom;
	va_list l;
	int n;
	
	if(!(bloom=malloc(sizeof(BLOOM)))) return NULL;
	if(!(bloom-&gt;a=calloc((size+CHAR_BIT-1)/CHAR_BIT, sizeof(char)))) {
		free(bloom);
		return NULL;
	}
	if(!(bloom-&gt;funcs=(hashfunc_t*)malloc(nfuncs*sizeof(hashfunc_t)))) {
		free(bloom-&gt;a);
		free(bloom);
		return NULL;
	}

	va_start(l, nfuncs);
	for(n=0; n&lt;nfuncs; ++n) {
		bloom-&gt;funcs[n]=va_arg(l, hashfunc_t);
	}
	va_end(l);

	bloom-&gt;nfuncs=nfuncs;
	bloom-&gt;asize=size;

	return bloom;
}

int bloom_destroy(BLOOM *bloom)
{
	free(bloom-&gt;a);
	free(bloom-&gt;funcs);
	free(bloom);

	return 0;
}

int bloom_add(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		SETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize);
	}

	return 0;
}

int bloom_check(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		if(!(GETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize))) return 0;
	}

	return 1;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;test.c&gt;&gt;=

#include&lt;stdio.h&gt;
#include&lt;string.h&gt;

#include&quot;bloom.h&quot;

unsigned int sax_hash(const char *key)
{
	unsigned int h=0;

	while(*key) h^=(h@&lt;&lt;5)+(h&gt;&gt;2)+(unsigned char)*key++;

	return h;
}

unsigned int sdbm_hash(const char *key)
{
	unsigned int h=0;
	while(*key) h=(unsigned char)*key++ + (h&lt;&lt;6) + (h&lt;&lt;16) - h;
	return h;
}

int main(int argc, char *argv[])
{
	FILE *fp;
	char line[1024];
	char *p;
	BLOOM *bloom;
	
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: No word file specified\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(bloom=bloom_create(2500000, 2, sax_hash, sdbm_hash))) {
		fprintf(stderr, &quot;ERROR: Could not create bloom filter\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(fp=fopen(argv[1], &quot;r&quot;))) {
		fprintf(stderr, &quot;ERROR: Could not open file %s\n&quot;, argv[1]);
		return EXIT_FAILURE;
	}

	while(fgets(line, 1024, fp)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		bloom_add(bloom, line);
	}

	fclose(fp);

	while(fgets(line, 1024, stdin)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		p=strtok(line, &quot; \t,.;:\r\n?!-/()&quot;);
		while(p) {
			if(!bloom_check(bloom, p)) {
				printf(&quot;No match for ford \&quot;%s\&quot;\n&quot;, p);
			}
			p=strtok(NULL, &quot; \t,.;:\r\n?!-/()&quot;);
		}
	}

	bloom_destroy(bloom);

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=Makefile&gt;
&lt;&lt;Makefile&gt;&gt;=
all: bloom

bloom: bloom.o test.o
	cc -o bloom -Wall -pedantic bloom.o test.o

bloom.o: bloom.c bloom.h
	cc -o bloom.o -Wall -pedantic -ansi -c bloom.c

test.o: test.c bloom.h
	cc -o test.o -Wall -pedantic -ansi -c test.c
&lt;/codeblock&gt;


[[Category:Bloom filter|C]]
[[Category:programming language:C]]</text>
    </revision>
    <revision>
      <id>16877</id>
      <timestamp>2010-09-23T13:25:31Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">I HURD YOU LIEK MUDKIPZ</text>
    </revision>
    <revision>
      <id>16893</id>
      <timestamp>2010-09-23T15:47:23Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{codedump}}

This is an implementation of a [http://en.wikipedia.org/wiki/Bloom_filter Bloom filter] in C.

&lt;codeblock language=c&gt;
&lt;&lt;bloom.h&gt;&gt;=
#ifndef __BLOOM_H__
#define __BLOOM_H__

#include&lt;stdlib.h&gt;

typedef unsigned int (*hashfunc_t)(const char *);
typedef struct {
	size_t asize;
	unsigned char *a;
	size_t nfuncs;
	hashfunc_t *funcs;
} BLOOM;

BLOOM *bloom_create(size_t size, size_t nfuncs, ...);
int bloom_destroy(BLOOM *bloom);
int bloom_add(BLOOM *bloom, const char *s);
int bloom_check(BLOOM *bloom, const char *s);

#endif
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;bloom.c&gt;&gt;=
#include&lt;limits.h&gt;
#include&lt;stdarg.h&gt;

#include&quot;bloom.h&quot;

#define SETBIT(a, n) (a[n/CHAR_BIT] |= (1&lt;&lt;(n%CHAR_BIT)))
#define GETBIT(a, n) (a[n/CHAR_BIT] &amp; (1&lt;&lt;(n%CHAR_BIT)))

BLOOM *bloom_create(size_t size, size_t nfuncs, ...)
{
	BLOOM *bloom;
	va_list l;
	int n;
	
	if(!(bloom=malloc(sizeof(BLOOM)))) return NULL;
	if(!(bloom-&gt;a=calloc((size+CHAR_BIT-1)/CHAR_BIT, sizeof(char)))) {
		free(bloom);
		return NULL;
	}
	if(!(bloom-&gt;funcs=(hashfunc_t*)malloc(nfuncs*sizeof(hashfunc_t)))) {
		free(bloom-&gt;a);
		free(bloom);
		return NULL;
	}

	va_start(l, nfuncs);
	for(n=0; n&lt;nfuncs; ++n) {
		bloom-&gt;funcs[n]=va_arg(l, hashfunc_t);
	}
	va_end(l);

	bloom-&gt;nfuncs=nfuncs;
	bloom-&gt;asize=size;

	return bloom;
}

int bloom_destroy(BLOOM *bloom)
{
	free(bloom-&gt;a);
	free(bloom-&gt;funcs);
	free(bloom);

	return 0;
}

int bloom_add(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		SETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize);
	}

	return 0;
}

int bloom_check(BLOOM *bloom, const char *s)
{
	size_t n;

	for(n=0; n&lt;bloom-&gt;nfuncs; ++n) {
		if(!(GETBIT(bloom-&gt;a, bloom-&gt;funcs[n](s)%bloom-&gt;asize))) return 0;
	}

	return 1;
}
&lt;/codeblock&gt;


&lt;codeblock language=c&gt;
&lt;&lt;test.c&gt;&gt;=

#include&lt;stdio.h&gt;
#include&lt;string.h&gt;

#include&quot;bloom.h&quot;

unsigned int sax_hash(const char *key)
{
	unsigned int h=0;

	while(*key) h^=(h@&lt;&lt;5)+(h&gt;&gt;2)+(unsigned char)*key++;

	return h;
}

unsigned int sdbm_hash(const char *key)
{
	unsigned int h=0;
	while(*key) h=(unsigned char)*key++ + (h&lt;&lt;6) + (h&lt;&lt;16) - h;
	return h;
}

int main(int argc, char *argv[])
{
	FILE *fp;
	char line[1024];
	char *p;
	BLOOM *bloom;
	
	if(argc&lt;2) {
		fprintf(stderr, &quot;ERROR: No word file specified\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(bloom=bloom_create(2500000, 2, sax_hash, sdbm_hash))) {
		fprintf(stderr, &quot;ERROR: Could not create bloom filter\n&quot;);
		return EXIT_FAILURE;
	}

	if(!(fp=fopen(argv[1], &quot;r&quot;))) {
		fprintf(stderr, &quot;ERROR: Could not open file %s\n&quot;, argv[1]);
		return EXIT_FAILURE;
	}

	while(fgets(line, 1024, fp)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		bloom_add(bloom, line);
	}

	fclose(fp);

	while(fgets(line, 1024, stdin)) {
		if((p=strchr(line, '\r'))) *p='\0';
		if((p=strchr(line, '\n'))) *p='\0';

		p=strtok(line, &quot; \t,.;:\r\n?!-/()&quot;);
		while(p) {
			if(!bloom_check(bloom, p)) {
				printf(&quot;No match for ford \&quot;%s\&quot;\n&quot;, p);
			}
			p=strtok(NULL, &quot; \t,.;:\r\n?!-/()&quot;);
		}
	}

	bloom_destroy(bloom);

	return EXIT_SUCCESS;
}
&lt;/codeblock&gt;


&lt;codeblock language=Makefile&gt;
&lt;&lt;Makefile&gt;&gt;=
all: bloom

bloom: bloom.o test.o
	cc -o bloom -Wall -pedantic bloom.o test.o

bloom.o: bloom.c bloom.h
	cc -o bloom.o -Wall -pedantic -ansi -c bloom.c

test.o: test.c bloom.h
	cc -o test.o -Wall -pedantic -ansi -c test.c
&lt;/codeblock&gt;


[[Category:Bloom filter|C]]
[[Category:programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Box-Muller transform (C)</title>
    <id>2173</id>
    <revision>
      <id>5202</id>
      <timestamp>2006-05-26T13:13:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Implementation, test driver</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d, n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double y = 0.0;
    static int y_cached = 0;
    double x, r;
    if (!y_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        y_cached = 1;
        return result;
        }
    } else {
        y_cached = 0;
        return y;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)round(val);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5203</id>
      <timestamp>2006-05-26T13:13:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>language=&quot;c&quot;</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d, n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double y = 0.0;
    static int y_cached = 0;
    double x, r;
    if (!y_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        y_cached = 1;
        return result;
        }
    } else {
        y_cached = 0;
        return y;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)round(val);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5204</id>
      <timestamp>2006-05-26T13:14:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Headers</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d, n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double y = 0.0;
    static int y_cached = 0;
    double x, r;
    if (!y_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        y_cached = 1;
        return result;
        }
    } else {
        y_cached = 0;
        return y;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)round(val);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5205</id>
      <timestamp>2006-05-26T13:16:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix up var names</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n1 = 0.0;
    static int n1_cached = 0;
    if (!n1_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n1_cached = 1;
        return result;
        }
    } else {
        n1_cached = 0;
        return n1;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)round(val);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5206</id>
      <timestamp>2006-05-26T13:18:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Var name, no round in C</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5207</id>
      <timestamp>2006-05-26T13:19:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>}</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX;
y = 2.0*rand()/RAND_MAX;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5208</id>
      <timestamp>2006-05-26T13:24:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix two bugs - wasn't translating initial x, y values, and wasn't scaling/translating cached value</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[12] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(6.0, 2.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5209</id>
      <timestamp>2006-05-26T13:26:30Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Less iterations for 80 cols, more rows to show shape better</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;600; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5210</id>
      <timestamp>2006-05-26T13:27:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Still a bit much</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

(todo)</text>
    </revision>
    <revision>
      <id>5211</id>
      <timestamp>2006-05-26T13:27:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Sample output</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

All those fancy math functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>5213</id>
      <timestamp>2006-05-26T17:04:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add diagram - looks a little messed up right now</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

[[Image:Box_Muller.svg|thumb|160px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]
Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>5214</id>
      <timestamp>2006-05-26T17:05:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move diagram up bit</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|160px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>5215</id>
      <timestamp>2006-05-26T18:56:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak for updated image</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|161px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>5216</id>
      <timestamp>2006-05-26T19:59:44Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|161px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;

[[Category:Box-Muller transform|C]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6752</id>
      <timestamp>2006-07-11T12:44:27Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Box-Muller transform (C)]] moved to [[Box-Muller transform (C) on Wheels]]</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|161px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;

[[Category:Box-Muller transform|C]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6796</id>
      <timestamp>2006-07-11T12:46:48Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Box-Muller transform (C) on Wheels]] moved to [[Box-Muller transform (C) on Wheels on Wheels]]</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|161px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;

[[Category:Box-Muller transform|C]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>7011</id>
      <timestamp>2006-07-11T19:31:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Box-Muller transform (C) on Wheels on Wheels]] moved to [[Box-Muller transform (C)]]: Revert vandalism</comment>
      <text xml:space="preserve">{{Category:Box-Muller transform}}

Suppose our random number generator is &lt;code&gt;rand()&lt;/code&gt; and returns an integer between 0 and &lt;code&gt;RAND_MAX&lt;/code&gt;, inclusive; any uniform random number generator will suffice. We produce two random integers and scale them to floating-point numbers between &amp;minus;1 and 1:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;=
x = 2.0*rand()/RAND_MAX - 1;
y = 2.0*rand()/RAND_MAX - 1;
&lt;/codeblock&gt;

To use the standard library's &lt;code&gt;rand()&lt;/code&gt; we add stdlib.h:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

[[Image:Box_Muller.svg|thumb|161px|Diagram of the Box Muller transform. The initial circles, uniformly spaced about the origin, are mapped to another set of circles about the origin that are closely spaced near the origin but quickly spread out. The largest circles in the domain map to the smallest circles in the range and vice versa.]]

In order to use the polar form of the Box-Muller transform, it is necessary that the point (''x'',''y'') falls inside the unit circle (the circle of radius 1 about the origin), and not at the origin. To ensure this, we simply reject any pairs that don't meet these criteria and try again:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;=
double x, y, r;
do {
    &lt;&lt;scale two random integers to doubles between -1 and 1&gt;&gt;
    r = x*x + y*y;
} while (r == 0.0 || r &gt; 1.0);
&lt;/codeblock&gt;

Above, &lt;code&gt;r&lt;/code&gt; is just the square of the Euclidean distance of the point (''x'',''y'') from the origin (0,0). We don't need to take the square root because if the square falls between 0 and 1, so will the distance, and likewise if it is greater than 1 (this is a property of the square root function).

Next, we compute the desired normally distributed value pair using the Box Muller transform:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;=
double d = sqrt(-2.0*log(r)/r);
double n1 = x*d;
n2 = y*d;
&lt;/codeblock&gt;

This is the most complex part to understand. Intuitively, it maps each circle of points around the origin to another circle of points around the origin, as shown in the diagram, where larger outer circles are mapped to closely-spaced inner circles and inner circles to outer circles. The &lt;code&gt;sqrt()&lt;/code&gt; and &lt;code&gt;log()&lt;/code&gt; functions require a header:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

These points will be distributed with a mean of 0 and a standard deviation of 1. To achieve any mean and standard deviation, we simply scale and translate:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;=
double result = n1*stddev + mean;
&lt;/codeblock&gt;

Some applications may want both values returned; however, since most will want only a single value at a time, we simply return one of the values and cache the other one for the next call, like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;complete Box-Muller function&gt;&gt;=
double rand_normal(double mean, double stddev) {
    static double n2 = 0.0;
    static int n2_cached = 0;
    if (!n2_cached) {
        &lt;&lt;choose a point x,y in the unit circle uniformly at random&gt;&gt;
        {
        &lt;&lt;Apply Box-Muller transform on x, y&gt;&gt;
        &lt;&lt;scale and translate to get desired mean and standard deviation&gt;&gt;
        n2_cached = 1;
        return result;
        }
    } else {
        n2_cached = 0;
        return n2*stddev + mean;
    }
}
&lt;/codeblock&gt;

Alternatively we could just drop the second value, but the &lt;code&gt;sqrt&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; values are expensive enough that it's worth calling them less often.

We can now call the code with a simple test driver like this:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;box_muller.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;time.h&gt;
#include &lt;stdio.h&gt;

&lt;&lt;complete Box-Muller function&gt;&gt;

int main() {
    int buckets[20] = {0};
    int i, j;

    srand(time(NULL));
    for(i=0; i&lt;500; i++) {
        double val = rand_normal(10.0, 3.0);
        int i = (int)floor(val + 0.5);
        if (i &gt;= 0 &amp;&amp; i &lt; sizeof(buckets)/sizeof(*buckets))
            buckets[i]++;
    }
    for(i=0; i&lt;sizeof(buckets)/sizeof(*buckets); i++) {
        for(j=0; j&lt;buckets[i]; j++) {
            printf(&quot;#&quot;);
        }
        printf(&quot;\n&quot;);
    }
    return 0;
}

&lt;/codeblock&gt;

The test driver creates a simple histogram of the output values by incrementing the &quot;bucket&quot; that each value falls into. After doing enough of these, the shape should appear roughly like a normal curve. Here's some sample output:

&lt;pre&gt;


#
###
############
################
########################
##################################################
###########################################################
##############################################################
####################################################################
##########################################################
###############################################
############################################
########################
#################
########
######
#

&lt;/pre&gt;

[[Category:Box-Muller transform|C]]
[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Boyer-Moore string search algorithm (Java)</title>
    <id>3283</id>
    <revision>
      <id>12049</id>
      <timestamp>2008-01-12T03:15:54Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Boyer-Moore without good-suffix-shift rule</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : alignedAt + 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = new BoyerMoore().match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Vector;

public class BoyerMoore {
	public List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new Vector&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15394</id>
      <timestamp>2008-11-02T09:55:35Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : alignedAt + 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = new BoyerMoore().match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Vector;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new Vector&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15395</id>
      <timestamp>2008-11-02T09:57:17Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>/* Program */</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : alignedAt + 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = new BoyerMoore().match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15396</id>
      <timestamp>2008-11-02T10:03:15Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>/* Usage */</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : alignedAt + 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15397</id>
      <timestamp>2008-11-02T10:03:45Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>/* Program */</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : alignedAt + 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16631</id>
      <timestamp>2010-01-21T16:56:26Z</timestamp>
      <contributor>
        <username>Bgy</username>
        <id>1969</id>
      </contributor>
      <minor/>
      <comment>/* Matching */</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16915</id>
      <timestamp>2010-09-24T07:58:16Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <minor/>
      <comment>[[Boyer-Moore string search algorithm (Java)]] moved to [[Mwhahahaha]]: Hehehe</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16950</id>
      <timestamp>2010-09-24T20:25:17Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>[[Mwhahahaha]] moved to [[Boyer-Moore string search algorithm (Java)]]: rv</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=java&gt;
&lt;&lt;lengths&gt;&gt;=
int m = text.length();
int n = pattern.length();
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;preprop_call&gt;&gt;=
Map&lt;Character, Integer&gt; rightMostIndexes = preprocessForBadCharacterShift(pattern);
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=java&gt;
&lt;&lt;align_start&gt;&gt;=
int alignedAt = 0;
while (alignedAt + (n - 1) &lt; m) {
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=java&gt;
&lt;&lt;loop&gt;&gt;=
for (int indexInPattern = n - 1; indexInPattern &gt;= 0; indexInPattern--) {
	int indexInText = alignedAt + indexInPattern;
	char x = text.charAt(indexInText);
	char y = pattern.charAt(indexInPattern);
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=java&gt;
&lt;&lt;break&gt;&gt;=
if (indexInText &gt;= m)
	break;
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=java&gt;
&lt;&lt;mismatch&gt;&gt;=
if (x != y) {
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=java&gt;
&lt;&lt;get_index&gt;&gt;=
Integer r = rightMostIndexes.get(x);
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=java&gt;
&lt;&lt;big_skip&gt;&gt;=
if (r == null) {
	alignedAt = indexInText + 1;
}
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=java&gt;
&lt;&lt;small_skip&gt;&gt;=
else {
	int shift = indexInText - (alignedAt + r);
	alignedAt += shift &gt; 0 ? shift : 1;
}
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=java&gt;
&lt;&lt;match&gt;&gt;=
else if (indexInPattern == 0) {
	matches.add(alignedAt);
	alignedAt++;
}
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=java&gt;
&lt;&lt;preprop&gt;&gt;=
Map&lt;Character, Integer&gt; map = new HashMap&lt;Character, Integer&gt;();
for (int i = pattern.length() - 1; i &gt;= 0; i--) {
	char c = pattern.charAt(i);
	if (!map.containsKey(c)) map.put(c, i);
}
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=java&gt;
&lt;&lt;usage&gt;&gt;=
List&lt;Integer&gt; matches = match(&quot;ana&quot;, &quot;bananas&quot;);
for (Integer integer : matches) System.out.println(&quot;Match at: &quot; + integer);
System.out.println((matches.equals(Arrays.asList(1, 3)) ? &quot;OK&quot; : &quot;Failed&quot;));
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=java&gt;
&lt;&lt;BoyerMoore.java&gt;&gt;=

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Map;

public class BoyerMoore {
	public static List&lt;Integer&gt; match(String pattern, String text) {
		List&lt;Integer&gt; matches = new ArrayList&lt;Integer&gt;();
		&lt;&lt;lengths&gt;&gt;
		&lt;&lt;preprop_call&gt;&gt;	
		&lt;&lt;align_start&gt;&gt;
			&lt;&lt;loop&gt;&gt;
				&lt;&lt;break&gt;&gt;
				&lt;&lt;mismatch&gt;&gt;
					&lt;&lt;get_index&gt;&gt;
					&lt;&lt;big_skip&gt;&gt;
					&lt;&lt;small_skip&gt;&gt;
					break;
				}
				&lt;&lt;match&gt;&gt;
			}
		}
		return matches;
	}
	private static Map&lt;Character, Integer&gt; preprocessForBadCharacterShift(
			String pattern) {
		&lt;&lt;preprop&gt;&gt;
		return map;
	}
	public static void main(String[] args) {
		&lt;&lt;usage&gt;&gt;
	}
}
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Java]]
[[Category:Programming_language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Boyer-Moore string search algorithm (Python)</title>
    <id>3661</id>
    <revision>
      <id>15398</id>
      <timestamp>2008-11-02T10:05:10Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=python&gt;
&lt;&lt;lengths&gt;&gt;=
m = len(text)
n = len(pattern)
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=python&gt;
&lt;&lt;preprop_call&gt;&gt;=
rightMostIndexes = preprocessForBadCharacterShift(pattern)
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=python&gt;
&lt;&lt;align_start&gt;&gt;=
alignedAt = 0
while alignedAt + (n - 1) &lt; m:
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=python&gt;
&lt;&lt;loop&gt;&gt;=
for indexInPattern in xrange(n-1, -1, -1):
	indexInText = alignedAt + indexInPattern
	x = text[indexInText]
	y = pattern[indexInPattern]
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=python&gt;
&lt;&lt;break&gt;&gt;=
if indexInText &gt;= m:
	break
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=python&gt;
&lt;&lt;mismatch&gt;&gt;=
if x != y:
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=python&gt;
&lt;&lt;get_index&gt;&gt;=
r = rightMostIndexes.get(x)
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=python&gt;
&lt;&lt;big_skip&gt;&gt;=
if not r:
	alignedAt = indexInText + 1
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=python&gt;
&lt;&lt;small_skip&gt;&gt;=
else:
	shift = indexInText - (alignedAt + r)
	alignedAt += (shift &gt; 0 and shift or alignedAt + 1)
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=python&gt;
&lt;&lt;match&gt;&gt;=
elif indexInPattern == 0:
	matches.append(alignedAt)
	alignedAt += 1
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=python&gt;
&lt;&lt;preprop&gt;&gt;=
map = { }
for i in xrange(len(pattern)-1, -1, -1):
	c = pattern[i]
	if c not in map:
		map[c] = i
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=python&gt;
&lt;&lt;usage&gt;&gt;=
matches = match(&quot;ana&quot;, &quot;bananas&quot;)
for integer in matches:
	print &quot;Match at:&quot;, integer
print (matches == [1, 3] and &quot;OK&quot; or &quot;Failed&quot;)
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=python&gt;
&lt;&lt;boyer_moore.py&gt;&gt;=

def match(pattern, text):
	matches = []
	&lt;&lt;lengths&gt;&gt;
	&lt;&lt;preprop_call&gt;&gt;	
	&lt;&lt;align_start&gt;&gt;
		&lt;&lt;loop&gt;&gt;
			&lt;&lt;break&gt;&gt;
			&lt;&lt;mismatch&gt;&gt;
				&lt;&lt;get_index&gt;&gt;
				&lt;&lt;big_skip&gt;&gt;
				&lt;&lt;small_skip&gt;&gt;
				break
			&lt;&lt;match&gt;&gt;

	return matches

def preprocessForBadCharacterShift(pattern):
	&lt;&lt;preprop&gt;&gt;
	return map

if __name__ == &quot;__main__&quot;:
	&lt;&lt;usage&gt;&gt;
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Python]]
[[Category:Programming_language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16836</id>
      <timestamp>2010-09-09T17:48:31Z</timestamp>
      <contributor>
        <username>Kostmo</username>
        <id>2115</id>
      </contributor>
      <comment>/* Matching */</comment>
      <text xml:space="preserve">=Introduction=
  
A basic (without any good-suffix-shift rule) implementation of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string matching algorithm], with right-to-left scan and a standard bad-character-shift rule. This algorithm has a sub-linear typical runtime (see Gusfield, p. 17). It can be extended using a refined version of the bad-character-shift rule which improves efficiency for small alphabets, e.g. for usage in bioinformatics (see Gusfield, p. 18) and by the strong good-suffix rule for provable worst-case linear runtime (see Gusfield, p. 20). As an alternative for even faster matching (dependent on the pattern length, not the text length, after linear-time preprocessing) consider suffix-tree based algorithms (see Gusfield, p. 89).

=Matching=

We match a pattern of length ''n'' in a text of length ''m'':

&lt;codeblock language=python&gt;
&lt;&lt;lengths&gt;&gt;=
m = len(text)
n = len(pattern)
&lt;/codeblock&gt;

Preprocess the pattern for the right-to-left-scan and bad-character-shift rules by finding the right-most positions of all characters in the pattern:

&lt;codeblock language=python&gt;
&lt;&lt;preprop_call&gt;&gt;=
rightMostIndexes = preprocessForBadCharacterShift(pattern)
&lt;/codeblock&gt;

We align ''p'' and ''t'', starting on index 0 (meaning the beginning of the pattern is aligned with position 0, i.e. the beginning, of the text), and shift ''p'' to the left, until we reach the end of ''t'':

&lt;codeblock language=python&gt;
&lt;&lt;align_start&gt;&gt;=
alignedAt = 0
while alignedAt + (n - 1) &lt; m:
&lt;/codeblock&gt;

On each aligned position, we scan the pattern from right to left, comparing the aligned characters at the current position in the text ''x'' and at the current position in the pattern ''y'':

&lt;codeblock language=python&gt;
&lt;&lt;loop&gt;&gt;=
for indexInPattern in xrange(n-1, -1, -1):
	indexInText = alignedAt + indexInPattern
	x = text[indexInText]
	y = pattern[indexInPattern]
&lt;/codeblock&gt;

If the pattern is longer than the text, we have no match here:

&lt;codeblock language=python&gt;
&lt;&lt;break&gt;&gt;=
if indexInText &gt;= m:
	break
&lt;/codeblock&gt;

In the case of a mismatch, we do the shifting:

&lt;codeblock language=python&gt;
&lt;&lt;mismatch&gt;&gt;=
if x != y:
&lt;/codeblock&gt;

We first retrieve the right-most index of the mismatching text-character in the pattern:

&lt;codeblock language=python&gt;
&lt;&lt;get_index&gt;&gt;=
r = rightMostIndexes.get(x)
&lt;/codeblock&gt;

If the mismatching character in the text is not in the pattern we can shift until we are aligned behind the mismatch-position, resulting in sub-linear runtime, as this will result in some characters never being inspected:
 
&lt;codeblock language=python&gt;
&lt;&lt;big_skip&gt;&gt;=
if x not in rightMostIndexes:
	alignedAt = indexInText + 1
&lt;/codeblock&gt;

Else we shift the pattern to the right until the right-most occurrence of ''x'' in the pattern is under the mismatch position in the text (if this shift is a forward shift, i.e. to the right), as this is the next possible place where an occurrence of the pattern can begin in the text:
 
&lt;codeblock language=python&gt;
&lt;&lt;small_skip&gt;&gt;=
else:
	shift = indexInText - (alignedAt + r)
	alignedAt += (shift &gt; 0 and shift or alignedAt + 1)
&lt;/codeblock&gt;

If the characters are equal and the pattern has been scanned completely from right to left, we have a match at the currently aligned position in the text. We store the match and shift the pattern one position to the right:

&lt;codeblock language=python&gt;
&lt;&lt;match&gt;&gt;=
elif indexInPattern == 0:
	matches.append(alignedAt)
	alignedAt += 1
&lt;/codeblock&gt;

=Preprocessing=

For each character in the string to preprocess, we store its right-most position by scanning the string from right to left, storing the character as a key and its position as a value in a hash-map, if it is not in the map already:

&lt;codeblock language=python&gt;
&lt;&lt;preprop&gt;&gt;=
map = { }
for i in xrange(len(pattern)-1, -1, -1):
	c = pattern[i]
	if c not in map:
		map[c] = i
&lt;/codeblock&gt;

=Usage=

A bit of basic testing: match ''ana'' in ''bananas'', print the matches found and simulate a simple unit test.

&lt;codeblock language=python&gt;
&lt;&lt;usage&gt;&gt;=
matches = match(&quot;ana&quot;, &quot;bananas&quot;)
for integer in matches:
	print &quot;Match at:&quot;, integer
print (matches == [1, 3] and &quot;OK&quot; or &quot;Failed&quot;)
&lt;/codeblock&gt;

=Program=
		
This results in the full program when we put the pieces together:

&lt;codeblock language=python&gt;
&lt;&lt;boyer_moore.py&gt;&gt;=

def match(pattern, text):
	matches = []
	&lt;&lt;lengths&gt;&gt;
	&lt;&lt;preprop_call&gt;&gt;	
	&lt;&lt;align_start&gt;&gt;
		&lt;&lt;loop&gt;&gt;
			&lt;&lt;break&gt;&gt;
			&lt;&lt;mismatch&gt;&gt;
				&lt;&lt;get_index&gt;&gt;
				&lt;&lt;big_skip&gt;&gt;
				&lt;&lt;small_skip&gt;&gt;
				break
			&lt;&lt;match&gt;&gt;

	return matches

def preprocessForBadCharacterShift(pattern):
	&lt;&lt;preprop&gt;&gt;
	return map

if __name__ == &quot;__main__&quot;:
	&lt;&lt;usage&gt;&gt;
&lt;/codeblock&gt;

=References=

* Gusfield, Dan (1999), ''Algorithms on Strings, Sequences and Trees''. Cambridge: University Press.

[[Category:Boyer-Moore string search algorithm|Python]]
[[Category:Programming_language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bresenham's circle algorithm (Python)</title>
    <id>3154</id>
    <revision>
      <id>10479</id>
      <timestamp>2007-06-13T01:28:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>initial dump with minimal text</comment>
      <text xml:space="preserve">{{codedump}}
Scan converts a circle of a specified radius, centered at the specified location. Scan conversion is performed using a Bresenham-style midpoint decision approach to compute pixels in one octant of the circle (from x = 0 to x = y = R/sqrt(2). Points in other octants are drawn via symmetry. 

At each step of the iteration, we:
# Determine whether to move east (E) or south-east (SE) based on the sign of the decision variable 'd'.
:*d &lt; 0  ==&gt; move E  (i.e. x' = x+1, y' = y)
:*d &gt;= 0 ==&gt; move SE (i.e. x' = x+1, y' = y-1)
# Update the decision variable with a delta-value that depends on the direction selected
# Update the delta-values based on the move direction
#Draw a pixel at x', y'

&lt;codeblock language=&quot;python&quot;&gt;
from Tkinter import *

class BresenhamCanvas(Canvas):

    def draw_point(self, x, y, color=&quot;red&quot;):
        self.create_line(x, y, x+1, y+1, fill=color)

    def draw_circle_points(self, x, y, center_x, center_y, color=&quot;red&quot;):
        '''Draw 8 points on a circle centered
           at center_x, center_y, by symmetry.'''
        self.draw_point(center_x + x, center_y + y, color)
        self.draw_point(center_x - x, center_y - y, color)  
        self.draw_point(center_x + x, center_y - y, color)
        self.draw_point(center_x - x, center_y + y, color)

        # If x == y then these points will simply duplicate
        # points already drawn above. No need to repeat them then.
        if x != y:
            self.draw_point(center_x + y, center_y + x, color)
            self.draw_point(center_x - y, center_y - x, color)
            self.draw_point(center_x + y, center_y - x, color)
            self.draw_point(center_x - y, center_y + x, color) 

    def draw_circle(self, center_x, center_y, radius, line_thickness, color=&quot;red&quot;):

        # Start at the top of the circle
        x = 0
        yin = radius - int(line_thickness/2)
        yout = radius + int(line_thickness/2)

        din = 1 - radius - int(line_thickness/2) # midpoint decision variable
        deltaEin = 3     # initial delta for move E
        deltaSEin = -2*(radius - int(line_thickness/2)) + 5 # initial delta for move SE
        dout = 1 - radius + int(line_thickness/2) # midpoint decision variable
        deltaEout = 3     # initial delta for move E
        deltaSEout = -2*(radius + int(line_thickness/2)) + 5 # initial delta for move SE

        # First point
        for y in range(yin,yout):
            self.draw_circle_points(x, y, center_x, center_y, color)

        # Stop when we cross the line y == x, which is the edge
        # of the first octant of the circle
        while yout &gt; x:
            if din &lt; 0:
                # Moving E
                din = din + deltaEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 2
            else:
                # Moving SE
                din = din + deltaSEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 4
                yin = yin - 1
            if dout &lt; 0:
                # Moving E
                dout = dout + deltaEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 2
            else:
                # Moving SE
                dout = dout + deltaSEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 4
                yout = yout - 1
            x = x + 1
            for y in range(yin,yout):
                self.draw_circle_points(x, y, center_x, center_y, color)

def run():
    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    origin_x = int(CANVAS_SIZE / 2)
    origin_y = int(CANVAS_SIZE / 2)
    center_dist = ((CANVAS_SIZE / 2) - 2*margin)
    radius = margin*2
    
    n_circles = 10
    angle_step = (2 * math.pi) / n_circles
    
    for i in range(n_circles):
        theta = angle_step * i
        center_x = int(center_dist * math.cos(theta)) + origin_x
        center_y = int(center_dist * math.sin(theta)) + origin_y
        canvas.draw_circle(center_x, center_y, radius, 10, color=&quot;blue&quot;)
       
    root.mainloop()
    
                
if __name__ == &quot;__main__&quot;:
    run()
&lt;/codeblock&gt;

== References ==
* Foley, Van Dam, Feiner, and Hughes, ''Computer Graphics: Principles and Practice'', 2nd Ed. Addison-Wesley, 1996.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>12601</id>
      <timestamp>2008-02-24T20:35:50Z</timestamp>
      <contributor>
        <username>Djshaw</username>
        <id>1637</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{codedump}}

[http://en.wikipedia.org/wiki/Midpoint_circle_algorithm Bresenham's circle algorithm] (also known as a midpoint circle algorithm) is an algorithm for determining the points needed for drawing a circle with a given radius and origin for the circle.

Scan converts a circle of a specified radius, centered at the specified location. Scan conversion is performed using a Bresenham-style midpoint decision approach to compute pixels in one octant of the circle (from x = 0 to x = y = R/sqrt(2). Points in other octants are drawn via symmetry. 

At each step of the iteration, we:
# Determine whether to move east (E) or south-east (SE) based on the sign of the decision variable 'd'.
:*d &lt; 0  ==&gt; move E  (i.e. x' = x+1, y' = y)
:*d &gt;= 0 ==&gt; move SE (i.e. x' = x+1, y' = y-1)
# Update the decision variable with a delta-value that depends on the direction selected
# Update the delta-values based on the move direction
#Draw a pixel at x', y'

&lt;codeblock language=&quot;python&quot;&gt;
from Tkinter import *

class BresenhamCanvas(Canvas):

    def draw_point(self, x, y, color=&quot;red&quot;):
        self.create_line(x, y, x+1, y+1, fill=color)

    def draw_circle_points(self, x, y, center_x, center_y, color=&quot;red&quot;):
        '''Draw 8 points on a circle centered
           at center_x, center_y, by symmetry.'''
        self.draw_point(center_x + x, center_y + y, color)
        self.draw_point(center_x - x, center_y - y, color)  
        self.draw_point(center_x + x, center_y - y, color)
        self.draw_point(center_x - x, center_y + y, color)

        # If x == y then these points will simply duplicate
        # points already drawn above. No need to repeat them then.
        if x != y:
            self.draw_point(center_x + y, center_y + x, color)
            self.draw_point(center_x - y, center_y - x, color)
            self.draw_point(center_x + y, center_y - x, color)
            self.draw_point(center_x - y, center_y + x, color) 

    def draw_circle(self, center_x, center_y, radius, line_thickness, color=&quot;red&quot;):

        # Start at the top of the circle
        x = 0
        yin = radius - int(line_thickness/2)
        yout = radius + int(line_thickness/2)

        din = 1 - radius - int(line_thickness/2) # midpoint decision variable
        deltaEin = 3     # initial delta for move E
        deltaSEin = -2*(radius - int(line_thickness/2)) + 5 # initial delta for move SE
        dout = 1 - radius + int(line_thickness/2) # midpoint decision variable
        deltaEout = 3     # initial delta for move E
        deltaSEout = -2*(radius + int(line_thickness/2)) + 5 # initial delta for move SE

        # First point
        for y in range(yin,yout):
            self.draw_circle_points(x, y, center_x, center_y, color)

        # Stop when we cross the line y == x, which is the edge
        # of the first octant of the circle
        while yout &gt; x:
            if din &lt; 0:
                # Moving E
                din = din + deltaEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 2
            else:
                # Moving SE
                din = din + deltaSEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 4
                yin = yin - 1
            if dout &lt; 0:
                # Moving E
                dout = dout + deltaEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 2
            else:
                # Moving SE
                dout = dout + deltaSEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 4
                yout = yout - 1
            x = x + 1
            for y in range(yin,yout):
                self.draw_circle_points(x, y, center_x, center_y, color)

def run():
    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    origin_x = int(CANVAS_SIZE / 2)
    origin_y = int(CANVAS_SIZE / 2)
    center_dist = ((CANVAS_SIZE / 2) - 2*margin)
    radius = margin*2
    
    n_circles = 10
    angle_step = (2 * math.pi) / n_circles
    
    for i in range(n_circles):
        theta = angle_step * i
        center_x = int(center_dist * math.cos(theta)) + origin_x
        center_y = int(center_dist * math.sin(theta)) + origin_y
        canvas.draw_circle(center_x, center_y, radius, 10, color=&quot;blue&quot;)
       
    root.mainloop()
    
                
if __name__ == &quot;__main__&quot;:
    run()
&lt;/codeblock&gt;

== References ==
* Foley, Van Dam, Feiner, and Hughes, ''Computer Graphics: Principles and Practice'', 2nd Ed. Addison-Wesley, 1996.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>16282</id>
      <timestamp>2009-03-20T05:23:47Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <text xml:space="preserve">{{codedump}}

[http://en.wikipedia.org/wiki/Midpoint_circle_algorithm Bresenham's circle algorithm] (also known as a midpoint circle algorithm) is an algorithm for determining the points needed for drawing a circle with a given radius and origin for the circle.

Scan converts a circle of a specified radius, centered at the specified location. Scan conversion is performed using a Bresenham-style midpoint decision approach to compute pixels in one octant of the circle (from x = 0 to x = y = R/sqrt(2). Points in other octants are drawn via symmetry. 

At each step of the iteration, we:
# Determine whether to move east (E) or south-east (SE) based on the sign of the decision variable 'd'.
:*d &lt; 0  ==&gt; move E  (i.e. x' = x+1, y' = y)
:*d &gt;= 0 ==&gt; move SE (i.e. x' = x+1, y' = y-1)
# Update the decision variable with a delta-value that depends on the direction selected
# Update the delta-values based on the move direction
#Draw a pixel at x', y'

&lt;codeblock language=&quot;python&quot;&gt;
from Tkinter import *

class BresenhamCanvas(Canvas):

    def draw_point(self, x, y, color=&quot;red&quot;):
        self.create_line(x, y, x+1, y+1, fill=color)

    def draw_circle_points(self, x, y, center_x, center_y, color=&quot;red&quot;):
        '''Draw 8 points on a circle centered
           at center_x, center_y, by symmetry.'''
        self.draw_point(center_x + x, center_y + y, color)
        self.draw_point(center_x - x, center_y - y, color)  
        self.draw_point(center_x + x, center_y - y, color)
        self.draw_point(center_x - x, center_y + y, color)

        # If x == y then these points will simply duplicate
        # points already drawn above. No need to repeat them then.
        if x != y:
            self.draw_point(center_x + y, center_y + x, color)
            self.draw_point(center_x - y, center_y - x, color)
            self.draw_point(center_x + y, center_y - x, color)
            self.draw_point(center_x - y, center_y + x, color) 

    def draw_circle(self, center_x, center_y, radius, line_thickness, color=&quot;red&quot;):

        # Start at the top of the circle
        x = 0
        yin = radius - int(line_thickness/2)
        yout = radius + int(line_thickness/2)

        din = 1 - radius - int(line_thickness/2) # midpoint decision variable
        deltaEin = 3     # initial delta for move E
        deltaSEin = -2*(radius - int(line_thickness/2)) + 5 # initial delta for move SE
        dout = 1 - radius + int(line_thickness/2) # midpoint decision variable
        deltaEout = 3     # initial delta for move E
        deltaSEout = -2*(radius + int(line_thickness/2)) + 5 # initial delta for move SE

        # First point
        for y in range(yin,yout):
            self.draw_circle_points(x, y, center_x, center_y, color)

        # Stop when we cross the line y == x, which is the edge
        # of the first octant of the circle
        while yout &gt; x:
            if din &lt; 0:
                # Moving E
                din = din + deltaEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 2
            else:
                # Moving SE
                din = din + deltaSEin
                deltaEin = deltaEin + 2
                deltaSEin = deltaSEin + 4
                yin = yin - 1
            if dout &lt; 0:
                # Moving E
                dout = dout + deltaEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 2
            else:
                # Moving SE
                dout = dout + deltaSEout
                deltaEout = deltaEout + 2
                deltaSEout = deltaSEout + 4
                yout = yout - 1
            x = x + 1
            for y in range(yin,yout):
                self.draw_circle_points(x, y, center_x, center_y, color)

def run():
    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    origin_x = int(CANVAS_SIZE / 2)
    origin_y = int(CANVAS_SIZE / 2)
    center_dist = ((CANVAS_SIZE / 2) - 2*margin)
    radius = margin*2
    
    n_circles = 10
    angle_step = (2 * math.pi) / n_circles
    
    for i in range(n_circles):
        theta = angle_step * i
        center_x = int(center_dist * math.cos(theta)) + origin_x
        center_y = int(center_dist * math.sin(theta)) + origin_y
        canvas.draw_circle(center_x, center_y, radius, 10, color=&quot;blue&quot;)
       
    root.mainloop()
    
                
if __name__ == &quot;__main__&quot;:
    run()
&lt;/codeblock&gt;

== References ==
* Foley, Van Dam, Feiner, and Hughes, ''Computer Graphics: Principles and Practice'', 2nd Ed. Addison-Wesley, 1996.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Bresenham's line algorithm (Python)</title>
    <id>3138</id>
    <revision>
      <id>10241</id>
      <timestamp>2007-05-18T08:00:37Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>initial dump with minimal text</comment>
      <text xml:space="preserve">{{codedump}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

class BresenhamCanvas(Canvas):
    def draw_point(self, x, y, color=&quot;red&quot;):
        '''Draw a point at location x, y'''
        self.create_line(x, y, x, y, fill=color)

    def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
        '''Use Bresenham's line algorithm to draw a line
           from x0, y0 to x1, y1'''
        steep = abs(y1 - y0) &gt; abs(x1 - x0)
        if steep:
            # swap x and y
            x0, y0 = y0, x0  
            x1, y1 = y1, x1
            
        if x0 &gt; x1:
            # swap x and y
            x0, x1 = x1, x0
            y0, y1 = y1, y0
    
        if y0 &lt; y1: 
            ystep = 1
        else:
            ystep = -1
        
        deltax = x1 - x0
        deltay = abs(y1 - y0)
        error = -deltax / 2
        y = y0
        
        for x in range(x0, x1):
            if steep:
                self.draw_point(y, x, color)
            else:
                self.draw_point(x, y, color)
                
            error = error + deltay
            if error &gt; 0:
                y = y + ystep
                error = error - deltax
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xstart = int(CANVAS_SIZE / 2)
    ystart = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xend = int(line_length * math.cos(theta)) + xstart
        yend = int(line_length * math.sin(theta)) + ystart
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10273</id>
      <timestamp>2007-05-19T05:18:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>begin to split code</comment>
      <text xml:space="preserve">{{codedump}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

Before we can draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;


&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        # swap x and y
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
            
    if x0 &gt; x1:
        # swap x and y
        x0, x1 = x1, x0
        y0, y1 = y1, y0
    
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
        
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
        
    for x in range(x0, x1):
        if steep:
            self.draw_point(y, x, color)
        else:
            self.draw_point(x, y, color)
                
        error = error + deltay
        if error &gt; 0:
            y = y + ystep
            error = error - deltax
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xstart = int(CANVAS_SIZE / 2)
    ystart = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xend = int(line_length * math.cos(theta)) + xstart
        yend = int(line_length * math.sin(theta)) + ystart
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10274</id>
      <timestamp>2007-05-19T05:19:09Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{codedump}} -&gt; {{develop}}</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

Before we can draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;


&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        # swap x and y
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
            
    if x0 &gt; x1:
        # swap x and y
        x0, x1 = x1, x0
        y0, y1 = y1, y0
    
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
        
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
        
    for x in range(x0, x1):
        if steep:
            self.draw_point(y, x, color)
        else:
            self.draw_point(x, y, color)
                
        error = error + deltay
        if error &gt; 0:
            y = y + ystep
            error = error - deltax
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xstart = int(CANVAS_SIZE / 2)
    ystart = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xend = int(line_length * math.cos(theta)) + xstart
        yend = int(line_length * math.sin(theta)) + ystart
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10275</id>
      <timestamp>2007-05-19T05:34:08Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>sections and slight code revision</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==


&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        # swap x and y
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
            
    if x0 &gt; x1:
        # swap x and y
        x0, x1 = x1, x0
        y0, y1 = y1, y0
    
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
        
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
        
    for x in range(x0, x1):
        if steep:
            self.draw_point(y, x, color)
        else:
            self.draw_point(x, y, color)
                
        error = error + deltay
        if error &gt; 0:
            y = y + ystep
            error = error - deltax
&lt;/codeblock&gt;

== Get to the point ==
Before we can draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10277</id>
      <timestamp>2007-05-19T05:38:11Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Round and round we go */ sample output</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==


&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        # swap x and y
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
            
    if x0 &gt; x1:
        # swap x and y
        x0, x1 = x1, x0
        y0, y1 = y1, y0
    
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
        
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
        
    for x in range(x0, x1):
        if steep:
            self.draw_point(y, x, color)
        else:
            self.draw_point(x, y, color)
                
        error = error + deltay
        if error &gt; 0:
            y = y + ystep
            error = error - deltax
&lt;/codeblock&gt;

== Get to the point ==
Before we can draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10398</id>
      <timestamp>2007-05-30T04:59:14Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Here's where we draw the line */ add some exposition</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
deltax = x1 - x0
deltay = abs(y1 - y0)
error = -deltax / 2
y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
steep = abs(y1 - y0) &gt; abs(x1 - x0)
if steep:
    x0, y0 = y0, x0  
    x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
if x0 &gt; x1:
    x0, x1 = x1, x0
    y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
if y0 &lt; y1: 
    ystep = 1
else:
    ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    &lt;&lt;steep&gt;&gt;

    &lt;&lt;endpoint swap&gt;&gt;
    
    &lt;&lt;ystep&gt;&gt;
        
    &lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
Before we can draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10399</id>
      <timestamp>2007-05-30T05:00:30Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Get to the point */ clarify</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
deltax = x1 - x0
deltay = abs(y1 - y0)
error = -deltax / 2
y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
steep = abs(y1 - y0) &gt; abs(x1 - x0)
if steep:
    x0, y0 = y0, x0  
    x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
if x0 &gt; x1:
    x0, x1 = x1, x0
    y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
if y0 &lt; y1: 
    ystep = 1
else:
    ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    &lt;&lt;steep&gt;&gt;

    &lt;&lt;endpoint swap&gt;&gt;
    
    &lt;&lt;ystep&gt;&gt;
        
    &lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10400</id>
      <timestamp>2007-05-30T05:04:07Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Round and round we go */ explanation</comment>
      <text xml:space="preserve">{{develop}}

[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
deltax = x1 - x0
deltay = abs(y1 - y0)
error = -deltax / 2
y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
steep = abs(y1 - y0) &gt; abs(x1 - x0)
if steep:
    x0, y0 = y0, x0  
    x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
if x0 &gt; x1:
    x0, x1 = x1, x0
    y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
if y0 &lt; y1: 
    ystep = 1
else:
    ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    &lt;&lt;steep&gt;&gt;

    &lt;&lt;endpoint swap&gt;&gt;
    
    &lt;&lt;ystep&gt;&gt;
        
    &lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10401</id>
      <timestamp>2007-05-30T05:04:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>not really under development (although it could use proof-reading, and perhaps some additional explanation, if anyone wants to help)</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
deltax = x1 - x0
deltay = abs(y1 - y0)
error = -deltax / 2
y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
steep = abs(y1 - y0) &gt; abs(x1 - x0)
if steep:
    x0, y0 = y0, x0  
    x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
if x0 &gt; x1:
    x0, x1 = x1, x0
    y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
if y0 &lt; y1: 
    ystep = 1
else:
    ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
    &lt;&lt;steep&gt;&gt;

    &lt;&lt;endpoint swap&gt;&gt;
    
    &lt;&lt;ystep&gt;&gt;
        
    &lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10413</id>
      <timestamp>2007-06-01T03:22:16Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Here's where we draw the line */ try to fix indentations</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>10478</id>
      <timestamp>2007-06-13T01:21:32Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* References */ fix cat</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:Bresenham line python sample output.png|thumb|right|200px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>13434</id>
      <timestamp>2008-05-21T23:58:15Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Round and round we go */ add sample image</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1):
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:BresenhamLine_py.png|thumb|right|400px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>14789</id>
      <timestamp>2008-09-29T16:50:51Z</timestamp>
      <contributor>
        <ip>79.92.52.146</ip>
      </contributor>
      <comment>/* Here's where we draw the line */</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1 + 1):# range(1, 3), gives [1, 2] with Python 2.5. So you have to had &quot;+1&quot; [range(1, 3 + 1)] to have the [1,2,3] list (Vincent Vansuyt modification &quot;+1&quot;)
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:BresenhamLine_py.png|thumb|right|400px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>16268</id>
      <timestamp>2009-03-13T05:09:17Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Here's where we draw the line */</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1 + 1): # We add 1 to x1 so that the range includes x1
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:BresenhamLine_py.png|thumb|right|400px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python|Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
    <revision>
      <id>16281</id>
      <timestamp>2009-03-20T05:23:36Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Bresenham's_line_algorithm Bresenham's line algorithm] is an algorithm for drawing a line on a [http://en.wikipedia.org/wiki/Raster_graphics raster] display. It was originally developed by [http://en.wikipedia.org/wiki/Jack_E._Bresenham Jack Bresenham] in 1962. 

== Here's where we draw the line ==

The basic approach taken in Bresenham's algorithm is to step along the line from one end to the other in the x-direction, coloring successive pixels in a given row until the error between the actual line and the row being colored grows too great. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;core loop&gt;&gt;=
for x in range(x0, x1 + 1): # We add 1 to x1 so that the range includes x1
    if steep:
        self.draw_point(y, x, color)
    else:
        self.draw_point(x, y, color)
            
    error = error + deltay
    if error &gt; 0:
        y = y + ystep
        error = error - deltax
&lt;/codeblock&gt;
 
The error is essentially a function of the gradient of the line (i.e. &lt;code&gt;deltay/deltax&lt;/code&gt;. But in order to avoid floating point arithmetic, the expressions involving error are multiplied through by &lt;code&gt;deltax&lt;/code&gt; (this may be an unnecessary optimization in Python, but is done here for consistency with other implementations). The initial values of &lt;code&gt;y&lt;/code&gt; and the error are

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;init&gt;&gt;=
    deltax = x1 - x0
    deltay = abs(y1 - y0)
    error = -deltax / 2
    y = y0
&lt;/codeblock&gt;

The loop shown above contains a conditional over the variable &lt;code&gt;steep&lt;/code&gt;. Since the basic Bresenham algorithm only works for lines with a slope less than 1, if the line to be plotted is &quot;steep&quot; then we step along the y-direction instead. That is:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;steep&gt;&gt;=
    steep = abs(y1 - y0) &gt; abs(x1 - x0)
    if steep:
        x0, y0 = y0, x0  
        x1, y1 = y1, x1
&lt;/codeblock&gt;

Similarly, the basic algorithm can only really handle lines that start on an x-value closer to the origin than the end-point. Thus, to provide a more general capability for drawing lines we swap the end-points if necessary, to ensure that the preceding condition holds.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;endpoint swap&gt;&gt;=
    if x0 &gt; x1:
        x0, x1 = x1, x0
        y0, y1 = y1, y0
&lt;/codeblock&gt;

The direction in which the y-values are stepped depends on whether the end-point of the line is above or below the start-point.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ystep&gt;&gt;=
    if y0 &lt; y1: 
        ystep = 1
    else:
        ystep = -1
&lt;/codeblock&gt;

For convenience, we'll wrap the whole Bresenham implementation in a method which simply takes the end-points of the line to be drawn, and then draws the specified line.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_line&gt;&gt;=
def draw_line(self, x0, y0, x1, y1, color=&quot;red&quot;):
&lt;&lt;steep&gt;&gt;

&lt;&lt;endpoint swap&gt;&gt;
    
&lt;&lt;ystep&gt;&gt;
        
&lt;&lt;init&gt;&gt;
        
    &lt;&lt;core loop&gt;&gt;
&lt;/codeblock&gt;

== Get to the point ==
In order to draw lines, we need to be able to draw points. We'll use the standard Python &lt;code&gt;Tkinter&lt;/code&gt; library to produce graphics, and do our drawing on a customized &lt;code&gt;Canvas&lt;/code&gt;. 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;BresenhamCanvas&gt;&gt;=
class BresenhamCanvas(Canvas):
&lt;/codeblock&gt;

The &lt;code&gt;Canvas&lt;/code&gt; object doesn't directly support drawing points, so we implement a point-drawing function by drawing a zero-length line (yes, it's a little silly to implement a line-drawing algorithm by using lines - just ignore how &lt;code&gt;draw_point&lt;/code&gt; is actually implemented internally, and focus on the fact that it produces points).

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;draw_point&gt;&gt;=
def draw_point(self, x, y, color=&quot;red&quot;):
    self.create_line(x, y, x, y, fill=color)
&lt;/codeblock&gt;

== Round and round we go ==

[[Image:BresenhamLine_py.png|thumb|right|400px|Sample output]]

To test the implementation of the Bresenham line algorithm, we should try to draw lines with a wide variety of slopes (both &gt;1 and &lt;1), as well as various end-points. One way to accomplish that task is to plot a circular pattern of radial lines at different angles. The test function defined below does exactly that.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;bresenham_line.py&gt;&gt;=
from Tkinter import *

&lt;&lt;BresenhamCanvas&gt;&gt;
    &lt;&lt;draw_point&gt;&gt;

    &lt;&lt;draw_line&gt;&gt;
                
if __name__ == &quot;__main__&quot;:

    import math
    CANVAS_SIZE = 600

    root = Tk()
    canvas = BresenhamCanvas(root, width=CANVAS_SIZE, height=CANVAS_SIZE)
    canvas.pack()
    
    margin = CANVAS_SIZE / 10
    
    xcenter = int(CANVAS_SIZE / 2)
    ycenter = int(CANVAS_SIZE / 2)
    line_length = ((CANVAS_SIZE / 2) - margin)
    
    n_lines = 100
    angle_step = (2 * math.pi) / n_lines
    
    for i in range(n_lines):
        theta = angle_step * i
        xstart = int(margin * math.cos(theta)) + xcenter
        ystart = int(margin * math.sin(theta)) + ycenter
        xend = int(line_length * math.cos(theta)) + xcenter
        yend = int(line_length * math.sin(theta)) + ycenter
        canvas.draw_line(xstart, ystart, xend, yend, color=&quot;blue&quot;)
        
    root.mainloop()

&lt;/codeblock&gt;

== References ==
* NIST, [http://www.nist.gov/dads/HTML/bresenham.html Bresenham's algorithm], accessed 2007-05-18.

[[Category:Programming language:Python]]
[[Category:Raster algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (C Plus Plus)</title>
    <id>1793</id>
    <revision>
      <id>3309</id>
      <timestamp>2006-03-14T17:11:03Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Based on [Quick sort (C Plus Plus)]</comment>
      <text xml:space="preserve">{{develop}}

An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.&lt;br&gt;
This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in c++ so that it can work on different containers and data types.&lt;br&gt;
The IT template parameter can be any random-access iterator type (including raw pointers).&lt;br&gt;
A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.&lt;br&gt;

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
					std::swap(*it, *(it+1));
					done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>3336</id>
      <timestamp>2006-03-16T18:43:16Z</timestamp>
      <contributor>
        <ip>195.216.9.219</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.&lt;br&gt;
This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in c++ so that it can work on different containers and data types.&lt;br&gt;
The IT template parameter can be any random-access iterator type (including raw pointers).&lt;br&gt;
A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.&lt;br&gt;

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
					std::swap(*it, *(it+1));
					done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>3636</id>
      <timestamp>2006-03-27T00:27:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>-{{develop}}</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.&lt;br&gt;
This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in c++ so that it can work on different containers and data types.&lt;br&gt;
The IT template parameter can be any random-access iterator type (including raw pointers).&lt;br&gt;
A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.&lt;br&gt;

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
					std::swap(*it, *(it+1));
					done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>3723</id>
      <timestamp>2006-04-03T16:08:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Cleanup</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.&lt;br&gt;
This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in c++ so that it can work on different containers and data types.&lt;br&gt;
The IT template parameter can be any random-access iterator type (including raw pointers).&lt;br&gt;
A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.&lt;br&gt;

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
				std::swap(*it, *(it+1));
				done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>4763</id>
      <timestamp>2006-05-15T03:00:58Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.&lt;br&gt;
This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in c++ so that it can work on different containers and data types.&lt;br&gt;
The IT template parameter can be any random-access iterator type (including raw pointers).&lt;br&gt;
A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.&lt;br&gt;

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
				std::swap(*it, *(it+1));
				done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>6660</id>
      <timestamp>2006-07-10T22:10:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Overview */ rm html markup</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any random-access iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	for(IT n=end-1; n&gt;=begin &amp;&amp; !done; --n) {
		done=true;
		for(IT it=begin; it!=n; ++it) {
			if(*it&gt;*(it+1)) {
				std::swap(*it, *(it+1));
				done=false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17096</id>
      <timestamp>2011-04-10T11:49:43Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Bubble sort */ Fixed code to avoid UB and actually be correct</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any random-access iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{	
	if (begin == end) {
		return;
	}
	IT itEnd(end - 1);
	bool done(false);
	for (It itEnd(end - 1); itEnd != begin &amp;&amp; !done; --itEnd) {
		done = true;
		for (IT it = begin; it != itEnd; ++it) {
			if (*(it+1)&lt;*it) {
				swap(*it, *(it+1));
				done = false;
			}
		}
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17097</id>
      <timestamp>2011-04-10T11:52:59Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Bubble sort */ Fixed up fail in first try</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any random-access iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	if (begin == end) {
		return;
	}
	end -= 1;
	bool done(false);
	while (end != begin &amp;&amp; !done) {
		done = true;
		for (IT it = begin; it != end; ++it) {
			if (*(it+1)&lt;*it) {
				swap(*it, *(it+1));
				done = false;
			}
		}
		--end;
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17098</id>
      <timestamp>2011-04-11T03:25:05Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Bubble sort */ Touchup, now only needs bidirectional iterators.</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any random-access iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	while (begin != end &amp;&amp; !done) {
		done = true;
		IT it(begin);
		IT next(begin);
		++next;
		while (next != end) {
			if (*next &lt; *it) {
				swap(*next, *it);
				done = false;
			}
			++it;
			++next;
		}
		--end;
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17099</id>
      <timestamp>2011-04-11T03:25:45Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Overview */ Changed to say bidirectional iterator</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any bidirectional iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	while (begin != end &amp;&amp; !done) {
		done = true;
		IT it(begin);
		IT next(begin);
		++next;
		while (next != end) {
			if (*next &lt; *it) {
				swap(*next, *it);
				done = false;
			}
			++it;
			++next;
		}
		--end;
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17100</id>
      <timestamp>2011-04-11T03:32:12Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Bubble sort */ Now uses qualified call to swap.</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any bidirectional iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	while (begin != end &amp;&amp; !done) {
		done = true;
		IT it(begin);
		IT next(begin);
		++next;
		while (next != end) {
			if (*next &lt; *it) {
				::std::swap(*next, *it);
				done = false;
			}
			++it;
			++next;
		}
		--end;
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>17101</id>
      <timestamp>2011-04-11T03:34:16Z</timestamp>
      <contributor>
        <username>Mankarse</username>
        <id>2254</id>
      </contributor>
      <comment>/* Bubble sort */ Changed to use ADL</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in c++.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubblesort.cpp&gt;&gt;=
#include&lt;iostream&gt;
#include&lt;algorithm&gt;	// std::swap()
#include&lt;vector&gt;
&lt;&lt;bubble_sort&gt;&gt;
&lt;&lt;test_driver&gt;&gt;
&lt;/codeblock&gt;

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses the [http://en.wikibooks.org/wiki/Programming:C_plus_plus/Templates template]-functionality in C++, allowing it to be used generically with different containers and data types. The &lt;code&gt;IT&lt;/code&gt; template parameter can be any bidirectional iterator type (including raw pointers). A complete generic implementation would also include a comparison function parameter, so that the user could choose the sort order.

== Bubble sort ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
template&lt;typename IT&gt; 
void bubble_sort(IT begin, IT end)
{
	bool done(false);
	while (begin != end &amp;&amp; !done) {
		done = true;
		IT it(begin);
		IT next(begin);
		++next;
		while (next != end) {
			if (*next &lt; *it) {
				using ::std::swap;
				swap(*next, *it);
				done = false;
			}
			++it;
			++next;
		}
		--end;
	}
}
&lt;/codeblock&gt;

== Testing ==

This test program will first run bubble_sort() on a vector of strings, and then do the same on an array of integers.&lt;br&gt;
Note that sorting of strings (and other classes) implies calling copy-constructor and destructor many times, which might lead to bad performance.

[ A good implementation of 'swap' will eliminate the usual dynamic heap memory overheads of copy-constructors and destructors, by simply swaping the pointers to the heap memory.  I expect most standard library implementations of std::string::swap are implemented this way.  For vectors of user-defined classes, the user will need to provide their own overloaded implementation of swap, or else incur overhead of dynamic memory allocation and deallocation ]

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;test_driver&gt;&gt;=
template&lt;typename T&gt; void print(const T &amp;data)
{
	std::cout&lt;&lt;&quot; &quot;&lt;&lt;data;
}

int main()
{
	std::vector&lt;std::string&gt; v(10);
	v[0]=&quot;Paris&quot;;
	v[1]=&quot;London&quot;;
	v[2]=&quot;Stockholm&quot;;
	v[3]=&quot;Berlin&quot;;
	v[4]=&quot;Oslo&quot;;
	v[5]=&quot;Rome&quot;;
	v[6]=&quot;Madrid&quot;;
	v[7]=&quot;Tallinn&quot;;
	v[8]=&quot;Amsterdam&quot;;
	v[9]=&quot;Dublin&quot;;

	std::cout&lt;&lt;&quot;v before bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(v.begin(), v.end());

	std::cout&lt;&lt;&quot;v after bubble_sort(): &quot;;
	std::for_each(v.begin(), v.end(), print&lt;std::string&gt;);
	std::cout&lt;&lt;'\n';

	int a[]={3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9};
	int *a_end=a+sizeof a/sizeof(int);

	std::cout&lt;&lt;&quot;a before bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	bubble_sort(a, a_end);
	
	std::cout&lt;&lt;&quot;a after bubble_sort(): &quot;;
	std::for_each(a, a_end, print&lt;int&gt;);
	std::cout&lt;&lt;'\n';

	return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C Plus Plus]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (C Sharp)</title>
    <id>2405</id>
    <revision>
      <id>6638</id>
      <timestamp>2006-07-06T22:40:42Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <comment>bubble sort in C#</comment>
      <text xml:space="preserve">This article covers an implementation of 'bubble' sorting algorithm in C# language.

Bubble sorting is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while &lt;code&gt;i&lt;/code&gt;-th element greater than next, swap them and go next.
Thus, elements with greater values 'float' to the end of array. Like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort an simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps index where last exchange happened at previous iteration of 'do' cycle. This variable keeps a border, right border of not yet sorted sequence in array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of array. And it is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at tne next iteration. And it is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that array is sorted.

== Generic implementation (C# 2.0) ==

Generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but everything that support &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element greater or less than other while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;SelectionSortExample.cs&gt;&gt;=

using System;

class SelectionSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
	{
		// create test array and fill it with random values
		int[] array = new int[1024];
		Random rnd = new Random( Environment.TickCount );
		for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

		// sort our array
		bubble_sort_generic( array );

		// check if it really sorted now
		bool sorted = true;
		for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
		{
			if ( array[i] &gt; array[i + 1] ) sorted = false;
		}

		Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
	}
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>6639</id>
      <timestamp>2006-07-06T22:42:44Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <minor/>
      <comment>wron class name</comment>
      <text xml:space="preserve">This article covers an implementation of 'bubble' sorting algorithm in C# language.

Bubble sorting is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while &lt;code&gt;i&lt;/code&gt;-th element greater than next, swap them and go next.
Thus, elements with greater values 'float' to the end of array. Like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort an simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps index where last exchange happened at previous iteration of 'do' cycle. This variable keeps a border, right border of not yet sorted sequence in array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of array. And it is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at tne next iteration. And it is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that array is sorted.

== Generic implementation (C# 2.0) ==

Generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but everything that support &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element greater or less than other while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;SelectionSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>6642</id>
      <timestamp>2006-07-06T23:14:47Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <text xml:space="preserve">This article covers an implementation of 'bubble' sorting algorithm in C# language.

Bubble sorting is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while &lt;code&gt;i&lt;/code&gt;-th element greater than next, swap them and go next.
Thus, elements with greater values 'float' to the end of array. Like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort an simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps index where last exchange happened at previous iteration of 'do' cycle. This variable keeps a border, right border of not yet sorted sequence in array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of array. And it is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at tne next iteration. And it is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that array is sorted.

== Generic implementation (C# 2.0) ==

Generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but everything that support &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element greater or less than other while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>6646</id>
      <timestamp>2006-07-07T00:09:10Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <comment>categories added</comment>
      <text xml:space="preserve">This article covers an implementation of 'bubble' sorting algorithm in C# language.

Bubble sorting is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while &lt;code&gt;i&lt;/code&gt;-th element greater than next, swap them and go next.
Thus, elements with greater values 'float' to the end of array. Like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort an simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps index where last exchange happened at previous iteration of 'do' cycle. This variable keeps a border, right border of not yet sorted sequence in array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of array. And it is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at tne next iteration. And it is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that array is sorted.

== Generic implementation (C# 2.0) ==

Generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but everything that support &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element greater or less than other while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>6647</id>
      <timestamp>2006-07-07T16:52:15Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>gramar, link to wp article</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while the &lt;code&gt;i&lt;/code&gt;-th element is greater than the next, swap them and go to next.
Thus, elements with greater values 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. It is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that support the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>6738</id>
      <timestamp>2006-07-11T12:44:04Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (C Sharp)]] moved to [[Bubble sort (C Sharp) on Wheels]]</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while the &lt;code&gt;i&lt;/code&gt;-th element is greater than the next, swap them and go to next.
Thus, elements with greater values 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. It is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that support the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>6912</id>
      <timestamp>2006-07-11T14:23:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (C Sharp) on Wheels]] moved to [[Bubble sort (C Sharp)]]: revert</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very - maybe the most - simple sorting algorithm,
which use one simple rule for it's work: while the &lt;code&gt;i&lt;/code&gt;-th element is greater than the next, swap them and go to next.
Thus, elements with greater values 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sort a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement of 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. It is possible only if these elements are placed in correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is simple to decide when to stop sorting now - when there were no excanges at all and right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that support the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with test &lt;code&gt;Main&lt;/code&gt; function to one working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>10482</id>
      <timestamp>2007-06-14T19:59:54Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>copyedit</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while the &lt;code&gt;i&lt;/code&gt;-th element examined is greater than the next, swap them.
Thus, elements with greater values 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that supports the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>10483</id>
      <timestamp>2007-06-14T20:01:51Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>clarify</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an &lt;code&gt;i&lt;/code&gt;-th element that is greater than the &lt;code&gt;(i + 1)&lt;/code&gt;-th element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that supports the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>10484</id>
      <timestamp>2007-06-14T20:06:06Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that supports the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort]]</text>
    </revision>
    <revision>
      <id>11634</id>
      <timestamp>2007-11-19T20:16:12Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that supports the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort|C Sharp]]</text>
    </revision>
    <revision>
      <id>15596</id>
      <timestamp>2008-12-17T06:20:18Z</timestamp>
      <contributor>
        <ip>89.19.172.22</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

FIELD_MESSAGE_bocerricd

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort|C Sharp]]</text>
    </revision>
    <revision>
      <id>15600</id>
      <timestamp>2008-12-17T06:34:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rv</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in C#.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays (C# 1.0) ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
static void bubble_sort( int[] array )
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for (long i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation (C# 2.0) ==

The generic implementation of bubble sort takes advantages of 'generics' in C# 2.0: now our function can sort not only integers but anything that supports the &lt;code&gt;IComparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
static void bubble_sort_generic&lt;T&gt;( T[] array ) where T : IComparable
{
	long right_border = array.Length - 1;

	do
	{
		long last_exchange = 0;

		for ( long i = 0; i &lt; right_border; i++ )
		{
			if ( array[i].CompareTo(array[i + 1]) &gt; 0 )
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;Main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

using System;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    static void Main(string[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random( Environment.TickCount );
        for ( int i = 0; i &lt; array.Length; i++ ) array[i] = rnd.Next();

        // sort our array
        bubble_sort_generic( array );

        // check if it really sorted now
        bool sorted = true;
        for ( int i = 0; sorted &amp;&amp; (i &lt; array.Length - 1); i++ )
        {
             if ( array[i] &gt; array[i + 1] ) sorted = false;
        }

        Console.WriteLine( sorted ? &quot;array sorted&quot; : &quot;something wrong&quot; );
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:.NET]]
[[Category:Bubble sort|C Sharp]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (C)</title>
    <id>2383</id>
    <revision>
      <id>6484</id>
      <timestamp>2006-06-26T08:24:40Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <comment>initial version</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock langauge=C&gt;
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;
  void *ptmp;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=C&gt;
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=C&gt;
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=C&gt;
static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.</text>
    </revision>
    <revision>
      <id>6485</id>
      <timestamp>2006-06-26T08:26:04Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock langauge=C&gt;
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;
  void *ptmp;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=C&gt;
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=C&gt;
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=C&gt;
static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6486</id>
      <timestamp>2006-06-26T08:27:42Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <comment>fixed a type</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=C&gt;
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;
  void *ptmp;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=C&gt;
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=C&gt;
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=C&gt;
static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6643</id>
      <timestamp>2006-07-06T23:21:35Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <comment>formatted: downloadable code</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;
  void *ptmp;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6644</id>
      <timestamp>2006-07-06T23:24:36Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;
  void *ptmp;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6645</id>
      <timestamp>2006-07-06T23:27:22Z</timestamp>
      <contributor>
        <username>Cfyz</username>
        <id>72</id>
      </contributor>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6730</id>
      <timestamp>2006-07-11T12:43:51Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (C)]] moved to [[Bubble sort (C) on Wheels]]</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>6836</id>
      <timestamp>2006-07-11T12:47:45Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (C) on Wheels]] moved to [[Bubble sort (C) on Wheels on Wheels on Wheels]]</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>7009</id>
      <timestamp>2006-07-11T19:31:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (C) on Wheels on Wheels on Wheels]] moved to [[Bubble sort (C)]]: Revert vandalism</comment>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrows from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to C-outsider why one has to fall back to some characterwise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
    <revision>
      <id>15710</id>
      <timestamp>2008-12-29T12:48:06Z</timestamp>
      <contributor>
        <ip>192.165.213.18</ip>
      </contributor>
      <text xml:space="preserve">== A somewhat generic implementation ==
The support for functional programming is not very elaborated in C. However you can have function pointers and this come in very handy, especially for sorting algorithms. 

I have mimiced the interface of the standard function qsort. So it looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort function&gt;&gt;=
/* mimics the qsort interface */
void bubble_sort(void *base, size_t nmemb, size_t size,
                 int (*compar)(const void *, const void *)) {
  int i, j;
  char *pc =  base;
  char *pc_at_i;
  char *pc_at_j;

  for (i = nmemb -1; i &gt; 0; --i){
    for (j = 0; j &lt; i; ++j) {
	 /* we have to calculate the offsets, by defintion the size of
	 char is 1 in C, so we do not have to include  the size of the
	 elements while doing this address calculations */
      pc_at_i = pc + (i * size);
      pc_at_j = pc + (j * size);
      if (compar (pc_at_i, pc_at_j) &lt;  0) {
		  swap_fun(base, size, i, j);
      }
    }
  }
}
&lt;/codeblock&gt;

I used two extra functions for comparison and swapping of elements. The swapping of elements was borrowed from the [[C++|Quicksort]] page and looks like this:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;swap_fun function&gt;&gt;=
/* Swapping of elements in an array. Because there is a void* we need to give
this function the element_size of the to be sorted elements, we then can exchange the
array elements character by character. */
static void swap_fun (void *base, size_t element_size,
	                  int index1, int index2) {
	char *pc = base;
	char tmp;
	int i;
	for (i = 0; i &lt; element_size; ++i) {
		tmp = pc[index1 * element_size + i];
        pc[index1 * element_size + i] = pc[index2*element_size + i];
        pc[index2 * element_size + i] = tmp;
	}
}
&lt;/codeblock&gt;

I just commented it a bit, because it's not fully clear to a C-outsider why one has to fall back to some character-wise operations. 

Now the thing left is the comparison function. Here's the implementation:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;int_cmp_fun function&gt;&gt;=
int int_cmp_fun (const void * v1, const void * v2) {
  const int * i1 = v1;
  const int * i2 = v2;
  int result;
  if (*i1 == *i2) {
    result = 0;
  } else if (*i1 &lt; *i2) {
    result = -1;
  } else {
    result = 1;
  }
  return result;
}
&lt;/codeblock&gt;

We can use the functions as follows
==  Bubble-sort in action == 
Here a simple example for this sorting function:
&lt;codeblock language=&quot;C&quot;&gt;
&lt;&lt;bubble_sort.c&gt;&gt;=

#include &lt;stdio.h&gt;

&lt;&lt;swap_fun function&gt;&gt;

&lt;&lt;bubble_sort function&gt;&gt;

&lt;&lt;int_cmp_fun function&gt;&gt;

static void print_int_arr(int *arr, size_t size_of_arr) {
  int i;
  for (i = 0; i &lt; size_of_arr; i++) {
    printf(&quot;%d &quot;, arr[i]);
  }
  putchar('\n');
}


int main(void) {
  enum { T_SIZE = 7};
  int arr[T_SIZE] = {-1, 2, 1, 3, 5, -10, -11};

  printf(&quot;array before sorting: &quot;);
  print_int_arr(arr, T_SIZE);
  printf(&quot;array after bubblesort: &quot;);
  bubble_sort(arr, T_SIZE, sizeof(int), int_cmp_fun);
  print_int_arr(arr, T_SIZE);
  return 0;
}

&lt;/codeblock&gt;

We get the following output:
&lt;pre&gt;
./a.out
array before sorting: -1 2 1 3 5 -10 -11
array after bubblesort: -11 -10 -1 1 2 3 5

&lt;/pre&gt;

So if you are using C, consider using function pointers, the are a really helpful utility.


[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|C]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (CLIPS)</title>
    <id>3749</id>
    <revision>
      <id>15716</id>
      <timestamp>2008-12-31T15:48:04Z</timestamp>
      <contributor>
        <username>Krriggs</username>
        <id>1760</id>
      </contributor>
      <text xml:space="preserve">NASA '''CLIPS'''[http://en.wikipedia.org/wiki/CLIPS] the (C Language Integrated Production rule System) matches rules against facts choosing one possible match (an 'instantiaion') to perform ('fire') and then repeating the process as long as possible. 

Below we show two ways to 'bubble' sort a sequence of values, first when they are collected into a single long list (called a 'multifield) and then when they are independent but indexed facts. 


== Sorting in a Simple Fact ==

&lt;codeblock&gt;
&lt;&lt;bubbleSortNumericMultifield.clp&gt;&gt;=
(defrule sort 
    (data $?X ?a ?b $?Y)
    (test (&lt; ?b ?a))
=&gt;
    (assert (data $?X ?b ?a $?Y)))
&lt;/codeblock&gt;

The data fact is simply a list of numbers like '(data 51 33 87 1 200)'. The patterns $?X and $?Y match any 0 or more umbers, so the two numbers ?a and ?b may are a pair anywhere in the list. There are generally many ways to match a fact! The test '(test (&lt; ?b ?a))' makes sure that ?a &lt; ?b in the fact match. When everything matches we have an &quot;instantiation&quot;.

One chosen instantiation is fired. Here the only action is to make a new fact similar to the old, but with these two elements now in order. Note we are not assured of the order of swaps as we would be in a procedural language. 

Since the rule is applied to exhaustion, MANY data facts will be made. Since each will have 1 less set of 'out of order' elements, eventually we will reduce the out of order number to zero. For the same reason we must stop eventually - since CLIPS does not normally record duplicate facts, thereby avoiding a possible infinite regression.

We can avoid the plethora of facts by removing old facts as we make new. The fact assignment '?f&lt;-' captures an id of the matched fact. The retract function removes it from memory.:

&lt;codeblock&gt;
&lt;&lt;bubbleSortNumericMultifieldDeterminate.clp&gt;&gt;=
(defrule sort 
?f&lt;-(data $?X ?a ?b $?Y)
    (test (&lt; ?b ?a))
=&gt;
    (retract ?f)
    (assert (data $?X ?b ?a $?Y)))
&lt;/codeblock&gt;

We are still correct:
 Since the rule must reduce the number of out-of-order's we must stop.
 Since it stops only when none are out of order we are sorted (Turn around the test for descending order.)

Of course we could use a test other than '&lt;' for other types, even mixed types, so our routine is quite general - as long as we have a single fact.


== Sorting Facts ==
To sort individual facts we need some index to tell the place in the order. We assume unique random places to start with. Here we also keep the bubble sort characteristic of swapping only adjacent pairs by adding a test for that: (test (= (+ ?place1 1) ?place2))
 
&lt;codeblock&gt;
&lt;&lt;bubbleSortNumericIndexedFacts.clp&gt;&gt;=
(defrule bubble
?f&lt;-(datum ?datum1 ?place1)
?g&lt;-(datum ?datum2 ?place2)
    (test (&gt; ?datum1 ?datum2))
    (test (= (+ ?place1 1) ?place2)))   ; (&lt; ?place1 ?place2) is better, but no known sort
=&gt;
    (retract ?f ?g)
    (assert (datum ?datum1 ?place2)
            (datum ?datum2 ?place1))
)
&lt;/codeblock&gt;


The reasoning for correctness is similar to the previous: The rule fires whenever then is an adjacent pair out-of-order. It stops when no adjacent pairs are out of order.

Of course more complex data sorts would require a specific comparison, but we still only need to find the data order and the current place.</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Eiffel)</title>
    <id>1950</id>
    <revision>
      <id>4400</id>
      <timestamp>2006-05-06T06:41:58Z</timestamp>
      <contributor>
        <username>Leland McInnes</username>
        <id>4</id>
      </contributor>
      <comment>start</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing felxibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble Sort]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4762</id>
      <timestamp>2006-05-15T03:00:36Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing felxibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble Sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>5094</id>
      <timestamp>2006-05-21T12:32:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat: s/Bubble Sort/Bubble sort/</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing felxibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>6659</id>
      <timestamp>2006-07-10T22:08:51Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Overview */ sp</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>6766</id>
      <timestamp>2006-07-11T12:44:54Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (Eiffel)]] moved to [[Bubble sort (Eiffel) on Wheels]]</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>6938</id>
      <timestamp>2006-07-11T14:25:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Bubble sort (Eiffel) on Wheels]] moved to [[Bubble sort (Eiffel)]]: revert</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort(a : ARRAY[X]) is
    require
        a /= Void
    local
        i, j : INTEGER
        done : BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a@j &gt;= a@(j+1) then
                    a.swap(j,j+1)
                end

                j := j + 1
            end

            i := i + 1
        end
    ensure
        a.count = old a.count
        is_sorted(a, a.lower, a.upper)
    end -- bubble_sort
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalised code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted(a: ARRAY[X]; min, max : INTEGER) : BOOLEAN is
    require
        a /= Void
    local
        i : INTEGER
    do
        Result := True
        
        from 
            i := min
        invariant
            a.valid_index(i)
        until
            i &gt;= max or not Result
        loop
            if not (a@i &lt;= a@(i+1)) then
                Result := False
            end
              
            i := i + 1
        end
    end -- is_sorted
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT[X -&gt; COMPARABLE]

feature {ANY}

    &lt;&lt;bubble sort&gt;&gt;

feature {NONE}

    &lt;&lt;is sorted&gt;&gt;

end -- class BUBBLE_SORT
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

creation
    make
    
feature

    make is
        local
            i : INTEGER
            testarray_numeric : ARRAY[INTEGER_8]
            testarray_string : ARRAY[STRING]
            sorter_numeric : BUBBLE_SORT[INTEGER_8]
            sorter_string : BUBBLE_SORT[STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort(testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer(testarray_numeric@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_integer(testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort(testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string(testarray_string@i)
                io.put_string(&quot;,&quot;)
                
                i := i + 1
            end
            
            io.put_string(testarray_string.last)
            io.put_new_line
            
        end

        
end -- class BUBBLE_SORT_TEST
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>10904</id>
      <timestamp>2007-08-18T21:16:47Z</timestamp>
      <contributor>
        <username>Manus eiffel</username>
        <id>1004</id>
      </contributor>
      <comment>Updated to Eiffel ECMA style</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort (a: ARRAY [X])
    require
        a_not_void: a /= Void
    local
        i, j: INTEGER
        temp: X
        done: BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a [j] &gt;= a [j + 1] then
                    temp := a [j]
                    a [j] := a [j + 1]
                    a [j + 1] := temp
                end
                j := j + 1
            end
            i := i + 1
        end
    ensure
        same_count: a.count = old a.count
        sorted: is_sorted (a, a.lower, a.upper)
    end
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalized code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is sorted&gt;&gt;=
is_sorted (a: ARRAY[X]; min, max: INTEGER): BOOLEAN
    require
        a_not_void: a /= Void
        min_valid: a.valid_index (min)
        max_valid: a.valid_index (max)
    local
        i: INTEGER
    do
        Result := True
        from 
            i := min
        invariant
            a.valid_index (i)
        until
            i &gt;= max or not Result
        loop
            Result := a [i] &lt;= a [i + 1]
            i := i + 1
        end
    end
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT [X -&gt; COMPARABLE]

feature -- Sorting

    &lt;&lt;bubble sort&gt;&gt;

feature -- Status report

    &lt;&lt;is sorted&gt;&gt;

end
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

create
    make
    
feature

    make is
        local
            i: INTEGER
            testarray_numeric: ARRAY [INTEGER_8]
            testarray_string: ARRAY [STRING]
            sorter_numeric: BUBBLE_SORT [INTEGER_8]
            sorter_string: BUBBLE_SORT [STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort (testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer (testarray_numeric [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_integer (testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort (testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string (testarray_string [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_string (testarray_string.last)
            io.put_new_line
        end
        
end
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>10905</id>
      <timestamp>2007-08-18T21:18:03Z</timestamp>
      <contributor>
        <username>Manus eiffel</username>
        <id>1004</id>
      </contributor>
      <comment>Fixed reference error</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort (a: ARRAY [X])
    require
        a_not_void: a /= Void
    local
        i, j: INTEGER
        temp: X
        done: BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a [j] &gt;= a [j + 1] then
                    temp := a [j]
                    a [j] := a [j + 1]
                    a [j + 1] := temp
                end
                j := j + 1
            end
            i := i + 1
        end
    ensure
        same_count: a.count = old a.count
        sorted: is_sorted (a, a.lower, a.upper)
    end
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalized code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is_sorted&gt;&gt;=
is_sorted (a: ARRAY[X]; min, max: INTEGER): BOOLEAN
    require
        a_not_void: a /= Void
        min_valid: a.valid_index (min)
        max_valid: a.valid_index (max)
    local
        i: INTEGER
    do
        Result := True
        from 
            i := min
        invariant
            a.valid_index (i)
        until
            i &gt;= max or not Result
        loop
            Result := a [i] &lt;= a [i + 1]
            i := i + 1
        end
    end
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT [X -&gt; COMPARABLE]

feature -- Sorting

    &lt;&lt;bubble_sort&gt;&gt;

feature -- Status report

    &lt;&lt;is_sorted&gt;&gt;

end
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

create
    make
    
feature

    make is
        local
            i: INTEGER
            testarray_numeric: ARRAY [INTEGER_8]
            testarray_string: ARRAY [STRING]
            sorter_numeric: BUBBLE_SORT [INTEGER_8]
            sorter_string: BUBBLE_SORT [STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort (testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer (testarray_numeric [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_integer (testarray_numeric.last)
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort (testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string (testarray_string [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_string (testarray_string.last)
            io.put_new_line
        end
        
end
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>10909</id>
      <timestamp>2007-08-18T21:35:58Z</timestamp>
      <contributor>
        <username>Manus eiffel</username>
        <id>1004</id>
      </contributor>
      <comment>Fixed usage of non-standard routine</comment>
      <text xml:space="preserve">An implementation of [http://en.wikipedia.org/Bubble_sort bubble sort] in Eiffel.

== Overview ==

Bubble sort works by repeatedly iterating through a container, swapping adjacent items when the first item is larger than the second. When no swapping is done, the container is sorted.

This implementation uses Eiffel generic facilities to enable sorting of arrays of elements of any type that inherits from COMPARABLE, providing flexibility while ensuring that comparison operators are meaningful.

== Bubble sort ==

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort&gt;&gt;=
bubble_sort (a: ARRAY [X])
    require
        a_not_void: a /= Void
    local
        i, j: INTEGER
        temp: X
        done: BOOLEAN
    do
        from
            i := a.lower + 1
            done := False
        until
            i &gt;= a.upper or done
        loop
            from
                j := a.lower
            until
                j &gt;= a.upper
            loop
                if a [j] &gt;= a [j + 1] then
                    temp := a [j]
                    a [j] := a [j + 1]
                    a [j + 1] := temp
                end
                j := j + 1
            end
            i := i + 1
        end
    ensure
        same_count: a.count = old a.count
        sorted: is_sorted (a, a.lower, a.upper)
    end
&lt;/codeblock&gt;

== Correctness ==

Eiffel provides facility for Design by Contract, here taking the form of pre- and post-conditions requiring that the input array be non-empty, and ensuring that the resulting array have the same number of elements and be sorted. These contracts are converted into runtime checks after compilation for debugging, or can be turned off for finalized code. We do, however, require a definition of a routine to determine if the array is sorted:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;is_sorted&gt;&gt;=
is_sorted (a: ARRAY[X]; min, max: INTEGER): BOOLEAN
    require
        a_not_void: a /= Void
        min_valid: a.valid_index (min)
        max_valid: a.valid_index (max)
    local
        i: INTEGER
    do
        Result := True
        from 
            i := min
        invariant
            a.valid_index (i)
        until
            i &gt;= max or not Result
        loop
            Result := a [i] &lt;= a [i + 1]
            i := i + 1
        end
    end
&lt;/codeblock&gt;

== Class Declaration ==

As Eiffel is a fully object oriented language we must package these routines as features of a class

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort.e&gt;&gt;=
class BUBBLE_SORT [X -&gt; COMPARABLE]

feature -- Sorting

    &lt;&lt;bubble_sort&gt;&gt;

feature -- Status report

    &lt;&lt;is_sorted&gt;&gt;

end
&lt;/codeblock&gt;

== Testing ==

To test the BUBBLE_SORT class we can construct a simple test class demonstrating bubble sort running first over an array of integers, then over an array of strings.

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;bubble_sort_test.e&gt;&gt;=
class BUBBLE_SORT_TEST

create
    make
    
feature

    make is
        local
            i: INTEGER
            testarray_numeric: ARRAY [INTEGER_8]
            testarray_string: ARRAY [STRING]
            sorter_numeric: BUBBLE_SORT [INTEGER_8]
            sorter_string: BUBBLE_SORT [STRING]
        do
            create sorter_numeric
            create sorter_string
            
            testarray_numeric := &lt;&lt;3,8,0,6,7,4,2,1,9,3,1,8,3,9,2,0,9,
                                   4,6,3,0,5,7,9,3,2,5,7,9,0,1,9,3,1&gt;&gt;
            sorter_numeric.bubble_sort (testarray_numeric)
            
            from
                i := testarray_numeric.lower
            until
                i &gt;= testarray_numeric.upper
            loop
                io.put_integer (testarray_numeric [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_integer (testarray_numeric [i])
            io.put_new_line
            
            testarray_string := &lt;&lt;&quot;Paris&quot;,&quot;London&quot;,&quot;Stockholm&quot;,&quot;Berlin&quot;,&quot;Oslo&quot;,
                                  &quot;Rome&quot;,&quot;Madrid&quot;,&quot;Tallinn&quot;,&quot;Amsterdam&quot;,&quot;Dublin&quot;&gt;&gt;
            sorter_string.bubble_sort (testarray_string)
            
            from
                i := testarray_string.lower
            until
                i &gt;= testarray_string.upper
            loop
                io.put_string (testarray_string [i])
                io.put_string (&quot;,&quot;)
                i := i + 1
            end
            io.put_string (testarray_string [i])
            io.put_new_line
        end
        
end
&lt;/codeblock&gt;

[[Category:Bubble sort|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Erlang)</title>
    <id>3364</id>
    <revision>
      <id>13114</id>
      <timestamp>2008-04-17T09:43:09Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">On each comparison step we'll need 3 variables: for the part processed on the current pass, yet unprocessed part, and a flag, whether there were transpositions of the current pass, that is whether sorting should stop after the current pass.

So we redefine the basic call to use the notation with three arguments. At the beginning, we have no transpositions, so halting flag is true.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
-module(bubblesort).
-export([sort/1]).
-import(lists, [reverse/1]).

sort(L) -&gt; sort(L, [], true).
&lt;/codeblock&gt;

If we have no items in the unprocessed list, we return the resulting list, if there were no transpositions during the last pass, else we start the next pass. Note, that since we're going to add items to the head of the resulting list, it is reversed and we must reverse it back before returning it or starting the next pass.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([], L, Halt) -&gt;
    case Halt of
        true -&gt; reverse(L);
        false -&gt; sort(reverse(L), [], true)
    end;
&lt;/codeblock&gt;

If unprocessed part contains the only item, then we just add it to the head of the resulting list, passing the halting flag through.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ H ], L, Halt) -&gt; sort([], [ H | L ], Halt);
&lt;/codeblock&gt;

If unprocessed part contains two or more items, then unless the first item is greater than the second, we add the first item to the head of the resulting list, leaving the second in the head of the unprocessed list. If the first item is greater than the second, then we do vice versa, and set the halting flag to false, since we're changing the order of items in the resulting list.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X, Y | T ], L, Halt) -&gt;
    case X &gt; Y of
        false -&gt; sort([ Y | T ], [ X | L ], Halt);
        true -&gt; sort([ X | T ], [ Y | L ], false)
    end.
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>13115</id>
      <timestamp>2008-04-17T09:48:38Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>variable name</comment>
      <text xml:space="preserve">On each comparison step we'll need 3 variables: for the part processed on the current pass, yet unprocessed part, and a flag, whether there were transpositions of the current pass, that is whether sorting should stop after the current pass.

So we redefine the basic call to use the notation with three arguments. At the beginning, we have no transpositions, so halting flag is true.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
-module(bubblesort).
-export([sort/1]).
-import(lists, [reverse/1]).

sort(L) -&gt; sort(L, [], true).
&lt;/codeblock&gt;

If we have no items in the unprocessed list, we return the resulting list, if there were no transpositions during the last pass, else we start the next pass. Note, that since we're going to add items to the head of the resulting list, it is reversed and we must reverse it back before returning it or starting the next pass.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([], L, Halt) -&gt;
    case Halt of
        true -&gt; reverse(L);
        false -&gt; sort(reverse(L), [], true)
    end;
&lt;/codeblock&gt;

If unprocessed part contains the only item, then we just add it to the head of the resulting list, passing the halting flag through.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X ], L, Halt) -&gt; sort([], [ X | L ], Halt);
&lt;/codeblock&gt;

If unprocessed part contains two or more items, then unless the first item is greater than the second, we add the first item to the head of the resulting list, leaving the second in the head of the unprocessed list. If the first item is greater than the second, then we do vice versa, and set the halting flag to false, since we're changing the order of items in the resulting list.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X, Y | T ], L, Halt) -&gt;
    case X &gt; Y of
        false -&gt; sort([ Y | T ], [ X | L ], Halt);
        true -&gt; sort([ X | T ], [ Y | L ], false)
    end.
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>13134</id>
      <timestamp>2008-04-18T01:42:29Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">On each comparison step we'll need 3 variables: for the part processed on the current pass, yet unprocessed part, and a flag, whether there were transpositions of the current pass, that is whether sorting should stop after the current pass.

So we redefine the basic call to use the notation with three arguments. At the beginning, we have no transpositions, so halting flag is true.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
-module(bubblesort).
-export([sort/1]).
-import(lists, [reverse/1]).

sort(L) -&gt; sort(L, [], true).
&lt;/codeblock&gt;

If we have no items in the unprocessed list, we return the resulting list, if there were no transpositions during the last pass, else we start the next pass. Note, that since we're going to add items to the head of the resulting list, it is reversed and we must reverse it back before returning it or starting the next pass.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([], L, Halt) -&gt;
    case Halt of
        true -&gt; reverse(L);
        false -&gt; sort(reverse(L), [], true)
    end;
&lt;/codeblock&gt;

If unprocessed part contains the only item, then we just add it to the head of the resulting list, passing the halting flag through.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X ], L, Halt) -&gt; sort([], [ X | L ], Halt);
&lt;/codeblock&gt;

If unprocessed part contains two or more items, then unless the first item is greater than the second, we add the first item to the head of the resulting list, leaving the second in the head of the unprocessed list. If the first item is greater than the second, then we do vice versa, and set the halting flag to false, since we're changing the order of items in the resulting list.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X, Y | T ], L, Halt) -&gt;
    case X &gt; Y of
        false -&gt; sort([ Y | T ], [ X | L ], Halt);
        true -&gt; sort([ X | T ], [ Y | L ], false)
    end.
&lt;/codeblock&gt;

[[Category:Bubble sort|Erlang]]
[[Category:Programming language:Erlang]]</text>
    </revision>
    <revision>
      <id>13141</id>
      <timestamp>2008-04-18T06:21:56Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>reduction</comment>
      <text xml:space="preserve">On each comparison step we'll need 3 variables: for the part processed on the current pass, yet unprocessed part, and a flag, whether there were transpositions of the current pass, that is whether sorting should stop after the current pass.

So we redefine the basic call to use the notation with three arguments. At the beginning, we have no transpositions, so halting flag is true.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
-module(bubblesort).
-export([sort/1]).
-import(lists, [reverse/1]).

sort(L) -&gt; sort(L, [], true).
&lt;/codeblock&gt;

If we have no items in the unprocessed list, we return the resulting list, if there were no transpositions during the last pass, else we start the next pass. Note, that since we're going to add items to the head of the resulting list, it is reversed and we must reverse it back before returning it or starting the next pass.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([], L, true) -&gt; reverse(L);

sort([], L, false) -&gt; sort(reverse(L), [], true);
&lt;/codeblock&gt;

If unprocessed part contains two or more items and the first item is greater than the second, then we add the second item to the head of the resulting list, leaving the first in the head of the unprocessed list, and set the halting flag to false, since we're changing the order of items in the resulting list.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X, Y | T ], L, _) when X &gt; Y -&gt;
    sort([ X | T ], [ Y | L ], false);
&lt;/codeblock&gt;

Else we just add the first item in the unprocessed list to the head of the resulting list, passing the halting flag through.

&lt;codeblock language=erlang&gt;
&lt;&lt;bubblesort.erl&gt;&gt;=
sort([ X | T ], L, Halt) -&gt; sort(T, [ X | L ], Halt).
&lt;/codeblock&gt;

[[Category:Bubble sort|Erlang]]
[[Category:Programming language:Erlang]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Io)</title>
    <id>3332</id>
    <revision>
      <id>12737</id>
      <timestamp>2008-03-08T13:49:01Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <comment>initial revision, in a non to &quot;literate&quot; way.</comment>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)

&lt;/codeblock&gt;
Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io|Programming language:Io]]
[[Category:Bubble sort|Bubble sort]]&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>12738</id>
      <timestamp>2008-03-08T13:49:58Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codeblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)


Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;/codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io|Programming language:Io]]
[[Category:Bubble sort|Bubble sort]]&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>12739</id>
      <timestamp>2008-03-08T13:50:43Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codeblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)


Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;/codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io|Programming language:Io]]
[[Category:Bubble sort|Bubble sort]]</text>
    </revision>
    <revision>
      <id>12740</id>
      <timestamp>2008-03-08T13:52:53Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <comment>[[BubleSort (Io)]] moved to [[BubbleSort (Io)]]: typo in Bubble</comment>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codeblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)


Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;/codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io|Programming language:Io]]
[[Category:Bubble sort|Bubble sort]]</text>
    </revision>
    <revision>
      <id>12761</id>
      <timestamp>2008-03-10T02:30:02Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codeblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)


Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;/codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io]]
[[Category:Bubble sort|Io]]</text>
    </revision>
    <revision>
      <id>12762</id>
      <timestamp>2008-03-10T02:30:33Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>[[BubbleSort (Io)]] moved to [[Bubble sort (Io)]]: consistent name with other languages</comment>
      <text xml:space="preserve">BubbleSort is well famous, at least as an example &quot;how not to do programming&quot;. But it's simply and that
counts obviously. Here now a complete BubbleSort for Io (modeled after the Common Lisp solution.

I added the whole stuff to the Protoyp List again (but be aware a List in Io is an resizable array) so this solution 
is not that worth as if we'd have a linked List...
&lt;codeblock language=Io&gt;
List  do (
    bubbleSort := method(cmpBlock,
      for(i, size -1 , 0, -1,
        for(j, 0, i, 1,
          if ((cmpBlock call(at(i),at(j)))
            ,
            swapIndices(j,i)
    ))))
)
&lt;/codeblock&gt;

I used a block again as in the Insertion Sort, but will implement other approaches of using function (or blocks) later
I think you'd hardly finda a more concise algorithm in any of the languages. Let's talk about a few area

&lt;codeblock language=Io&gt;
bubbleSort := method
&lt;/codeblock&gt;

This creates a new method named bubbleSort  and because before we have an List do we are extending the prototyp for the &quot;class&quot; 
List. The for loop may look a bit unusual but using this syntax makes it very easy to extend Io to you liking. You do not like the provided if then just write a new one, and the same was done for the 'for' loop here.
I introduce a new variable at the beginning (firt an i) then I wrote
size - 1 this means in fact the same as if I'd written &lt;code&gt; self size - 1&lt;/code&gt; but because we're in the List anyway this means that we'd call the size method on a list. Io is a prototyp based language, getting a new derived object is hardly recognicable. If I'd not like to add the sort the List I could have written:
&lt;codeblock language=Io&gt;
MyList := clone List
MyList bubbleSort := .....
&lt;/codeblock&gt;

and then I have a new object derived from List but with an additional bubbleSort. There is not need on syntacic sugar. Just write it down and you have it.

But now back to the algorithm, I have another loop in the first loop starting the next parameter after 'size -1' is 0, that's the 
end condition so I iterate from the last element to the first element. Now we have to get the &quot;bubbling&quot; for that we use another loop this time with the loop variable j from 0 up to i. Please remember that the outer loop runs from the end of the list to the 
first element in the list. this explains the next if .
&lt;codeblock language=Io&gt;
if ((cmpBlock call...

&lt;/codeblock&gt;

This way a closure is called in Io. If you'd the same in Smalltalk you'd use something like codeblock value.... But now let's see what happens if we do a comparisn of a(i=6) = 24  and a(j=0) = 1 with the comparison &lt;.

The question is: 'if 24 &lt; 1' then
&lt;codeblock language=Io&gt;
 swapIndices(j,i)
&lt;/codeblock&gt;

swapIndices does the exchange. Quite handy wouldn't you agree ;-)

So after we have looped through them all we hopefully have sorted the array. Let's see:
&lt;codeblock language=Io&gt;
tList := list (1,-2,-3,10,100,-23, 24)

tList bubbleSort(block(a,b, a &lt; b))
write (&quot;tList bubleSorted = &quot;, tList, &quot;\n&quot;)


Output:
tList bubleSorted = list(-23, -3, -2, 1, 10, 24, 100)
&lt;/codeblock&gt;

That's very fine, now if we feel that we'd like to sort something else, we simply can give bubbleSort another comparisonFunction and that's it. Closures and blocks are so handy, it's hard to believe that any language can survive without such thing....






[[Category:Programming language:Io]]
[[Category:Bubble sort|Io]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Java)</title>
    <id>3276</id>
    <revision>
      <id>11988</id>
      <timestamp>2008-01-09T11:12:51Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in Java.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
public static void bubble_sort(int[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation ==

The generic implementation of bubble sort takes advantages of 'generics' in Java 5: now our function can sort arrays of any reference type that implements the &lt;code&gt;Comparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
public static &lt;T extends Comparable&lt;? super T&gt;&gt; void bubble_sort_generic(T[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i].compareTo(array[i + 1]) &gt; 0)
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BubbleSortExample.cs&gt;&gt;=

import java.util.Random;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    public static void main(String[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random();
        for (int i = 0; i &lt; array.length; i++)
            array[i] = rnd.nextInt();

        // sort our array
        bubble_sort(array);

        // check if it really sorted now
        for (int i = 0; i &lt; array.length - 1; i++ )
        {
             if (array[i] &gt; array[i + 1])
             {
                 System.out.println(&quot;something wrong&quot;);
                 return;
             }
        }

        System.out.println(&quot;array sorted&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|Java]]</text>
    </revision>
    <revision>
      <id>11989</id>
      <timestamp>2008-01-09T11:13:28Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in Java.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
public static void bubble_sort(int[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation ==

The generic implementation of bubble sort takes advantages of 'generics' in Java 5: now our function can sort arrays of any reference type that implements the &lt;code&gt;Comparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
public static &lt;T extends Comparable&lt;? super T&gt;&gt; void bubble_sort_generic(T[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i].compareTo(array[i + 1]) &gt; 0)
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BubbleSortExample.java&gt;&gt;=

import java.util.Random;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    public static void main(String[] args)
    {
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random();
        for (int i = 0; i &lt; array.length; i++)
            array[i] = rnd.nextInt();

        // sort our array
        bubble_sort(array);

        // check if it really sorted now
        for (int i = 0; i &lt; array.length - 1; i++ )
        {
             if (array[i] &gt; array[i + 1])
             {
                 System.out.println(&quot;something wrong&quot;);
                 return;
             }
        }

        System.out.println(&quot;array sorted&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|Java]]</text>
    </revision>
    <revision>
      <id>13782</id>
      <timestamp>2008-06-25T07:23:22Z</timestamp>
      <contributor>
        <ip>58.71.38.175</ip>
      </contributor>
      <comment>/* Files */</comment>
      <text xml:space="preserve">This article covers an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] in Java.

Bubble sort is an inefficient but very simple - perhaps even the simplest - sorting algorithm,
which uses one straightforward rule for its work: while there remains an i&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element that is greater than the (i+1)&lt;small&gt;&lt;sup&gt;th&lt;/sup&gt;&lt;/small&gt; element, swap them.

Thus, elements with greater values will 'float' to the end of the array, like bubbles.

== Integer arrays ==

Firstly, let's write a function which sorts a simple array of integer values:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;integer array sort&gt;&gt;=
public static void bubble_sort(int[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i] &gt; array[i + 1])
			{
				int temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while (right_border &gt; 0);
}
&lt;/codeblock&gt;

In this function you may see one little improvement over the 'classic' bubble sort. The 'right_border' variable keeps an index to where the last exchange happened at the previous iteration of the 'do' cycle. This variable keeps a right border of the not yet sorted sequence in the array. If it has value of &lt;code&gt;i&lt;/code&gt;, it means that no exchanges were made within elements with indices from &lt;code&gt;i&lt;/code&gt; to the end of the array. That is possible only if these elements are placed in the correct order, if they are sorted. Thus it is not necessary to check them at the next iteration. It is then simple to decide when to stop sorting - when there were no exchanges at all and the right border is 0 we can say that the array is sorted.

== Generic implementation ==

The generic implementation of bubble sort takes advantages of 'generics' in Java 5: now our function can sort arrays of any reference type that implements the &lt;code&gt;Comparable&lt;/code&gt; interface. This interface is needed because there is no other way to decide if one element is greater or less than another while operating with unknown, 'generic', types.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generic array sort&gt;&gt;=
public static &lt;T extends Comparable&lt;? super T&gt;&gt; void bubble_sort_generic(T[] array)
{
	int right_border = array.length - 1;

	do
	{
		int last_exchange = 0;

		for (int i = 0; i &lt; right_border; i++)
		{
			if (array[i].compareTo(array[i + 1]) &gt; 0)
			{
				T temp = array[i];
				array[i] = array[i + 1];
				array[i + 1] = temp;

				last_exchange = i;
			}
		}

		right_border = last_exchange;
	}
	while ( right_border &gt; 0 );
}
&lt;/codeblock&gt;

== Files ==

Let's combine those methods with a test &lt;code&gt;main&lt;/code&gt; function to make a working program:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;BubbleSortExample.java&gt;&gt;=

import java.util.Random;

class BubbleSortExample
{
    &lt;&lt;integer array sort&gt;&gt;

    &lt;&lt;generic array sort&gt;&gt;

    public static void main(String[] args) {
    
        // create test array and fill it with random values
        int[] array = new int[1024];
        Random rnd = new Random();       //it randomize the integer
        for (int i = 0; i &lt; array.length; i++)
            array[i] = rnd.nextInt();       //it randomize the integer inside the array

        // sort our array
        bubble_sort(array);

        // check if it really sorted now
        for (int i = 0; i &lt; array.length - 1; i++ ){
        
             if (array[i] &gt; array[i + 1]){
             
                 System.out.println(&quot;something wrong&quot;);
                 
                 return;
                 

             }
        }

        System.out.println(&quot;array sorted&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Bubble sort|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Lisp)</title>
    <id>2411</id>
    <revision>
      <id>6663</id>
      <timestamp>2006-07-11T07:41:15Z</timestamp>
      <contributor>
        <ip>84.163.103.60</ip>
      </contributor>
      <comment>bubbel sort in common lisp with the extended loop facility</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the 
extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0
          do
          (loop for j from 0 to i
                do
                (when (funcall cmp-fun (aref result i) (aref result j))
                  (rotatef (aref result i)
                           (aref result j)))))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.</text>
    </revision>
    <revision>
      <id>6664</id>
      <timestamp>2006-07-11T07:45:29Z</timestamp>
      <contributor>
        <ip>84.163.103.60</ip>
      </contributor>
      <comment>Addded an example</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the 
extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0
          do
          (loop for j from 0 to i
                do
                (when (funcall cmp-fun (aref result i) (aref result j))
                  (rotatef (aref result i)
                           (aref result j)))))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.
== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function</text>
    </revision>
    <revision>
      <id>6665</id>
      <timestamp>2006-07-11T07:49:52Z</timestamp>
      <contributor>
        <ip>84.163.103.60</ip>
      </contributor>
      <comment>added categories</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the 
extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0
          do
          (loop for j from 0 to i
                do
                (when (funcall cmp-fun (aref result i) (aref result j))
                  (rotatef (aref result i)
                           (aref result j)))))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.
== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
    <revision>
      <id>8307</id>
      <timestamp>2006-12-04T23:16:03Z</timestamp>
      <contributor>
        <ip>72.66.43.181</ip>
      </contributor>
      <comment>removed &lt;cr&gt; from the comment</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0
          do
          (loop for j from 0 to i
                do
                (when (funcall cmp-fun (aref result i) (aref result j))
                  (rotatef (aref result i)
                           (aref result j)))))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.
== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
    <revision>
      <id>8308</id>
      <timestamp>2006-12-04T23:18:21Z</timestamp>
      <contributor>
        <ip>72.66.43.181</ip>
      </contributor>
      <comment>improved formatting and used the WHEN clause on the inner loop</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0 do
        (loop for j from 0 to i
            when (funcall cmp-fun (aref result i) (aref result j))
               do (rotatef (aref result i) (aref result j)) )))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.
== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
    <revision>
      <id>8309</id>
      <timestamp>2006-12-04T23:21:58Z</timestamp>
      <contributor>
        <ip>72.66.43.181</ip>
      </contributor>
      <comment>Added a note about CL Sort spec.</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0 do
        (loop for j from 0 to i
            when (funcall cmp-fun (aref result i) (aref result j))
               do (rotatef (aref result i) (aref result j)) )))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The Makro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;build-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.

Note: The Common Lisp specified loop is destructive.
== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
    <revision>
      <id>11554</id>
      <timestamp>2007-11-12T14:29:34Z</timestamp>
      <contributor>
        <ip>83.76.85.107</ip>
      </contributor>
      <comment>/* Implementation */ typos (de-&gt;en)</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0 do
        (loop for j from 0 to i
            when (funcall cmp-fun (aref result i) (aref result j))
               do (rotatef (aref result i) (aref result j)) )))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The macro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;built-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.

Note: The Common Lisp specified loop is destructive.

== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
    <revision>
      <id>15522</id>
      <timestamp>2008-12-01T10:08:36Z</timestamp>
      <contributor>
        <ip>140.120.14.16</ip>
      </contributor>
      <comment>/* Implementation */</comment>
      <text xml:space="preserve">Here's an implementation of bubble sort with Common Lisp

== Implementation == 
&lt;codeblock language=Lisp&gt;
(defun bubble-sort (array cmp-fun) 
  &quot;Bubble sort implementation in common lisp. Using the extended loop facility.&quot;
  (let ((result (copy-seq array)))
    (loop for i from (1- (length result)) downto 0 do
        (loop for j from 0 to i
            when (funcall cmp-fun (aref result i) (aref result j))
               do (rotatef (aref result i) (aref result j)) ))
    result))
&lt;/codeblock&gt;

It's quite generic, you just have to provide the proper &lt;em&gt; cmp-fun&lt;/em&gt;. The implementation uses the extended loop facility. You can see it as a small sub-language embedded into Common Lisp. 

Because I like to have a somewhat clean sort function, I did not change the parameter but created a new 
array as result. 

The macro &lt;em&gt;rotatef&lt;/em&gt; comes in handy here, one can use it as a &quot;built-in&quot; swap function as here.

In Common Lisp the array index starts at zero as it does e.g in C.

Note: The Common Lisp specified loop is destructive.

== Usage example ==
You can use the REPL for trying the sort function
Here for an array of integers:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(1 -1 2 -10) #'&lt;)
#(-10 -1 1 2)
&lt;/codeblock&gt;

or with strings:
&lt;codeblock language=Lisp&gt;
(bubble-sort #(&quot;one&quot; &quot;two&quot; &quot;three&quot;) #'string&lt;)
#(&quot;one&quot; &quot;three&quot; &quot;two&quot;)
&lt;/codeblock&gt;

Of course you can use it for self defined classes also. One could e.g implement the same interface as the normal sort function.

[[Category:Programming language:Lisp]]
[[Category:Bubble sort|Lisp]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort (Smalltalk)</title>
    <id>3670</id>
    <revision>
      <id>6656</id>
      <timestamp>2006-07-10T09:21:27Z</timestamp>
      <contributor>
        <ip>84.163.103.235</ip>
      </contributor>
      <comment>Initial revision</comment>
      <text xml:space="preserve">Here an implementation of Bubble-sort with Smalltalk. 

&lt;codeblock language=Smalltalk&gt;
bubbleSort: cmpFun 
	&quot;Implementing Bubble sort with Smalltalk&quot;
	| i j tmp funResult |
	i := self size.
	[i &gt; 0]
		whileTrue: [j := 1.
			[j &lt;= i]
				whileTrue: [funResult := cmpFun
								value: (self at: i)
								value: (self at: j).
					funResult
						ifTrue: [tmp := self at: i.
							self
								at: i
								put: (self at: j).
							self at: j put: tmp].
					j := j + 1].
			i := i - 1]
&lt;/codeblock&gt;

The only thing worth noting:
- it's quite generic according to the cmpFun

One hast to start with &lt;em&gt; i := self size &lt;/em&gt; because Arrays in Smalltalk are 1-based. So the first element in an Array is at position 1. In C it is zero based, therefor we have to remember the following in C:
int char[SOME_LIMIT] means an Array from 0 to SOME_LIMIT -1, which you have to remember to avoid the off-by-ones in C. 

Now in Smalltalk if the size of an Array is three we can access the last element like this
&lt;em&gt; arr at: 3 &lt;/em&gt;

I have inlined the swapping of elements, however generalizing it might be a good idea.

Another thing worth noting. Blocks are a really really useful tool. See especially (amusing!)
http://wiki.cs.uiuc.edu/VisualWorks/How+to+get+rid+of+Objects+in+Smalltalk

Happy smalltalking
[[User:84.163.103.235|84.163.103.235]] 02:21, 10 July 2006 (PDT)frido</text>
    </revision>
    <revision>
      <id>6657</id>
      <timestamp>2006-07-10T09:25:38Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Here an implementation of Bubble-sort with Smalltalk. 

&lt;codeblock language=Smalltalk&gt;
bubbleSort: cmpFun 
	&quot;Implementing Bubble sort with Smalltalk&quot;
	| i j tmp funResult |
	i := self size.
	[i &gt; 0]
		whileTrue: [j := 1.
			[j &lt;= i]
				whileTrue: [funResult := cmpFun
								value: (self at: i)
								value: (self at: j).
					funResult
						ifTrue: [tmp := self at: i.
							self
								at: i
								put: (self at: j).
							self at: j put: tmp].
					j := j + 1].
			i := i - 1]
&lt;/codeblock&gt;

The only thing worth noting:
- it's quite generic according to the cmpFun

One hast to start with &lt;em&gt; i := self size &lt;/em&gt; because Arrays in Smalltalk are 1-based. So the first element in an Array is at position 1. In C it is zero based, therefor we have to remember the following in C:
int char[SOME_LIMIT] means an Array from 0 to SOME_LIMIT -1, which you have to remember to avoid the off-by-ones in C. 

Now in Smalltalk if the size of an Array is three we can access the last element like this
&lt;em&gt; arr at: 3 &lt;/em&gt;

I have inlined the swapping of elements, however generalizing it might be a good idea.

Another thing worth noting. Blocks are a really really useful tool. See especially (amusing!)
http://wiki.cs.uiuc.edu/VisualWorks/How+to+get+rid+of+Objects+in+Smalltalk

Happy smalltalking</text>
    </revision>
    <revision>
      <id>6658</id>
      <timestamp>2006-07-10T17:04:46Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>wikilinks,  make code downloadable; cat; cleanup; spelling</comment>
      <text xml:space="preserve">Here an implementation of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort] algorithm in [http://en.wikipedia.org/wiki/Smalltalk_programming_language Smalltalk]. This implementation is generic in the comparison function, &lt;code&gt;cmpFun&lt;/code&gt;, that it uses for determining the sort order.

&lt;codeblock language=smalltalk&gt;
&lt;&lt;bubble sort&gt;&gt;=
bubbleSort: cmpFun 
	&quot;Implementing Bubble sort with Smalltalk&quot;
	| i j tmp funResult |
	i := self size.
	[i &gt; 0]
		whileTrue: [j := 1.
			[j &lt;= i]
				whileTrue: [funResult := cmpFun
								value: (self at: i)
								value: (self at: j).
					funResult
						ifTrue: [tmp := self at: i.
							self
								at: i
								put: (self at: j).
							self at: j put: tmp].
					j := j + 1].
			i := i - 1]
&lt;/codeblock&gt;

One has to start with &lt;code&gt;i := self size&lt;/code&gt; because Arrays in Smalltalk are 1-based. So the first element in an Array is at position 1. This is in contrast to languages such as C, in which array indexing is 0-based. 

Now in Smalltalk if the size of an Array is three we can access the last element like this &lt;code&gt;arr at: 3&lt;/code&gt;

The swapping of elements has been inlined, however generalizing it might be a good idea.

== Importing into Squeak ==
To allow this method to be easily imported into [http://www.squeak.org/ Squeak] Smalltalk, we place it in an .st file with the appropriate surrounding markup for importing into the Array class using file-in.

&lt;codeblock language=smalltalk&gt;
&lt;&lt;bubbleSort.st&gt;&gt;=
!Array methodsFor: 'sorting' stamp:''!
&lt;&lt;bubble sort&gt;&gt;! !
&lt;/codeblock&gt;

[[Category:Programming language:Smalltalk]]
[[Category:Bubble sort|Smalltalk]]</text>
    </revision>
  </page>
  <page>
    <title>Bubble sort(lisp)</title>
    <id>3246</id>
    <revision>
      <id>11552</id>
      <timestamp>2007-11-12T08:07:48Z</timestamp>
      <contributor>
        <ip>202.170.82.16</ip>
      </contributor>
      <text xml:space="preserve">I need a bubble sorting method in lisp, Is there any one have it?</text>
    </revision>
    <revision>
      <id>11553</id>
      <timestamp>2007-11-12T10:47:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>#redirect [[Bubble sort (Lisp)]]</comment>
      <text xml:space="preserve">#redirect [[Bubble sort (Lisp)]]</text>
    </revision>
  </page>
  <page>
    <title>BubbleSort (Io)</title>
    <id>3336</id>
    <revision>
      <id>12763</id>
      <timestamp>2008-03-10T02:30:33Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>[[BubbleSort (Io)]] moved to [[Bubble sort (Io)]]: consistent name with other languages</comment>
      <text xml:space="preserve">#REDIRECT [[Bubble sort (Io)]]</text>
    </revision>
  </page>
  <page>
    <title>BubleSort (Io)</title>
    <id>3333</id>
    <revision>
      <id>12741</id>
      <timestamp>2008-03-08T13:52:53Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <comment>[[BubleSort (Io)]] moved to [[BubbleSort (Io)]]: typo in Bubble</comment>
      <text xml:space="preserve">#REDIRECT [[BubbleSort (Io)]]</text>
    </revision>
  </page>
  <page>
    <title>Bucket sort (C)</title>
    <id>2879</id>
    <revision>
      <id>8393</id>
      <timestamp>2007-01-01T18:57:28Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=c&gt;
&lt;&lt;sort function&gt;&gt;=
void bucketSort(int array[], int n) {
  int i, j;
  int count[n];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
int count[n];
for(i=0; i &lt; n; i++) {
  count[i] = 0;
}
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=c&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i=0; i &lt; n; i++) {
  (count[array[i]])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=c&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; n; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    array[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
for (i = 0;i &lt; n;i++) {
  printf(&quot;%i &quot;, array[i]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;sort function&gt;&gt;

int main() {
  int array[] = {1,3,4,6,4,2,9,1,2,9};
  int n = 10;
  int i;

  &lt;&lt;output the array&gt;&gt;

  bucketSort(array, n);

  &lt;&lt;output the array&gt;&gt;

  return 0;
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort]]</text>
    </revision>
    <revision>
      <id>8394</id>
      <timestamp>2007-01-01T18:58:32Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>added categories</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=c&gt;
&lt;&lt;sort function&gt;&gt;=
void bucketSort(int array[], int n) {
  int i, j;
  int count[n];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
int count[n];
for(i=0; i &lt; n; i++) {
  count[i] = 0;
}
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=c&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i=0; i &lt; n; i++) {
  (count[array[i]])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=c&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; n; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    array[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
for (i = 0;i &lt; n;i++) {
  printf(&quot;%i &quot;, array[i]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;sort function&gt;&gt;

int main() {
  int array[] = {1,3,4,6,4,2,9,1,2,9};
  int n = 10;
  int i;

  &lt;&lt;output the array&gt;&gt;

  bucketSort(array, n);

  &lt;&lt;output the array&gt;&gt;

  return 0;
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8395</id>
      <timestamp>2007-01-01T18:59:24Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>correction</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=c&gt;
&lt;&lt;sort function&gt;&gt;=
void bucketSort(int array[], int n) {
  int i, j;
  int count[n];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
for(i=0; i &lt; n; i++) {
  count[i] = 0;
}
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=c&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i=0; i &lt; n; i++) {
  (count[array[i]])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=c&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; n; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    array[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
for (i = 0;i &lt; n;i++) {
  printf(&quot;%i &quot;, array[i]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;sort function&gt;&gt;

int main() {
  int array[] = {1,3,4,6,4,2,9,1,2,9};
  int n = 10;
  int i;

  &lt;&lt;output the array&gt;&gt;

  bucketSort(array, n);

  &lt;&lt;output the array&gt;&gt;

  return 0;
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11824</id>
      <timestamp>2007-12-27T18:03:15Z</timestamp>
      <contributor>
        <ip>59.180.176.80</ip>
      </contributor>
      <comment>/* Putting it together */</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=c&gt;
&lt;&lt;sort function&gt;&gt;=
void bucketSort(int array[], int n) {
  int i, j;
  int count[n];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
for(i=0; i &lt; n; i++) {
  count[i] = 0;
}
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=c&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i=0; i &lt; n; i++) {
  (count[array[i]])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=c&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; n; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    array[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
for (i = 0;i &lt; n;i++) {
  printf(&quot;%d &quot;, array[i]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;sort function&gt;&gt;

int main() {
  int array[] = {1,3,4,6,4,2,9,1,2,9};
  int n = 10;
  int i;

  &lt;&lt;output the array&gt;&gt;

  bucketSort(array, n);

  &lt;&lt;output the array&gt;&gt;

  return 0;
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bucket sort (Java)</title>
    <id>2881</id>
    <revision>
      <id>8402</id>
      <timestamp>2007-01-02T01:43:31Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>translated</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=java&gt;
&lt;&lt;initialize counters&gt;&gt;=
Arrays.fill(count, 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15526</id>
      <timestamp>2008-12-04T18:08:46Z</timestamp>
      <contributor>
        <ip>64.235.102.2</ip>
      </contributor>
      <comment>/* Putting it together */</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=java&gt;
&lt;&lt;initialize counters&gt;&gt;=
Arrays.fill(count, 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }NIGGER
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15527</id>
      <timestamp>2008-12-04T18:09:22Z</timestamp>
      <contributor>
        <ip>64.235.102.2</ip>
      </contributor>
      <comment>/* Putting it together */</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=java&gt;
&lt;&lt;initialize counters&gt;&gt;=
Arrays.fill(count, 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }CHICKEN FRIED RICE HALF PRICE
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15528</id>
      <timestamp>2008-12-04T20:22:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=java&gt;
&lt;&lt;initialize counters&gt;&gt;=
Arrays.fill(count, 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16278</id>
      <timestamp>2009-03-15T19:21:23Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). The elements of an integer array are initialized to 0 when created.

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16280</id>
      <timestamp>2009-03-16T07:51:27Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>removed use of now undefined chunk</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=java&gt;
&lt;&lt;sort function&gt;&gt;=
public static int[] bucketSort(int[] arr) {
  int i, j;
  int[] count = new int[arr.length];
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). The elements of an integer array are initialized to 0 when created.

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=java&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for(i = 0; i &lt; arr.length; i++ ) {
  count[arr[i]]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=java&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
for(i=0,j=0; i &lt; count.length; i++) {
  for(; count[i]&gt;0; (count[i])--) {
    arr[j++] = i;
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=java&gt;
&lt;&lt;output the array&gt;&gt;=
for(int i = 0; i &lt; arr.length; i++ ) {
  System.out.print(arr[i] + &quot; &quot;);
}
System.out.println();
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=java&gt;
&lt;&lt;Bucketsort.java&gt;&gt;=

import java.util.Arrays;

public class Bucketsort {

  &lt;&lt;sort function&gt;&gt;

  public static void main(String[] args) {
    int[] arr = new int[] {1,3,4,6,4,2,9,1,2,9};
  
    &lt;&lt;output the array&gt;&gt;

    arr = bucketSort(arr);

    &lt;&lt;output the array&gt;&gt;
  }
}
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bucket sort (PHP)</title>
    <id>2880</id>
    <revision>
      <id>8397</id>
      <timestamp>2007-01-02T00:24:30Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($array) {
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($array), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($array as $value) {
  ($count[$value])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$array = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($array, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
var_dump($array);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
&lt;&lt;sort function&gt;&gt;

$array = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

bucketSort($array);

&lt;&lt;output the array&gt;&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8398</id>
      <timestamp>2007-01-02T00:26:13Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>some fixes</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  $count = array();
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  ($count[$value])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=c&gt;
&lt;&lt;output the array&gt;&gt;=
var_dump($arr);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=c&gt;
&lt;&lt;bucketsort.c&gt;&gt;=
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8399</id>
      <timestamp>2007-01-02T00:27:05Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>corrections</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  $count = array();
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  ($count[$value])++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;code&gt;j&lt;/code&gt; holds the current position in the array to sort.
&lt;code&gt;i&lt;/code&gt; holds the current position in the counter array,
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
var_dump($arr);
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=pjp&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8400</id>
      <timestamp>2007-01-02T00:36:03Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>fixes</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  $count = array();
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=c&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  $count[$value]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
foreach ($arr as $val) {
  echo $val.&quot; &quot;;
}
echo &quot;\n&quot;;
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=pjp&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;?php
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

$arr = bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
?&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13657</id>
      <timestamp>2008-06-11T10:48:04Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  $count = array();
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=php&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  $count[$value]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
foreach ($arr as $val) {
  echo $val.&quot; &quot;;
}
echo &quot;\n&quot;;
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=php&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;?php
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

$arr = bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
?&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13658</id>
      <timestamp>2008-06-11T10:50:37Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $array;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=php&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  $count[$value]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
foreach ($arr as $val) {
  echo $val.&quot; &quot;;
}
echo &quot;\n&quot;;
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=php&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;?php
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

$arr = bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
?&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13659</id>
      <timestamp>2008-06-11T10:51:11Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=php&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  $count[$value]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
foreach ($arr as $val) {
  echo $val.&quot; &quot;;
}
echo &quot;\n&quot;;
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=php&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;?php
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

$arr = bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
?&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17117</id>
      <timestamp>2011-05-04T17:35:38Z</timestamp>
      <contributor>
        <username>Mhitza</username>
        <id>2272</id>
      </contributor>
      <comment>/* Putting it together */</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=php&gt;
&lt;&lt;sort function&gt;&gt;=
function bucketSort($arr) {
  &lt;&lt;initialize counters&gt;&gt;
  &lt;&lt;count amount of each array-number&gt;&gt;
  &lt;&lt;rearrange order of array&gt;&gt;
  return $arr;
}
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=php&gt;
&lt;&lt;initialize counters&gt;&gt;=
$count = array_fill(0, count($arr), 0);
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=php&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
foreach ($arr as $value) {
  $count[$value]++;
}
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=php&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
$arr = array();
foreach ($count as $nr =&gt; $amount) {
  for ($i=0; $i &lt; $amount;$i++) {
    array_push($arr, $nr);
  }
}
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=php&gt;
&lt;&lt;output the array&gt;&gt;=
echo implode(&quot; &quot;, $arr), &quot;\n&quot;;
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=php&gt;
&lt;&lt;bucketsort.php&gt;&gt;=
&lt;?php
&lt;&lt;sort function&gt;&gt;

$arr = array(1,3,4,6,4,2,9,1,2,9);

&lt;&lt;output the array&gt;&gt;

$arr = bucketSort($arr);

&lt;&lt;output the array&gt;&gt;
?&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|PHP]]
[[Category:Programming language:PHP]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Bucket sort (Python)</title>
    <id>3478</id>
    <revision>
      <id>13660</id>
      <timestamp>2008-06-11T11:00:01Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>translated from php</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=python&gt;
&lt;&lt;sort function&gt;&gt;=
def bucketSort(arr):
    &lt;&lt;initialize counters&gt;&gt;
    &lt;&lt;count amount of each array-number&gt;&gt;
    &lt;&lt;rearrange order of array&gt;&gt;
    return arr
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=python&gt;
&lt;&lt;initialize counters&gt;&gt;=
count = [0] * len(arr)
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=python&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for value in arr:
    count[value] += 1
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=python&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
arr = []
for nr, amount in enumerate(count):
    arr.extend([nr] * amount)
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=python&gt;
&lt;&lt;output the array&gt;&gt;=
for val in arr:
    print val,
print
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=python&gt;
&lt;&lt;bucketsort.py&gt;&gt;=
&lt;&lt;sort function&gt;&gt;

arr = [1,3,4,6,4,2,9,1,2,9]

&lt;&lt;output the array&gt;&gt;

arr = bucket_sort(arr)

&lt;&lt;output the array&gt;&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13661</id>
      <timestamp>2008-06-11T11:00:54Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Putting it together */</comment>
      <text xml:space="preserve">Bucket sort is possibly the simplest distribution sorting algorithm. The essential requirement is that the size of the array from which the elements to be sorted are drawn is a small, fixed constant, say n.

&lt;codeblock language=python&gt;
&lt;&lt;sort function&gt;&gt;=
def bucketSort(arr):
    &lt;&lt;initialize counters&gt;&gt;
    &lt;&lt;count amount of each array-number&gt;&gt;
    &lt;&lt;rearrange order of array&gt;&gt;
    return arr
&lt;/codeblock&gt;

For example, suppose that we are sorting elements drawn from {0, 1, . . ., n-1}. The integers in this set can be of the range 0 until (n-1). Bucket sort uses n counters. These counters first have to be initialized:
&lt;codeblock language=python&gt;
&lt;&lt;initialize counters&gt;&gt;=
count = [0] * len(arr)
&lt;/codeblock&gt;

To we can determine the amount of each number in the array we want to sort.
&lt;codeblock language=python&gt;
&lt;&lt;count amount of each array-number&gt;&gt;=
for value in arr:
    count[value] += 1
&lt;/codeblock&gt;

After we've determined all needed information about the array we want to sort. The array can be sorted.
&lt;codeblock language=python&gt;
&lt;&lt;rearrange order of array&gt;&gt;=
arr = []
for nr, amount in enumerate(count):
    arr.extend([nr] * amount)
&lt;/codeblock&gt;

== Putting it together ==

To check the bucket sort, we output the data:
&lt;codeblock language=python&gt;
&lt;&lt;output the array&gt;&gt;=
for val in arr:
    print val,
print
&lt;/codeblock&gt;

Putting it all together with a example array.

&lt;codeblock language=python&gt;
&lt;&lt;bucketsort.py&gt;&gt;=
&lt;&lt;sort function&gt;&gt;

arr = [1,3,4,6,4,2,9,1,2,9]

&lt;&lt;output the array&gt;&gt;

arr = bucketSort(arr)

&lt;&lt;output the array&gt;&gt;
&lt;/codeblock&gt;

This generates following output:
&lt;pre&gt;
1 3 4 6 4 2 9 1 2 9 
1 1 2 2 3 4 4 6 9 9 
&lt;/pre&gt;

[[Category:Bucket sort|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>CPU usage (C, Windows XP)</title>
    <id>2381</id>
    <revision>
      <id>6476</id>
      <timestamp>2006-06-24T12:31:02Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>CPU usage for Windows XP SP1 (with bugs)</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''

- This code have been known to report false results on systems with more than one CPU and/or hyperthreading.

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------

CHAR cpuusage(void)
{
  FILETIME                                      ft_sys_idle;
  FILETIME                                      ft_sys_kernel;
  FILETIME                                      ft_sys_user;

  FILETIME                                      ft_fun_time;
  SYSTEMTIME                                    st_fun_time;

  ULARGE_INTEGER                                ul_sys_idle;
  static ULARGE_INTEGER	                        ul_sys_idleold;
  ULARGE_INTEGER                                ul_sys_idle_diff;

  ULARGE_INTEGER	                        ul_fun_time;
  static ULARGE_INTEGER                         ul_fun_timeold;
  ULARGE_INTEGER                                ul_fun_time_diff;

  GetSystemTimes(&amp;ft_sys_idle,&amp;ft_sys_kernel,&amp;ft_sys_user);  // This API was introduced in WinXP SP1 
  GetSystemTime(&amp;st_fun_time);
  SystemTimeToFileTime(&amp;st_fun_time,&amp;ft_fun_time);

  ul_sys_idle.LowPart  = ft_sys_idle.dwLowDateTime;
  ul_sys_idle.HighPart = ft_sys_idle.dwHighDateTime;

  ul_fun_time.LowPart  = ft_fun_time.dwLowDateTime;
  ul_fun_time.HighPart = ft_fun_time.dwHighDateTime;

  ul_sys_idle_diff.QuadPart = ul_sys_idle.QuadPart - ul_sys_idleold.QuadPart;
  ul_fun_time_diff.QuadPart = ul_fun_time.QuadPart - ul_fun_timeold.QuadPart;

  ul_sys_idleold.QuadPart   = ul_sys_idle.QuadPart;
  ul_fun_timeold.QuadPart   = ul_fun_time.QuadPart;

  if(!ul_fun_time_diff.QuadPart)
    return 0;

  return 100-((ul_sys_idle_diff.QuadPart*100)/ul_fun_time_diff.QuadPart);
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  int n;
  for(n=0;n&lt;20;n++)
  {
    printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
    sleep(500);
  }
  printf(&quot;\n&quot;);
  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
    <revision>
      <id>10845</id>
      <timestamp>2007-08-03T20:13:56Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Cleaned up code, fixed calculation to handle more than one processor</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''
None

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------

CHAR cpuusage()
{
  FILETIME               ft_sys_idle;
  FILETIME               ft_sys_kernel;
  FILETIME               ft_sys_user;

  ULARGE_INTEGER         ul_sys_idle;
  ULARGE_INTEGER         ul_sys_kernel;
  ULARGE_INTEGER         ul_sys_user;

  static ULARGE_INTEGER	 ul_sys_idle_old;
  static ULARGE_INTEGER  ul_sys_kernel_old;
  static ULARGE_INTEGER  ul_sys_user_old;

  CHAR  usage = 0;

  GetSystemTimes(&amp;ft_sys_idle,    /* System idle time */
                 &amp;ft_sys_kernel,  /* system kernel time */
                 &amp;ft_sys_user);   /* System user time */

  CopyMemory(&amp;ul_sys_idle  , &amp;ft_sys_idle  , sizeof(FILETIME)); // Could been optimized away...
  CopyMemory(&amp;ul_sys_kernel, &amp;ft_sys_kernel, sizeof(FILETIME)); // Could been optimized away...
  CopyMemory(&amp;ul_sys_user  , &amp;ft_sys_user  , sizeof(FILETIME)); // Could been optimized away...

  usage  =
          (
           (
            (
             (
              (ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
              (ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
             )
             -
             (ul_sys_idle.QuadPart-ul_sys_idle_old.QuadPart)
            )
            *
            (100)
           )
           /
           (
            (ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
            (ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
           )
          );

  ul_sys_idle_old.QuadPart   = ul_sys_idle.QuadPart;
  ul_sys_user_old.QuadPart   = ul_sys_user.QuadPart;
  ul_sys_kernel_old.QuadPart = ul_sys_kernel.QuadPart;

  return usage;
}
//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  int n;
  for(n=0;n&lt;20;n++)
  {
    printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
    sleep(500);
  }
  printf(&quot;\n&quot;);
  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
    <revision>
      <id>12530</id>
      <timestamp>2008-02-20T08:19:11Z</timestamp>
      <contributor>
        <ip>58.136.118.11</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''
None

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//-----------------------------------------------------
typedef BOOL ( __stdcall * pfnGetSystemTimes)( LPFILETIME lpIdleTime, LPFILETIME lpKernelTime, LPFILETIME lpUserTime );
//-----------------------------------------------------
void GetSystemTimesAddress()
{
	if( s_hKernel == NULL )
	{   
		s_hKernel = LoadLibrary( &quot;Kernel32.dll&quot; );
		if( s_hKernel != NULL )
		{
			s_pfnGetSystemTimes = (pfnGetSystemTimes)GetProcAddress( s_hKernel, &quot;GetSystemTimes&quot; );
			if( s_pfnGetSystemTimes == NULL )
			{
				FreeLibrary( s_hKernel ); s_hKernel = NULL;
			}
		}
	}
}
//----------------------------------------------------------------------------------------------------------------

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------
CHAR cpuusage()
{
  FILETIME               ft_sys_idle;
  FILETIME               ft_sys_kernel;
  FILETIME               ft_sys_user;

  ULARGE_INTEGER         ul_sys_idle;
  ULARGE_INTEGER         ul_sys_kernel;
  ULARGE_INTEGER         ul_sys_user;

  static ULARGE_INTEGER	 ul_sys_idle_old;
  static ULARGE_INTEGER  ul_sys_kernel_old;
  static ULARGE_INTEGER  ul_sys_user_old;

  CHAR  usage = 0;

  // we cannot directly use GetSystemTimes on C language
  /* add this line :: pfnGetSystemTimes */
  s_pfnGetSystemTimes(&amp;ft_sys_idle,    /* System idle time */
                 &amp;ft_sys_kernel,  /* system kernel time */
                 &amp;ft_sys_user);   /* System user time */

  CopyMemory(&amp;ul_sys_idle  , &amp;ft_sys_idle  , sizeof(FILETIME)); // Could been optimized away...
  CopyMemory(&amp;ul_sys_kernel, &amp;ft_sys_kernel, sizeof(FILETIME)); // Could been optimized away...
  CopyMemory(&amp;ul_sys_user  , &amp;ft_sys_user  , sizeof(FILETIME)); // Could been optimized away...

  usage  =
          (
           (
            (
             (
              (ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
              (ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
             )
             -
             (ul_sys_idle.QuadPart-ul_sys_idle_old.QuadPart)
            )
            *
            (100)
           )
           /
           (
            (ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
            (ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
           )
          );

  ul_sys_idle_old.QuadPart   = ul_sys_idle.QuadPart;
  ul_sys_user_old.QuadPart   = ul_sys_user.QuadPart;
  ul_sys_kernel_old.QuadPart = ul_sys_kernel.QuadPart;

  return usage;
}
//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  int n;
  GetSystemTimesAddress();
  for(n=0;n&lt;20;n++)
  {
    printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
    sleep(500);
  }
  printf(&quot;\n&quot;);
  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
    <revision>
      <id>12531</id>
      <timestamp>2008-02-20T08:47:13Z</timestamp>
      <contributor>
        <ip>58.136.118.11</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''
None

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//-----------------------------------------------------
typedef BOOL ( __stdcall * pfnGetSystemTimes)( LPFILETIME lpIdleTime, LPFILETIME lpKernelTime, LPFILETIME lpUserTime );
static pfnGetSystemTimes s_pfnGetSystemTimes = NULL;

static HMODULE s_hKernel = NULL;
//-----------------------------------------------------
void GetSystemTimesAddress()
{
	if( s_hKernel == NULL )
	{   
		s_hKernel = LoadLibrary( &quot;Kernel32.dll&quot; );
		if( s_hKernel != NULL )
		{
			s_pfnGetSystemTimes = (pfnGetSystemTimes)GetProcAddress( s_hKernel, &quot;GetSystemTimes&quot; );
			if( s_pfnGetSystemTimes == NULL )
			{
				FreeLibrary( s_hKernel ); s_hKernel = NULL;
			}
		}
	}
}
//----------------------------------------------------------------------------------------------------------------

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------
CHAR cpuusage()
{
	FILETIME               ft_sys_idle;
	FILETIME               ft_sys_kernel;
	FILETIME               ft_sys_user;

	ULARGE_INTEGER         ul_sys_idle;
	ULARGE_INTEGER         ul_sys_kernel;
	ULARGE_INTEGER         ul_sys_user;

	static ULARGE_INTEGER	 ul_sys_idle_old;
	static ULARGE_INTEGER  ul_sys_kernel_old;
	static ULARGE_INTEGER  ul_sys_user_old;

	CHAR  usage = 0;

	// we cannot directly use GetSystemTimes on C language
	/* add this line :: pfnGetSystemTimes */
	s_pfnGetSystemTimes(&amp;ft_sys_idle,    /* System idle time */
		&amp;ft_sys_kernel,  /* system kernel time */
		&amp;ft_sys_user);   /* System user time */

	CopyMemory(&amp;ul_sys_idle  , &amp;ft_sys_idle  , sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_kernel, &amp;ft_sys_kernel, sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_user  , &amp;ft_sys_user  , sizeof(FILETIME)); // Could been optimized away...

	usage  =
		(
		(
		(
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		-
		(ul_sys_idle.QuadPart-ul_sys_idle_old.QuadPart)
		)
		*
		(100)
		)
		/
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		);

	ul_sys_idle_old.QuadPart   = ul_sys_idle.QuadPart;
	ul_sys_user_old.QuadPart   = ul_sys_user.QuadPart;
	ul_sys_kernel_old.QuadPart = ul_sys_kernel.QuadPart;

	return usage;
}
//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
	int n;
	GetSystemTimesAddress();
	for(n=0;n&lt;20;n++)
	{
		printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
		Sleep(200);
	}
	printf(&quot;\n&quot;);
	return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
    <revision>
      <id>12532</id>
      <timestamp>2008-02-20T09:01:16Z</timestamp>
      <contributor>
        <ip>58.136.118.11</ip>
      </contributor>
      <text xml:space="preserve">'''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''
None

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//-----------------------------------------------------
typedef BOOL ( __stdcall * pfnGetSystemTimes)( LPFILETIME lpIdleTime, LPFILETIME lpKernelTime, LPFILETIME lpUserTime );
static pfnGetSystemTimes s_pfnGetSystemTimes = NULL;

static HMODULE s_hKernel = NULL;
//-----------------------------------------------------
void GetSystemTimesAddress()
{
	if( s_hKernel == NULL )
	{   
		s_hKernel = LoadLibrary( &quot;Kernel32.dll&quot; );
		if( s_hKernel != NULL )
		{
			s_pfnGetSystemTimes = (pfnGetSystemTimes)GetProcAddress( s_hKernel, &quot;GetSystemTimes&quot; );
			if( s_pfnGetSystemTimes == NULL )
			{
				FreeLibrary( s_hKernel ); s_hKernel = NULL;
			}
		}
	}
}
//----------------------------------------------------------------------------------------------------------------

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------
CHAR cpuusage()
{
	FILETIME               ft_sys_idle;
	FILETIME               ft_sys_kernel;
	FILETIME               ft_sys_user;

	ULARGE_INTEGER         ul_sys_idle;
	ULARGE_INTEGER         ul_sys_kernel;
	ULARGE_INTEGER         ul_sys_user;

	static ULARGE_INTEGER	 ul_sys_idle_old;
	static ULARGE_INTEGER  ul_sys_kernel_old;
	static ULARGE_INTEGER  ul_sys_user_old;

	CHAR  usage = 0;

	// we cannot directly use GetSystemTimes on C language
	/* add this line :: pfnGetSystemTimes */
	s_pfnGetSystemTimes(&amp;ft_sys_idle,    /* System idle time */
		&amp;ft_sys_kernel,  /* system kernel time */
		&amp;ft_sys_user);   /* System user time */

	CopyMemory(&amp;ul_sys_idle  , &amp;ft_sys_idle  , sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_kernel, &amp;ft_sys_kernel, sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_user  , &amp;ft_sys_user  , sizeof(FILETIME)); // Could been optimized away...

	usage  =
		(
		(
		(
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		-
		(ul_sys_idle.QuadPart-ul_sys_idle_old.QuadPart)
		)
		*
		(100)
		)
		/
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		);

	ul_sys_idle_old.QuadPart   = ul_sys_idle.QuadPart;
	ul_sys_user_old.QuadPart   = ul_sys_user.QuadPart;
	ul_sys_kernel_old.QuadPart = ul_sys_kernel.QuadPart;

	return usage;
}
//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
	int n;
	GetSystemTimesAddress();
	for(n=0;n&lt;20;n++)
	{
		printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
		Sleep(200);
	}
	printf(&quot;\n&quot;);
	return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
    <revision>
      <id>12602</id>
      <timestamp>2008-02-24T21:32:42Z</timestamp>
      <contributor>
        <username>Djshaw</username>
        <id>1637</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{codedump}}

'''Minimum required version of Windows''':
 - '''WinXP SP1'''

This code sample will output the current CPU usage in percent where 100% means max usage.

''Known bugs:''
None

&lt;codeblock language=c&gt;
&lt;&lt;cpuusage.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
CHAR cpuusage(void);

//-----------------------------------------------------
typedef BOOL ( __stdcall * pfnGetSystemTimes)( LPFILETIME lpIdleTime, LPFILETIME lpKernelTime, LPFILETIME lpUserTime );
static pfnGetSystemTimes s_pfnGetSystemTimes = NULL;

static HMODULE s_hKernel = NULL;
//-----------------------------------------------------
void GetSystemTimesAddress()
{
	if( s_hKernel == NULL )
	{   
		s_hKernel = LoadLibrary( &quot;Kernel32.dll&quot; );
		if( s_hKernel != NULL )
		{
			s_pfnGetSystemTimes = (pfnGetSystemTimes)GetProcAddress( s_hKernel, &quot;GetSystemTimes&quot; );
			if( s_pfnGetSystemTimes == NULL )
			{
				FreeLibrary( s_hKernel ); s_hKernel = NULL;
			}
		}
	}
}
//----------------------------------------------------------------------------------------------------------------

//----------------------------------------------------------------------------------------------------------------
// cpuusage(void)
// ==============
// Return a CHAR value in the range 0 - 100 representing actual CPU usage in percent.
//----------------------------------------------------------------------------------------------------------------
CHAR cpuusage()
{
	FILETIME               ft_sys_idle;
	FILETIME               ft_sys_kernel;
	FILETIME               ft_sys_user;

	ULARGE_INTEGER         ul_sys_idle;
	ULARGE_INTEGER         ul_sys_kernel;
	ULARGE_INTEGER         ul_sys_user;

	static ULARGE_INTEGER	 ul_sys_idle_old;
	static ULARGE_INTEGER  ul_sys_kernel_old;
	static ULARGE_INTEGER  ul_sys_user_old;

	CHAR  usage = 0;

	// we cannot directly use GetSystemTimes on C language
	/* add this line :: pfnGetSystemTimes */
	s_pfnGetSystemTimes(&amp;ft_sys_idle,    /* System idle time */
		&amp;ft_sys_kernel,  /* system kernel time */
		&amp;ft_sys_user);   /* System user time */

	CopyMemory(&amp;ul_sys_idle  , &amp;ft_sys_idle  , sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_kernel, &amp;ft_sys_kernel, sizeof(FILETIME)); // Could been optimized away...
	CopyMemory(&amp;ul_sys_user  , &amp;ft_sys_user  , sizeof(FILETIME)); // Could been optimized away...

	usage  =
		(
		(
		(
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		-
		(ul_sys_idle.QuadPart-ul_sys_idle_old.QuadPart)
		)
		*
		(100)
		)
		/
		(
		(ul_sys_kernel.QuadPart - ul_sys_kernel_old.QuadPart)+
		(ul_sys_user.QuadPart   - ul_sys_user_old.QuadPart)
		)
		);

	ul_sys_idle_old.QuadPart   = ul_sys_idle.QuadPart;
	ul_sys_user_old.QuadPart   = ul_sys_user.QuadPart;
	ul_sys_kernel_old.QuadPart = ul_sys_kernel.QuadPart;

	return usage;
}
//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
	int n;
	GetSystemTimesAddress();
	for(n=0;n&lt;20;n++)
	{
		printf(&quot;CPU Usage: %3d%%\r&quot;,cpuusage());
		Sleep(200);
	}
	printf(&quot;\n&quot;);
	return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows XP]]</text>
    </revision>
  </page>
  <page>
    <title>CPU usage using performance counters (C, Windows 2000)</title>
    <id>2947</id>
    <revision>
      <id>8735</id>
      <timestamp>2007-01-29T01:06:23Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>New article: Performance counters for win2k and up</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows 2000]]</text>
    </revision>
    <revision>
      <id>8736</id>
      <timestamp>2007-01-29T01:07:37Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>fixed a stupid typo</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows_2000]]</text>
    </revision>
    <revision>
      <id>8738</id>
      <timestamp>2007-01-29T01:11:06Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <minor/>
      <comment>[[CPU usage using performance counters (C, Windows XP)]] moved to [[CPU usage using performance counters (C, Windows 2000)]]: Wrong title (operating system)</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows_2000]]</text>
    </revision>
    <revision>
      <id>15454</id>
      <timestamp>2008-11-16T08:42:08Z</timestamp>
      <contributor>
        <ip>67.170.13.129</ip>
      </contributor>
      <comment>The linker has to be asked to link the PDH library when using the object module.</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;
#pragma comment(lib, &quot;pdh.lib&quot;)

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows_2000]]</text>
    </revision>
    <revision>
      <id>15668</id>
      <timestamp>2008-12-23T10:34:51Z</timestamp>
      <contributor>
        <ip>217.225.196.107</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?
 - Return PDH_NO_DATA after call of PdhCollectQueryData(...);, i use AMD Athlon 64 X2 Dual

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;
#pragma comment(lib, &quot;pdh.lib&quot;)

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows_2000]]</text>
    </revision>
    <revision>
      <id>16864</id>
      <timestamp>2010-09-23T13:13:14Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">'''Bold text'''
== HELLO WORLD! My ass! ==</text>
    </revision>
    <revision>
      <id>16905</id>
      <timestamp>2010-09-23T15:52:25Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:217.225.196.107|217.225.196.107]]</comment>
      <text xml:space="preserve">{{develop}}
 '''Minimum required version of Windows''':
 - '''Win 2000 SP0''' (unconfirmed)
 - '''WinXP SP2''' (confirmed)

This code sample will output the current CPU usage data collected from the performance counters in Windows. The results are shown in percent where 100% means max usage and 0% means minimum usage.

 '''Known bugs:'''
 - ?
 - Return PDH_NO_DATA after call of PdhCollectQueryData(...);, i use AMD Athlon 64 X2 Dual

&lt;codeblock language=c&gt;
&lt;&lt;cpuusageperfcnt.c&gt;&gt;=
#include &lt;windows.h&gt;
#include &lt;pdh.h&gt;
#include &lt;pdhmsg.h&gt;
#include &lt;stdio.h&gt;
#pragma comment(lib, &quot;pdh.lib&quot;)

//------------------------------------------------------------------------------------------------------------------
// Prototype(s)...
//------------------------------------------------------------------------------------------------------------------
int cpuusage(void);

//------------------------------------------------------------------------------------------------------------------
// getcpuload()
//   directly prints the CPU usage on screen. This function need to be called twice with a minimum of 1 seconds
//   delay (msdn guideline) to display something usefull.
//   Also returns the usage in percent 0-100 where 100 means the system is working at maximum capacity.
//   Note for multiprocessor systems:
//   If one CPU is working at max capacity the result will (if using (_total) for PdhAddCounter() ) show a maximum
//   workload of 50% unless the other CPU(s) is also working at max load. 
//------------------------------------------------------------------------------------------------------------------
INT getcpuload()
{
  static PDH_STATUS            status;
  static PDH_FMT_COUNTERVALUE  value;
  static HQUERY                query;
  static HCOUNTER              counter;
  static DWORD                 ret;
  static char                  runonce=1;
  char                         cput=0;

  if(runonce)
  {
    status = PdhOpenQuery(NULL, 0, &amp;query);
    if(status != ERROR_SUCCESS)
    {
      printf(&quot;PdhOpenQuery() ***Error: 0x%X\n&quot;,status);
      return 0;
    }

    PdhAddCounter(query, TEXT(&quot;\\Processor(_Total)\\% Processor Time&quot;),0,&amp;counter); // A total of ALL CPU's in the system
    //PdhAddCounter(query, TEXT(&quot;\\Processor(0)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu0)
    //PdhAddCounter(query, TEXT(&quot;\\Processor(1)\\% Processor Time&quot;),0,&amp;counter);    // For systems with more than one CPU (Cpu1)
    runonce=0;
    PdhCollectQueryData(query); // No error checking here
    return 0;
  }

  status = PdhCollectQueryData(query);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PhdCollectQueryData() ***Error: 0x%X\n&quot;,status);
    if(status==PDH_INVALID_HANDLE) 
      printf(&quot;PDH_INVALID_HANDLE\n&quot;);
    else if(status==PDH_NO_DATA)
      printf(&quot;PDH_NO_DATA\n&quot;);
    else
      printf(&quot;Unknown error\n&quot;);
    return 0;
  }

  status = PdhGetFormattedCounterValue(counter, PDH_FMT_DOUBLE | PDH_FMT_NOCAP100 ,&amp;ret, &amp;value);
  if(status != ERROR_SUCCESS)
  {
    printf(&quot;PdhGetFormattedCounterValue() ***Error: 0x%X\n&quot;,status);
    return 0;
  }
  cput = value.doubleValue;

  printf(&quot;\n\n&quot;
         &quot;CPU Total usage: %3d%%\n&quot;,cput);
  
  return cput;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point
//------------------------------------------------------------------------------------------------------------------
int main(void)
{
  while(1)
  {
    getcpuload();
    sleep(1000);
  }
  return 0;
}
&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows_2000]]</text>
    </revision>
  </page>
  <page>
    <title>CPU usage using performance counters (C, Windows XP)</title>
    <id>2949</id>
    <revision>
      <id>8739</id>
      <timestamp>2007-01-29T01:11:06Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>[[CPU usage using performance counters (C, Windows XP)]] moved to [[CPU usage using performance counters (C, Windows 2000)]]: Wrong title (operating system)</comment>
      <text xml:space="preserve">#REDIRECT [[CPU usage using performance counters (C, Windows 2000)]]</text>
    </revision>
  </page>
  <page>
    <title>CTL model checker (CSP)</title>
    <id>2704</id>
    <revision>
      <id>7650</id>
      <timestamp>2006-09-16T06:24:53Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>initial rev</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [[http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal System Europe Ltd. [http://www.fsel.com/software.html FDR tool].

Note this this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
The model-checker takes as input a finite state model (expressed as sets of states, transitions, and labels), and a CTL formula (expressed in an AST-like form), and checks that the model satisfies the CTL formula.

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 
    
See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
-- A model consisting of
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }

-- Specifications, in the form of some CTL formulas
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))

-- Output
-- We use a trace refinement check to see if one of the 
-- possible states in the SAT set is the initial state, S.0

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP


-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- The syntax of CTL
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming languages:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7651</id>
      <timestamp>2006-09-16T06:25:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix cat</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [[http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal System Europe Ltd. [http://www.fsel.com/software.html FDR tool].

Note this this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
The model-checker takes as input a finite state model (expressed as sets of states, transitions, and labels), and a CTL formula (expressed in an AST-like form), and checks that the model satisfies the CTL formula.

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 
    
See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
-- A model consisting of
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }

-- Specifications, in the form of some CTL formulas
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))

-- Output
-- We use a trace refinement check to see if one of the 
-- possible states in the SAT set is the initial state, S.0

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP


-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- The syntax of CTL
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7656</id>
      <timestamp>2006-09-16T06:32:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix link format</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal System Europe Ltd. [http://www.fsel.com/software.html FDR tool].

Note this this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
The model-checker takes as input a finite state model (expressed as sets of states, transitions, and labels), and a CTL formula (expressed in an AST-like form), and checks that the model satisfies the CTL formula.

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 
    
See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
-- A model consisting of
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }

-- Specifications, in the form of some CTL formulas
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))

-- Output
-- We use a trace refinement check to see if one of the 
-- possible states in the SAT set is the initial state, S.0

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP


-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- The syntax of CTL
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7668</id>
      <timestamp>2006-09-17T19:05:27Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal System Europe Ltd. [http://www.fsel.com/software.html FDR tool].

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
The model-checker takes as input a finite state model (expressed as sets of states, transitions, and labels), and a CTL formula (expressed in an AST-like form), and checks that the model satisfies the CTL formula.

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 
    
See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
-- A model consisting of
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }

-- Specifications, in the form of some CTL formulas
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))

-- Output
-- We use a trace refinement check to see if one of the 
-- possible states in the SAT set is the initial state, S.0

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP


-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- The syntax of CTL
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7669</id>
      <timestamp>2006-09-17T19:05:51Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool].

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
The model-checker takes as input a finite state model (expressed as sets of states, transitions, and labels), and a CTL formula (expressed in an AST-like form), and checks that the model satisfies the CTL formula.

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 
    
See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
-- A model consisting of
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }

-- Specifications, in the form of some CTL formulas
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))

-- Output
-- We use a trace refinement check to see if one of the 
-- possible states in the SAT set is the initial state, S.0

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP


-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- The syntax of CTL
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7671</id>
      <timestamp>2006-09-17T19:34:20Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>begin making literate, add diagram</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool]. See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
== Inputs ==
The model-checker takes as input a finite state machine expressed as sets of states, transitions, and labels. For example, the finite state machine shown in the figure to the right can be represented as the sets:
[[Image:Ctl-fsm.png|thumb|right|200px|Example of a labelled finite state machine]]
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;inputs&gt;&gt;=
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }
&lt;/codeblock&gt;

CTL formulas are expressed using a datatype that provides an abstract syntax:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl syntax&gt;&gt;=
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
&lt;/codeblock&gt; 

Here are a few examples of CTL formulas expressed using the syntax defined above:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example ctl formulas&gt;&gt;=
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))
&lt;/codeblock&gt;

FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example refinement checks&gt;&gt;=
SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP
&lt;/codeblock&gt;

== Implementation ==

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
&lt;&lt;inputs&gt;&gt;

-- Specifications, in the form of some CTL formulas
&lt;&lt;example ctl formulas&gt;&gt;

&lt;&lt;example refinement checks&gt;&gt;

-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

&lt;&lt;ctl syntax&gt;&gt;

    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7672</id>
      <timestamp>2006-09-18T20:16:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Inputs */ clarify, and add heading</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool]. See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
== Inputs ==
The model-checker takes as input a finite state machine expressed as sets of states, possible transitions between, and labels consisting of atomic propositions that are true in each state. For example, the finite state machine shown in the figure to the right can be represented as the sets:
[[Image:Ctl-fsm.png|thumb|right|200px|Example of a labelled finite state machine]]
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;inputs&gt;&gt;=
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }
&lt;/codeblock&gt;

CTL formulas are expressed using a datatype that provides an abstract syntax for combining atomic propositions using various logical and temporal operators:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl syntax&gt;&gt;=
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
&lt;/codeblock&gt; 

Here are a few examples of CTL formulas expressed using the syntax defined above:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example ctl formulas&gt;&gt;=
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))
&lt;/codeblock&gt;

=== Refinement assertions ===
FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example refinement checks&gt;&gt;=
SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP
&lt;/codeblock&gt;

== Implementation ==

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
-- Inputs 
&lt;&lt;inputs&gt;&gt;

-- Specifications, in the form of some CTL formulas
&lt;&lt;example ctl formulas&gt;&gt;

&lt;&lt;example refinement checks&gt;&gt;

-- Implementation 
-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

&lt;&lt;ctl syntax&gt;&gt;

    
-- Primary SAT function (defined via pattern match)
-- Recurses through a CTL formula, and returns a set of states which
-- satisfy the formula
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)

-- SAT functions for temporal operators
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
-- Pre-Image functions
-- &quot;There exists&quot; pre-image
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }

-- &quot;For all&quot; pre-image
-- The set of states which transition to X, and do not transition
-- to any state outside of X
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )

-- Fixpoint function
-- Computes the fixpoint of a given mapping function when applied to 
-- a set of states
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7673</id>
      <timestamp>2006-09-18T20:45:19Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Implementation */ further exposition</comment>
      <text xml:space="preserve">{{develop}}
This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool]. See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
== Inputs ==
The model-checker takes as input a finite state machine expressed as sets of states, possible transitions between, and labels consisting of atomic propositions that are true in each state. For example, the finite state machine shown in the figure to the right can be represented as the sets:
[[Image:Ctl-fsm.png|thumb|right|200px|Example of a labelled finite state machine]]
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;inputs&gt;&gt;=
-- 1. A set of states
States = { S.0, S.1, S.2, S.3 }

-- 2. A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- 3. A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }
&lt;/codeblock&gt;

CTL formulas are expressed using a datatype that provides an abstract syntax for combining atomic propositions using various logical and temporal operators:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl syntax&gt;&gt;=
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
&lt;/codeblock&gt; 

Here are a few examples of CTL formulas expressed using the syntax defined above:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example ctl formulas&gt;&gt;=
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))
&lt;/codeblock&gt;

=== Refinement assertions ===
FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example refinement checks&gt;&gt;=
SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP
&lt;/codeblock&gt;

== Implementation ==

The core of the model-checker is a boolean satisfaction algorithm that examines a CTL formula, and returns the set of states in the input finite state machine that satisfy the formula. We define the SAT function using a recursive pattern-match on the syntax of CTL formulas. The return value of the function is a set containing the states which satisfy the given CTL formula.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;SAT&gt;&gt;=
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)
&lt;/codeblock&gt;

=== Temporal operators ===
The definitions of the SAT function for the temporal operators EX, EU, and AF are a little more complex than those required for the other operators: 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;temporal operators&gt;&gt;=
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
&lt;/codeblock&gt;

=== Auxiliary functions ===
The SAT_EX, SAT_AF and SAT_EU functions rely on three auxiliary functions. The first computes a &quot;preimage&quot; consisting of the set of all states that can transition to any state in the set X. 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage E&gt;&gt;=
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }
&lt;/codeblock&gt;

The second auxiliary function computes a &quot;preimage&quot; consisting of the set of all states which transition to states in X, and do not transition to any state outside of X. This is easily expressed in terms of set differences and the &lt;code&gt;pre_E&lt;/code&gt; function.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage A&gt;&gt;=
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )
&lt;/codeblock&gt;

The third auxiliary function computes a fixpoint for the application of a function from sets of states to sets of states.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;fixpoint&gt;&gt;=
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

=== Complete script ===

The complete CSP script combines the inputs, refinement checks, datatypes, and SAT functions into a single file, suitable for loading into FDR.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
&lt;&lt;inputs&gt;&gt;

&lt;&lt;example ctl formulas&gt;&gt;

&lt;&lt;example refinement checks&gt;&gt;

-- Auxiliary channel used to perform the refinement checks
channel state: STATE

-- Model state names
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

&lt;&lt;ctl syntax&gt;&gt;

&lt;&lt;temporal operators&gt;&gt;
        
&lt;&lt;preimage E&gt;&gt;
&lt;&lt;preimage A&gt;&gt;
&lt;&lt;fixpoint&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7674</id>
      <timestamp>2006-09-18T20:48:33Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>-{{develop}}</comment>
      <text xml:space="preserve">This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool]. See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
== Inputs ==
The model-checker takes as input a finite state machine expressed as sets of states, possible transitions between, and labels consisting of atomic propositions that are true in each state. For example, the finite state machine shown in the figure to the right can be represented as the sets:
[[Image:Ctl-fsm.png|thumb|right|200px|Example of a labelled finite state machine]]
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;inputs&gt;&gt;=
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- A set of states
States = { S.0, S.1, S.2, S.3 }

-- A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }
&lt;/codeblock&gt;

CTL formulas are expressed using a datatype that provides an abstract syntax for combining atomic propositions using various logical and temporal operators:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl syntax&gt;&gt;=
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
&lt;/codeblock&gt; 

Here are a few examples of CTL formulas expressed using the syntax defined above:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example ctl formulas&gt;&gt;=
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))
&lt;/codeblock&gt;

=== Refinement assertions ===
FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example refinement checks&gt;&gt;=
channel state: STATE

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP
&lt;/codeblock&gt;

== Implementation ==

The core of the model-checker is a boolean satisfaction algorithm that examines a CTL formula, and returns the set of states in the input finite state machine that satisfy the formula. We define the SAT function using a recursive pattern-match on the syntax of CTL formulas. The return value of the function is a set containing the states which satisfy the given CTL formula.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;SAT&gt;&gt;=
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)
&lt;/codeblock&gt;

=== Temporal operators ===
The definitions of the SAT function for the temporal operators EX, EU, and AF are a little more complex than those required for the other operators: 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;temporal operators&gt;&gt;=
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
&lt;/codeblock&gt;

=== Auxiliary functions ===
The SAT_EX, SAT_AF and SAT_EU functions rely on three auxiliary functions. The first computes a &quot;preimage&quot; consisting of the set of all states that can transition to any state in the set X. 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage E&gt;&gt;=
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }
&lt;/codeblock&gt;

The second auxiliary function computes a &quot;preimage&quot; consisting of the set of all states which transition to states in X, and do not transition to any state outside of X. This is easily expressed in terms of set differences and the &lt;code&gt;pre_E&lt;/code&gt; function.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage A&gt;&gt;=
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )
&lt;/codeblock&gt;

The third auxiliary function computes a fixpoint for the application of a function from sets of states to sets of states.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;fixpoint&gt;&gt;=
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

=== Complete script ===

The complete CSP script combines the inputs, refinement checks, datatypes, and SAT functions into a single file, suitable for loading into FDR.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
&lt;&lt;inputs&gt;&gt;

&lt;&lt;example ctl formulas&gt;&gt;

&lt;&lt;example refinement checks&gt;&gt;

&lt;&lt;ctl syntax&gt;&gt;

&lt;&lt;temporal operators&gt;&gt;
        
&lt;&lt;preimage E&gt;&gt;
&lt;&lt;preimage A&gt;&gt;
&lt;&lt;fixpoint&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
    <revision>
      <id>7675</id>
      <timestamp>2006-09-18T20:50:03Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>oops</comment>
      <text xml:space="preserve">This article describes a simple [http://en.wikipedia.org/wiki/Computational_tree_logic Computational Tree Logic (CTL)] [http://en.wikipedia.org/wiki/Model_checker model checker], written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP] and intended to be evaluated using the Formal Systems Europe Ltd. [http://www.fsel.com/software.html FDR tool]. See Huth and Ryan, [http://www.cs.bham.ac.uk/research/lics/ &quot;Logic in Computer Science&quot;] for details of the algorithm.

Note that this model-checker '''does not''' apply CTL formulas to CSP processes! It is a hack that tricks FDR into performing CTL model-checking of a user-defined finite state machine expressed as several different sets (not a labelled transition system, or a CSP process expression). 
    
== Inputs ==
The model-checker takes as input a finite state machine expressed as sets of states, possible transitions between, and labels consisting of atomic propositions that are true in each state. For example, the finite state machine shown in the figure to the right can be represented as the sets:
[[Image:Ctl-fsm.png|thumb|right|200px|Example of a labelled finite state machine]]
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;inputs&gt;&gt;=
const_MaxState = 10
datatype STATE = S.{0..const_MaxState}

-- A set of states
States = { S.0, S.1, S.2, S.3 }

-- A set of transitions
Trans = { (S.0, S.2), 
          (S.0, S.3),
          (S.1, S.0),
          (S.2, S.3),
          (S.3, S.0),
          (S.3, S.1) }
          
-- A labeling function
Labels = { (S.0, {Atom.A, Atom.C}),
           (S.1, {Atom.C}),
           (S.2, {Atom.A, Atom.B}),
           (S.3, {Atom.B}) }
&lt;/codeblock&gt;

CTL formulas are expressed using a datatype that provides an abstract syntax for combining atomic propositions using various logical and temporal operators:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl syntax&gt;&gt;=
datatype ATOM = A | B | C | D

datatype CTL_FORMULA 
    = Top
    | Bottom
    | Atom.ATOM
    | Not.CTL_FORMULA    
    | And.(CTL_FORMULA, CTL_FORMULA)
    | Or.(CTL_FORMULA, CTL_FORMULA)
    | Implic.(CTL_FORMULA, CTL_FORMULA)
    | AX.CTL_FORMULA
    | EX.CTL_FORMULA
    | AU.(CTL_FORMULA, CTL_FORMULA)
    | EU.(CTL_FORMULA, CTL_FORMULA)
    | EF.CTL_FORMULA
    | EG.CTL_FORMULA
    | AF.CTL_FORMULA
    | AG.CTL_FORMULA
&lt;/codeblock&gt; 

Here are a few examples of CTL formulas expressed using the syntax defined above:
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example ctl formulas&gt;&gt;=
Spec1 = EX.Atom.B
Spec2 = EU.(And.(Atom.A, Atom.B), Atom.C)
Spec3 = AF.Not.Atom.C
Spec4 = EX.Atom.C
Spec5 = AU.(Atom.C, And.(Atom.A, Atom.B))
&lt;/codeblock&gt;

=== Refinement assertions ===
FDR requires some kind of assertion about a process to be made in order to trigger the evaluation of a function. In the case of this script, evaluation of the model-checking function is triggered by performing a trace refinement (i.e language containment) check to see if the distinguished initial state (S.0 by convention) is a member of the set of states returned by the model-checking function. If the initial state ''is'' in the returned set of states then the model satisifes the spec, and the corresponding FDR assertion will succeed. 

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;example refinement checks&gt;&gt;=
channel state: STATE

SAT_States1 = SAT(Spec1)
assert state?s:SAT_States1 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States2 = SAT(Spec2)
assert state?s:SAT_States2 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States3 = SAT(Spec3)
assert state?s:SAT_States3 -&gt; STOP [T= state!S.0 -&gt; STOP 

SAT_States4 = SAT(Spec4)
assert not state?s:SAT_States4 -&gt; STOP [T= state!S.0 -&gt; STOP

SAT_States5 = SAT(Spec5)
assert not state?s:SAT_States5 -&gt; STOP [T= state!S.0 -&gt; STOP
&lt;/codeblock&gt;

== Implementation ==

The core of the model-checker is a boolean satisfaction algorithm that examines a CTL formula, and returns the set of states in the input finite state machine that satisfy the formula. We define the SAT function using a recursive pattern-match on the syntax of CTL formulas. The return value of the function is a set containing the states which satisfy the given CTL formula.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;SAT&gt;&gt;=
SAT(Top) = States
SAT(Bottom) = {}
SAT(Atom.p) = { s | (s, L) &lt;- Labels, member(Atom.p, L) }
SAT(Not.p) = diff(States, SAT(p))
SAT(And.(p, q)) = inter(SAT(p), SAT(q))
SAT(Or.(p, q)) = union(SAT(p), SAT(q))
SAT(Implic.(p, q)) = SAT(Or.(Not.p, q))
SAT(AX.p) = SAT(Not.EX.Not.p)
SAT(EX.p) = SAT_EX(p)
SAT(AU.(p, q)) = SAT(Not.Or.(EU.(Not.p, And.(Not.p, Not.q)), EG.Not.q))
SAT(EU.(p, q)) = SAT_EU(p, q)
SAT(EF.p) = SAT(EU.(Top, p))
SAT(EG.p) = SAT(Not.AF.Not.p)
SAT(AF.p) = SAT_AF(p)
SAT(AG.p) = SAT(Not.EF.Not.p)
&lt;/codeblock&gt;

=== Temporal operators ===
The definitions of the SAT function for the temporal operators EX, EU, and AF are a little more complex than those required for the other operators: 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;temporal operators&gt;&gt;=
SAT_EX(p) = 
    let
        X = SAT(p)
    within
        pre_E(X)
        
SAT_AF(p) = 
    let
        Y = SAT(p)
        f(X) = union(X, pre_A(X))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
        
SAT_EU(p,q) = 
    let
        W = SAT(p)
        Y = SAT(q)
        f(X) = union(X, inter(W, pre_E(X)))
    within
        if Y == States
        then Y
        else Fixpoint(f, Y)
&lt;/codeblock&gt;

=== Auxiliary functions ===
The SAT_EX, SAT_AF and SAT_EU functions rely on three auxiliary functions. The first computes a &quot;preimage&quot; consisting of the set of all states that can transition to any state in the set X. 
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage E&gt;&gt;=
pre_E(X) = { s0 | (s0, s1) &lt;- Trans, member(s1, X) }
&lt;/codeblock&gt;

The second auxiliary function computes a &quot;preimage&quot; consisting of the set of all states which transition to states in X, and do not transition to any state outside of X. This is easily expressed in terms of set differences and the &lt;code&gt;pre_E&lt;/code&gt; function.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;preimage A&gt;&gt;=
pre_A(X) = diff( pre_E(X), pre_E( diff(States, X) ) )
&lt;/codeblock&gt;

The third auxiliary function computes a fixpoint for the application of a function from sets of states to sets of states.
&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;fixpoint&gt;&gt;=
Fixpoint(f, X) = 
    let
        X' = f(X)
    within
        if X == X'
        then X
        else Fixpoint(f, X')
&lt;/codeblock&gt;

=== Complete script ===

The complete CSP script combines the inputs, refinement checks, datatypes, and SAT functions into a single file, suitable for loading into FDR.

&lt;codeblock language=&quot;csp&quot;&gt;
&lt;&lt;ctl_model_checker.csp&gt;&gt;=
&lt;&lt;inputs&gt;&gt;

&lt;&lt;example ctl formulas&gt;&gt;

&lt;&lt;example refinement checks&gt;&gt;

&lt;&lt;ctl syntax&gt;&gt;

&lt;&lt;SAT&gt;&gt;

&lt;&lt;temporal operators&gt;&gt;
        
&lt;&lt;preimage E&gt;&gt;
&lt;&lt;preimage A&gt;&gt;
&lt;&lt;fixpoint&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:CSP]]
[[Category:Formal specifications]]</text>
    </revision>
  </page>
  <page>
    <title>Carpet fishing (sh)</title>
    <id>3241</id>
    <revision>
      <id>11341</id>
      <timestamp>2007-10-28T17:11:10Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">==theory==

There is not much to an implementation of [http://www.dilbert.com/comics/dilbert/archive/dilbert-20070930.html Dilbert's carpet fishing game]; it is simply a loop of indefinitely iterated actions &amp;mdash; ''Lather.  Rinse.  Repeat.''

NB. $RANDOM produces a new pseudorandom value each time it is evaluated.

==practice==

Our actions are only slightly more involved than Lather and Rinse.

First we delay for a random time:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
sleep $((TIME*(30 + $RANDOM % 60)))
&lt;/codeblock&gt;

then we pick a random species:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
species=$(echo $fish | awk '{print $(1+('$RANDOM' % NF))}')
&lt;/codeblock&gt;

and report a niible in a random location:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;normal nibble&gt;&gt;=
echo $species nibbling in area $(($RANDOM % $grid))
&lt;/codeblock&gt;

===a complication===

At the risk of nearly doubling the code size, we can add the &quot;salmon run&quot; feature.  During a run, fish appear in several random grid locations.  As we do not keep state, we are choosing elements with replacement, and piping through ''sort'' and ''uniq'' allow us to remove any duplicates.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;salmon run&gt;&gt;=
echo $species running in areas: $(
        for i in 0 1 2 3 4 5 6; do
               echo $(($RANDOM % $grid))
        done | sort -n | uniq)
&lt;/codeblock&gt;

This code will be activated if &quot;salmon&quot; is the chosen species.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
if [ X$species != Xsalmon ]; then
        &lt;&lt;normal nibble&gt;&gt;
else
        &lt;&lt;salmon run&gt;&gt;
fi
&lt;/codeblock&gt;

==wrapping up==

Finally, we provide an overridable default configuration, and wrap the fish processing code up in an infinite loop.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;carpetfish.sh&gt;&gt;=
fish=${FISH:-&quot;salmon trout catfish bass sturgeon crappie shad&quot;} # species
time=${TIME:-60}                                                # time quantum
grid=${GRID:-36}                                                # grid size

while true; do
        &lt;&lt;process fish&gt;&gt;
done
&lt;/codeblock&gt;

Over the course of a day, this will produce output something along the lines of

 crappie nibbling in area 33
 trout nibbling in area 29
 bass nibbling in area 28
 crappie nibbling in area 23
 trout nibbling in area 10
 salmon running in areas: 0 5 14 15 19 21
 trout nibbling in area 24
 catfish nibbling in area 2


[[Category:Programming language:sh script]]
[[Category:Environment:All POSIX]]</text>
    </revision>
    <revision>
      <id>11342</id>
      <timestamp>2007-10-28T17:14:56Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>layout, +cat</comment>
      <text xml:space="preserve">==theory==

There is not much to an implementation of [http://www.dilbert.com/comics/dilbert/archive/dilbert-20070930.html Dilbert's carpet fishing game]; it is simply a loop of indefinitely iterated actions &amp;mdash; ''Lather.  Rinse.  Repeat.''

NB. $RANDOM produces a new pseudorandom value each time it is evaluated.

==practice==

Our actions are only slightly more involved than Lather and Rinse.

First we delay for a random time:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
sleep $((TIME*(30 + $RANDOM % 60)))&lt;/codeblock&gt;

then we pick a random species:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
species=$(echo $fish | awk '{print $(1+('$RANDOM' % NF))}')&lt;/codeblock&gt;

and report a niible in a random location:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;normal nibble&gt;&gt;=
echo $species nibbling in area $(($RANDOM % $grid))&lt;/codeblock&gt;

===a complication===

At the risk of nearly doubling the code size, we can add the &quot;salmon run&quot; feature.  During a run, fish appear in several random grid locations.  As we do not keep state, we are choosing elements with replacement, and piping through ''sort'' and ''uniq'' allow us to remove any duplicates.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;salmon run&gt;&gt;=
echo $species running in areas: $(
        for i in 0 1 2 3 4 5 6; do
               echo $(($RANDOM % $grid))
        done | sort -n | uniq)&lt;/codeblock&gt;

This code will be activated if &quot;salmon&quot; is the chosen species.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
if [ X$species != Xsalmon ]; then
        &lt;&lt;normal nibble&gt;&gt;
else
        &lt;&lt;salmon run&gt;&gt;
fi&lt;/codeblock&gt;

==wrapping up==

Finally, we provide an overridable default configuration, and wrap the fish processing code up in an infinite loop.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;carpetfish.sh&gt;&gt;=
fish=${FISH:-&quot;salmon trout catfish bass sturgeon crappie shad&quot;} # species
time=${TIME:-60}                                                # time quantum
grid=${GRID:-36}                                                # grid size

while true; do
        &lt;&lt;process fish&gt;&gt;
done
&lt;/codeblock&gt;

Over the course of a day, this will produce output something along the lines of

 crappie nibbling in area 33
 trout nibbling in area 29
 bass nibbling in area 28
 crappie nibbling in area 23
 trout nibbling in area 10
 salmon running in areas: 0 5 14 15 19 21
 trout nibbling in area 24
 catfish nibbling in area 2

[[Category:Games and entertainment]]
[[Category:Programming language:sh script]]
[[Category:Environment:All POSIX]]</text>
    </revision>
    <revision>
      <id>15707</id>
      <timestamp>2008-12-29T01:03:41Z</timestamp>
      <contributor>
        <ip>213.219.137.121</ip>
      </contributor>
      <comment>corrected url</comment>
      <text xml:space="preserve">==theory==

There is not much to an implementation of [http://www.dilbert.com/fast/2007-09-30/ Dilbert's carpet fishing game]; it is simply a loop of indefinitely iterated actions &amp;mdash; ''Lather.  Rinse.  Repeat.''

NB. $RANDOM produces a new pseudorandom value each time it is evaluated.

==practice==

Our actions are only slightly more involved than Lather and Rinse.

First we delay for a random time:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
sleep $((TIME*(30 + $RANDOM % 60)))&lt;/codeblock&gt;

then we pick a random species:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
species=$(echo $fish | awk '{print $(1+('$RANDOM' % NF))}')&lt;/codeblock&gt;

and report a niible in a random location:
&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;normal nibble&gt;&gt;=
echo $species nibbling in area $(($RANDOM % $grid))&lt;/codeblock&gt;

===a complication===

At the risk of nearly doubling the code size, we can add the &quot;salmon run&quot; feature.  During a run, fish appear in several random grid locations.  As we do not keep state, we are choosing elements with replacement, and piping through ''sort'' and ''uniq'' allow us to remove any duplicates.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;salmon run&gt;&gt;=
echo $species running in areas: $(
        for i in 0 1 2 3 4 5 6; do
               echo $(($RANDOM % $grid))
        done | sort -n | uniq)&lt;/codeblock&gt;

This code will be activated if &quot;salmon&quot; is the chosen species.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;process fish&gt;&gt;=
if [ X$species != Xsalmon ]; then
        &lt;&lt;normal nibble&gt;&gt;
else
        &lt;&lt;salmon run&gt;&gt;
fi&lt;/codeblock&gt;

==wrapping up==

Finally, we provide an overridable default configuration, and wrap the fish processing code up in an infinite loop.

&lt;codeblock language=&quot;sh&quot;&gt;
&lt;&lt;carpetfish.sh&gt;&gt;=
fish=${FISH:-&quot;salmon trout catfish bass sturgeon crappie shad&quot;} # species
time=${TIME:-60}                                                # time quantum
grid=${GRID:-36}                                                # grid size

while true; do
        &lt;&lt;process fish&gt;&gt;
done
&lt;/codeblock&gt;

Over the course of a day, this will produce output something along the lines of

 crappie nibbling in area 33
 trout nibbling in area 29
 bass nibbling in area 28
 crappie nibbling in area 23
 trout nibbling in area 10
 salmon running in areas: 0 5 14 15 19 21
 trout nibbling in area 24
 catfish nibbling in area 2

[[Category:Games and entertainment]]
[[Category:Programming language:sh script]]
[[Category:Environment:All POSIX]]</text>
    </revision>
  </page>
  <page>
    <title>Cat filter (Mercury)</title>
    <id>1892</id>
    <revision>
      <id>4126</id>
      <timestamp>2006-04-14T22:45:04Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>Introductory example -- Maybe category should be different ?</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The ''!X'' construct encloses two variables, the initial (!.X) and final (!:X) states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( Args = [] -&gt;
		cat(!IO)
	;
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
		Result = eof
	;
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4127</id>
      <timestamp>2006-04-14T22:47:07Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>Missing download tag on final chunk</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The ''!X'' construct encloses two variables, the initial (!.X) and final (!:X) states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( Args = [] -&gt;
		cat(!IO)
	;
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
		Result = eof
	;
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4128</id>
      <timestamp>2006-04-14T23:00:27Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Main block  */ highlight expr. with hard to see dot and semicolon</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( Args = [] -&gt;
		cat(!IO)
	;
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
		Result = eof
	;
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4129</id>
      <timestamp>2006-04-14T23:12:06Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>comments on disjunction case starts</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( Args = [] -&gt;
		cat(!IO)
	;
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4130</id>
      <timestamp>2006-04-14T23:30:30Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Main block */  added comments</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4131</id>
      <timestamp>2006-04-14T23:59:55Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>Added &quot;Compile and run&quot; section</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Set the open file handle as input stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;set_input_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;set_input_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4155</id>
      <timestamp>2006-04-16T12:11:26Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>better name for a chunk</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	;
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4156</id>
      <timestamp>2006-04-16T20:03:41Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Process input stream recursively, on a per line basis */ change cases order to make it tail recursive</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4176</id>
      <timestamp>2006-04-19T08:51:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>added src author name and public domain notice</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4317</id>
      <timestamp>2006-04-30T01:29:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Cat:File processing</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error)
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]

[[Category:File processing]]</text>
    </revision>
    <revision>
      <id>4518</id>
      <timestamp>2006-05-09T16:46:31Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>missing dot in type note</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Introductory examples]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]

[[Category:File processing]]</text>
    </revision>
    <revision>
      <id>4551</id>
      <timestamp>2006-05-11T02:59:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>recat</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]
[[Category:File processing]]</text>
    </revision>
    <revision>
      <id>6832</id>
      <timestamp>2006-07-11T12:47:41Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Cat filter (Mercury)]] moved to [[Cat filter (Mercury) on Wheels]]</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]
[[Category:File processing]]</text>
    </revision>
    <revision>
      <id>6994</id>
      <timestamp>2006-07-11T14:29:29Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Cat filter (Mercury) on Wheels]] moved to [[Cat filter (Mercury)]]: revert</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty */
           Args = [] -&gt;

           /* then */    
		cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]
[[Category:File processing]]</text>
    </revision>
    <revision>
      <id>8313</id>
      <timestamp>2006-12-07T15:47:08Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Main block */  readability</comment>
      <text xml:space="preserve">This is an example of basic input output handling from the compiler examples (source distrib).

&gt;&gt;Simple implementation of the standard unix ''cat'' filter: copy input files (or stdin, if no input files) to stdout.

Author acknowledgement. From the original file:
&lt;pre&gt;
% This source file is hereby placed in the public domain.  -fjh (the author).
&lt;/pre&gt;

== Main block == 

Command line arguments (list(string)) are never taken from the ''main'' entry point which only take as arguments the ''IO'' states ''of the world''.

The &quot;'''!X'''&quot; construct encloses two variables, the initial &quot;'''!.X'''&quot; and final &quot;'''!:X'''&quot; states of a ''state variable''.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;main&gt;&gt;=

main(!IO) :-
	io.command_line_arguments(Args, !IO),
	( 
           /* if Args is empty then process stdin */
           Args = [] -&gt; cat(!IO)
	;
           /* else */     
		cat_file_list(Args, !IO)
	).
&lt;/codeblock&gt;

== Process command line filename sequence ==

This routine takes as parameter the command line argument list of strings, plus the IO states.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_cmd_line_filename_seq&gt;&gt;=

/**
* @param Files list of filenames
* @param !IO  I/O initial and final states
*/
 
:- pred cat_file_list(list(string)::in, io::di, io::uo) is det.

cat_file_list([], !IO).

cat_file_list([File | Files], !IO) :-

	cat_file(File, !IO),
	cat_file_list(Files, !IO).

&lt;/codeblock&gt;

== Process one file ==

Note: io.open_input Result parameter is of type ''io.res( io.input_stream)''

where type io.res is 
&lt;pre&gt;
:- type io__res(T)
	---&gt;	ok(T)
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_one_file&gt;&gt;=

/**
* @param File filename
* @param !IO state of the world
*/
:- pred cat_file(string::in, io::di, io::uo) is det.

cat_file(File, !IO) :-

	io.open_input(File, Result, !IO),
	(
           /* case Result=ok */
		Result = ok(Stream),

		cat_stream(Stream, !IO),
		io.close_input(Stream, !IO)
	;
           /* case Result=error */
		Result = error(Error),

		io.progname(&quot;cat&quot;, Progname, !IO),
		io.error_message(Error, Message),

		io.write_strings([
			Progname, &quot;: &quot;,
			&quot;error opening file `&quot;, File, &quot;' for input:\n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	).
&lt;/codeblock&gt;

== Process file stream == 

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_file_stream&gt;&gt;=

:- pred cat_stream(io.input_stream::in, io::di, io::uo) is det.

cat_stream(Stream, !IO) :-
	io.set_input_stream(Stream, _OldStream, !IO),
	cat(!IO).
&lt;/codeblock&gt;

== Process input stream recursively, on a per line basis == 

Note: io.read_line_as_string Result parameter is of type ''io.result( string)''
&lt;pre&gt;
:- type io__result(T)
	---&gt;	ok(T)
	;	eof
	;	error(io__error).
&lt;/pre&gt;

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;process_input_stream&gt;&gt;=

:- pred cat(io::di, io::uo) is det.

cat(!IO) :-

	io.read_line_as_string(Result, !IO),
	(
           /* case Result=eof */
		Result = eof
	;
           /* case Result=error */
		Result = error(Error),

		io.error_message(Error, Message),
		io.input_stream_name(StreamName, !IO),
		io.progname(&quot;cat&quot;, ProgName, !IO),

		io.write_strings([
			ProgName, &quot;: &quot;,
			&quot;error reading input file `&quot;, StreamName, &quot;': \n\t&quot;,
			Message, &quot;\n&quot;
		], !IO)
	;
           /* case Result=ok */
		Result = ok(Line),

		io.write_string(Line, !IO),
		cat(!IO)
	).
&lt;/codeblock&gt;

== Enclosing module ==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;cat.m&gt;&gt;=

%-----------------------------------------------------------------------------%

:- module cat.

% Simple implementation of the standard unix `cat' filter:
% copy input files (or stdin, if no input files) to stdout.

% This source file is hereby placed in the public domain.  -fjh (the author).

%-----------------------------------------------------------------------------%

:- interface.
:- import_module io.

:- pred main(io::di, io::uo) is det.

%-----------------------------------------------------------------------------%

:- implementation.
:- import_module string, list, char.

&lt;&lt;main&gt;&gt;

&lt;&lt;process_cmd_line_filename_seq&gt;&gt;

&lt;&lt;process_one_file&gt;&gt;

&lt;&lt;process_file_stream&gt;&gt;

&lt;&lt;process_input_stream&gt;&gt;

%-----------------------------------------------------------------------------%
&lt;/codeblock&gt;

== Compile and run ==

# Compile cat.m
# Run cat

&lt;pre&gt;
mmc cat.m

cat testfile1 testfile2

&gt;testfile1 contents
&gt;testfile2 contents

cat unexistant_filename

&gt;cat: error opening file 'unexistant_filename' for input:
&gt;             can't open input file: No such file or directory
&lt;/pre&gt;

[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]
[[Category:File processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Binary heap</title>
    <id>3824</id>
    <revision>
      <id>15944</id>
      <timestamp>2009-01-12T15:14:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">Sorry, you must be logged in to edit this page. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:14, 12 January 2009 (EST)</text>
    </revision>
    <revision>
      <id>16225</id>
      <timestamp>2009-03-08T11:06:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Code dumps</title>
    <id>3771</id>
    <revision>
      <id>15834</id>
      <timestamp>2009-01-08T06:52:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">This page is a spam target. You will need to log in to edit it.</text>
    </revision>
    <revision>
      <id>16195</id>
      <timestamp>2009-03-08T10:55:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Communities:Matlab Community for Quantitative Finance</title>
    <id>3798</id>
    <revision>
      <id>15904</id>
      <timestamp>2009-01-09T16:30:33Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">You need to log in to edit this page</text>
    </revision>
    <revision>
      <id>16222</id>
      <timestamp>2009-03-08T11:05:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Euclidean algorithm</title>
    <id>3944</id>
    <revision>
      <id>16740</id>
      <timestamp>2010-05-23T03:12:56Z</timestamp>
      <contributor>
        <username>Ronw</username>
        <id>2051</id>
      </contributor>
      <text xml:space="preserve">There is no need for the a &gt; b part of the function. The first iteration through will swap the values if a &lt; b.</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Five coloring of planar graphs</title>
    <id>2616</id>
    <revision>
      <id>7197</id>
      <timestamp>2006-08-11T00:04:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Planning C impl</comment>
      <text xml:space="preserve">I'm working on a C implementation of the algorithm described at [http://en.wikipedia.org/wiki/Five_color_theorem Wikipedia's article on the five color theorem], based on [http://portal.acm.org/citation.cfm?id=237814.238005&amp;coll=ACM&amp;dl=ACM&amp;type=series&amp;idx=237814&amp;part=Proceedings&amp;WantType=Proceedings&amp;title=Annual%20ACM%20Symposium%20on%20Theory%20of%20Computing&amp;CFID=36220143&amp;CFTOKEN=50709087 this paper] (ACM login required). Will post at [[Five coloring of planar graphs (C)]] when ready. [[User:Deco|Deco]] 17:04, 10 August 2006 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Formal specifications</title>
    <id>2358</id>
    <revision>
      <id>6370</id>
      <timestamp>2006-06-21T02:53:56Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>Ruys</comment>
      <text xml:space="preserve">Theo Ruys' [http://wwwhome.cs.utwente.nl/~ruys/ruys-phd-thesis.pdf PhD thesis] includes some discussion of literate specification using Promela and SPIN. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 19:53, 20 June 2006 (PDT)</text>
    </revision>
    <revision>
      <id>10012</id>
      <timestamp>2007-05-11T22:12:16Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>Literate programming for FDA certification?</comment>
      <text xml:space="preserve">Theo Ruys' [http://wwwhome.cs.utwente.nl/~ruys/ruys-phd-thesis.pdf PhD thesis] includes some discussion of literate specification using Promela and SPIN. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 19:53, 20 June 2006 (PDT)

== Literate programming for FDA certification? ==

Greetings. Our company is looking at techniques for linking formal specifications to requirements to code, as required for many types of FDA certification. Has anyone used a literate programming system like this wiki for such things?  --[[User:IanOsgood|IanOsgood]] 15:12, 11 May 2007 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Fuzzy string search algorithms</title>
    <id>3282</id>
    <revision>
      <id>12048</id>
      <timestamp>2008-01-12T00:16:10Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <text xml:space="preserve">Created this category to collect articles from categories [[:Category:Mismatch]], [[:Category:Wildcards]] and [[:Category:Longest common extension]], which were too specialized and can be deleted, IMO. Didn't find a way to mark them for deletion. --[[User:Fabian Steeg|Fabian Steeg]]</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Input</title>
    <id>3635</id>
    <revision>
      <id>15085</id>
      <timestamp>2008-10-17T21:24:29Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>This page intentionally blank</comment>
      <text xml:space="preserve">== Blank Page ==</text>
    </revision>
    <revision>
      <id>16205</id>
      <timestamp>2009-03-08T10:56:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Mathematics</title>
    <id>3081</id>
    <revision>
      <id>9544</id>
      <timestamp>2007-03-21T14:37:40Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>related articles</comment>
      <text xml:space="preserve">I have a few related articles
that I'd written
to populate existing categories:
[[:Category:Computational geometry]] and [[:Category:Computer algebra systems]].
Should I move them here?
[[User:Dave|Dave]] 07:37, 21 March 2007 (PDT)</text>
    </revision>
    <revision>
      <id>9547</id>
      <timestamp>2007-03-21T17:04:01Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <text xml:space="preserve">I have a few related articles
that I'd written
to populate existing categories:
[[:Category:Computational geometry]] and [[:Category:Computer algebra systems]].
Should I move them here?
[[User:Dave|Dave]] 07:37, 21 March 2007 (PDT)

: Maybe it would make sense to simply make those categories subcategories of this one? --[[User:Ce|Ce]] 10:04, 21 March 2007 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Pi with Machin's formula</title>
    <id>1615</id>
    <revision>
      <id>2399</id>
      <timestamp>2006-03-05T21:44:15Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>comments</comment>
      <text xml:space="preserve">I think it might make sense to have a visually distinct box for the general summary of the topic, with links to all the specific implementations, Wikipedia pages, etc. Perhaps the software could be tweaked to recognize these introductions and place them above the article's H1 heading? Or maybe this isn't a good idea at all... but I felt that I had to try it out :-) [[User:Fredrik|Fredrik]] 13:44, 5 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>2414</id>
      <timestamp>2006-03-06T01:02:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Reply</comment>
      <text xml:space="preserve">I think it might make sense to have a visually distinct box for the general summary of the topic, with links to all the specific implementations, Wikipedia pages, etc. Perhaps the software could be tweaked to recognize these introductions and place them above the article's H1 heading? Or maybe this isn't a good idea at all... but I felt that I had to try it out :-) [[User:Fredrik|Fredrik]] 13:44, 5 March 2006 (PST)
:My initial idea was for this stuff to go on the category page, which works out nicely because it already has links to the implementations. On the other hand, it can be nice (especially for people dropping in from Google) to view the summary together with the implementation. We might transclude the category page into the articles. [[User:Deco|Deco]] 17:02, 5 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>2474</id>
      <timestamp>2006-03-06T04:22:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Template talk:Pi with Machin's formula language-independent summary moved to Category talk:Pi with Machin's formula</comment>
      <text xml:space="preserve">I think it might make sense to have a visually distinct box for the general summary of the topic, with links to all the specific implementations, Wikipedia pages, etc. Perhaps the software could be tweaked to recognize these introductions and place them above the article's H1 heading? Or maybe this isn't a good idea at all... but I felt that I had to try it out :-) [[User:Fredrik|Fredrik]] 13:44, 5 March 2006 (PST)
:My initial idea was for this stuff to go on the category page, which works out nicely because it already has links to the implementations. On the other hand, it can be nice (especially for people dropping in from Google) to view the summary together with the implementation. We might transclude the category page into the articles. [[User:Deco|Deco]] 17:02, 5 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>2476</id>
      <timestamp>2006-03-06T04:24:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>My changes</comment>
      <text xml:space="preserve">I think it might make sense to have a visually distinct box for the general summary of the topic, with links to all the specific implementations, Wikipedia pages, etc. Perhaps the software could be tweaked to recognize these introductions and place them above the article's H1 heading? Or maybe this isn't a good idea at all... but I felt that I had to try it out :-) [[User:Fredrik|Fredrik]] 13:44, 5 March 2006 (PST)
:My initial idea was for this stuff to go on the category page, which works out nicely because it already has links to the implementations. On the other hand, it can be nice (especially for people dropping in from Google) to view the summary together with the implementation. We might transclude the category page into the articles. [[User:Deco|Deco]] 17:02, 5 March 2006 (PST)
:Hey Fredrik. I decided to move this content into the category, because I didn't want a redundant list of implementations and it seems like a nice logical place and can still be transcluded (albeit without the list). The list is still a click away via the category at the bottom though, and we could even link the category from itself (as odd as that sounds). I hope this is an okay solution with you, I'm open to debate. [[User:Deco|Deco]] 20:24, 5 March 2006 (PST)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:BASIC</title>
    <id>2625</id>
    <revision>
      <id>7249</id>
      <timestamp>2006-08-13T08:59:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Name</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7254</id>
      <timestamp>2006-08-13T17:09:36Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Stone-age BASIC</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7255</id>
      <timestamp>2006-08-13T17:34:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Name */ reply</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)

::Maybe I am just stuck in the stone age (not the 60s but early 80s). It isn't a big deal, but it just looks to me like two different languages. Maybe we should have [[:Category:Programming language:QBASIC]] and [[:Category:Programming language:Classic BASIC]] as sub-categories under [[:Category:Programming language:BASIC]]. That is how it is done in [[:Category:Programming language:Shell script]], where there are sub-categories for ''bash'', ''csh'' and the &quot;stone age&quot; bourne shell.

::I didn't mean to suggest adding line numbers to your code. The code looks nice as it is, and adding line numbers, gotos etc. would probably make a mess out of it. [[User:Ahy1|Ahy1]] 10:34, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7256</id>
      <timestamp>2006-08-13T19:00:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Name */</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)

::Maybe I am just stuck in the stone age (not the 60s but early 80s). It isn't a big deal, but it just looks to me like two different languages. Maybe we should have [[:Category:Programming language:QBASIC]] and [[:Category:Programming language:Classic BASIC]] as sub-categories under [[:Category:Programming language:BASIC]]. That is how it is done in [[:Category:Programming language:Shell script]], where there are sub-categories for ''bash'', ''csh'' and the &quot;stone age&quot; bourne shell.

::I didn't mean to suggest adding line numbers to your code. The code looks nice as it is, and adding line numbers, gotos etc. would probably make a mess out of it. [[User:Ahy1|Ahy1]] 10:34, 13 August 2006 (PDT)

:Fair enough. I'll make a couple of sub-categories as you suggest. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 12:00, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7257</id>
      <timestamp>2006-08-13T19:04:45Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Name */ fair enough</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)

::Maybe I am just stuck in the stone age (not the 60s but early 80s). It isn't a big deal, but it just looks to me like two different languages. Maybe we should have [[:Category:Programming language:QBASIC]] and [[:Category:Programming language:Classic BASIC]] as sub-categories under [[:Category:Programming language:BASIC]]. That is how it is done in [[:Category:Programming language:Shell script]], where there are sub-categories for ''bash'', ''csh'' and the &quot;stone age&quot; bourne shell.

::I didn't mean to suggest adding line numbers to your code. The code looks nice as it is, and adding line numbers, gotos etc. would probably make a mess out of it. [[User:Ahy1|Ahy1]] 10:34, 13 August 2006 (PDT)

:Fair enough. I'll make a couple of sub-categories as you suggest. However if you don't mind I'll name them [[:Category:Programming language:Modern BASIC]]  and [[:Category:Programming language:Classic BASIC]] since, although the code is QBASIC, it is very similar to other modern ANSI-like BASICS's such as TrueBASIC, PowerBASIC, Visual BASIC and so on. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 12:00, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7258</id>
      <timestamp>2006-08-13T19:05:29Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Name */</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)

::Maybe I am just stuck in the stone age (not the 60s but early 80s). It isn't a big deal, but it just looks to me like two different languages. Maybe we should have [[:Category:Programming language:QBASIC]] and [[:Category:Programming language:Classic BASIC]] as sub-categories under [[:Category:Programming language:BASIC]]. That is how it is done in [[:Category:Programming language:Shell script]], where there are sub-categories for ''bash'', ''csh'' and the &quot;stone age&quot; bourne shell.

::I didn't mean to suggest adding line numbers to your code. The code looks nice as it is, and adding line numbers, gotos etc. would probably make a mess out of it. [[User:Ahy1|Ahy1]] 10:34, 13 August 2006 (PDT)

:Fair enough. I'll make a couple of sub-categories as you suggest. However if you don't mind I'll name them [[:Category:Programming language:Modern BASIC]]  and [[:Category:Programming language:Classic BASIC]] since, although the code is QBASIC, it is very similar to other modern ANSI-like BASICs such as TrueBASIC, PowerBASIC, Visual BASIC and so on. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 12:00, 13 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7259</id>
      <timestamp>2006-08-13T19:16:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Name */ &quot;Modern BASIC&quot;</comment>
      <text xml:space="preserve">== Name ==

The code in this category seems to be for the QBASIC dialect, which is different from traditional BASIC in that it doesn't require line numbers. Maybe these should be in [[:Category:Programming Language:QBASIC]] and named like this: &quot;Article name (QBASIC)&quot;. If I click on a link mentioning BASIC, I expect lots of line numbers and gotos... [[User:Ahy1|Ahy1]] 01:59, 13 August 2006 (PDT)

:Well, BASIC has moved on a bit since the 1960s. Line numbers and GOTOs haven't been necessary for a while but if you really want them I could add them. QBASIC accepts them quite happily. I could even replace the DO/LOOPs and IF/ENDIFs with GOTOs and the SELECT CASEs with ON x GOTOs, if there's enough demand, &lt;grin&gt;. 

:The reason that I used the QBASIC dialect is that it's the one that I'm most familiar with and can be compiled by the FreeBASIC compiler. It's also highly compatible with later dialects such as VB, VBscript, etcetera. I suppose that from a compatibility point of view it might be better to avoid a relatively modern BASIC and go for some prehistoric version but the majority of present-day working programmers using BASIC are far more likely to be using a dialect similar to QBASIC than one similar to GW-BASIC or C64 BASIC. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 10:09, 13 August 2006 (PDT)

::Maybe I am just stuck in the stone age (not the 60s but early 80s). It isn't a big deal, but it just looks to me like two different languages. Maybe we should have [[:Category:Programming language:QBASIC]] and [[:Category:Programming language:Classic BASIC]] as sub-categories under [[:Category:Programming language:BASIC]]. That is how it is done in [[:Category:Programming language:Shell script]], where there are sub-categories for ''bash'', ''csh'' and the &quot;stone age&quot; bourne shell.

::I didn't mean to suggest adding line numbers to your code. The code looks nice as it is, and adding line numbers, gotos etc. would probably make a mess out of it. [[User:Ahy1|Ahy1]] 10:34, 13 August 2006 (PDT)

:Fair enough. I'll make a couple of sub-categories as you suggest. However if you don't mind I'll name them [[:Category:Programming language:Modern BASIC]]  and [[:Category:Programming language:Classic BASIC]] since, although the code is QBASIC, it is very similar to other modern ANSI-like BASICs such as TrueBASIC, PowerBASIC, Visual BASIC and so on. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 12:00, 13 August 2006 (PDT)

::&quot;Modern BASIC&quot; looks like a good name. [[User:Ahy1|Ahy1]] 12:16, 13 August 2006 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:C</title>
    <id>3489</id>
    <revision>
      <id>13761</id>
      <timestamp>2008-06-23T20:57:51Z</timestamp>
      <contributor>
        <ip>129.113.28.56</ip>
      </contributor>
      <comment>Knuth's programs should be on this site!</comment>
      <text xml:space="preserve">Any chance of an effort to transliterate Knuth's literate programming examples into something more web-friendly (ie this site)?

   http://www-cs-faculty.stanford.edu/~knuth/programs.html

I doubt very many people ever fetch those .w.gz files, decompress them, and install Knuth's cweb to read them... :-/

By the way, I know this isn't true literate programming but you might find the folding trick here something you could incorporate into your site: http://techennui.blogspot.com/2008/04/semi-literate-programming.html (perhaps the example isn't the best I could come up with, but you should get the overall picture from it fairly easily)

G</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:MATLAB</title>
    <id>2653</id>
    <revision>
      <id>7429</id>
      <timestamp>2006-08-20T01:02:50Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Two categories for MATLAB</comment>
      <text xml:space="preserve">== Two categories for MATLAB ==

Having two almost exactly equal categories for MATLAB seems silly to me. For some reason, articles with [[:Category:Programming language:Matlab]] shows up here too. One of these categories should be deleted or made a redirect to the other. I don't know what the correct name is, but Wikipedia seems to use &quot;MATLAB&quot;. [[User:Ahy1|Ahy1]] 18:02, 19 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7431</id>
      <timestamp>2006-08-20T19:57:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>MATLAB</comment>
      <text xml:space="preserve">== Two categories for MATLAB ==

Having two almost exactly equal categories for MATLAB seems silly to me. For some reason, articles with [[:Category:Programming language:Matlab]] shows up here too. One of these categories should be deleted or made a redirect to the other. I don't know what the correct name is, but Wikipedia seems to use &quot;MATLAB&quot;. [[User:Ahy1|Ahy1]] 18:02, 19 August 2006 (PDT)

:I agree that it's silly to have two categories. FWIW, the creators of MATLAB, The Mathworks, seem to prefer presenting the name as [http://www.mathworks.com/products/matlab/ MATLAB]. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 12:57, 20 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7463</id>
      <timestamp>2006-08-21T17:05:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>done</comment>
      <text xml:space="preserve">== Two categories for MATLAB ==

Having two almost exactly equal categories for MATLAB seems silly to me. For some reason, articles with [[:Category:Programming language:Matlab]] shows up here too. One of these categories should be deleted or made a redirect to the other. I don't know what the correct name is, but Wikipedia seems to use &quot;MATLAB&quot;. [[User:Ahy1|Ahy1]] 18:02, 19 August 2006 (PDT)

:I agree that it's silly to have two categories. FWIW, the creators of MATLAB, The Mathworks, seem to prefer presenting the name as [http://www.mathworks.com/products/matlab/ MATLAB]. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 12:57, 20 August 2006 (PDT)

:: Ok, now [[:Category:Programming language:Matlab]] redirects here. I had to copy the old category, as I don't know of a way to move categories. Because of that, the history is still in the old category. [[User:Ahy1|Ahy1]] 10:05, 21 August 2006 (PDT)</text>
    </revision>
    <revision>
      <id>7464</id>
      <timestamp>2006-08-21T17:08:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Namin conventions</comment>
      <text xml:space="preserve">== Two categories for MATLAB ==

Having two almost exactly equal categories for MATLAB seems silly to me. For some reason, articles with [[:Category:Programming language:Matlab]] shows up here too. One of these categories should be deleted or made a redirect to the other. I don't know what the correct name is, but Wikipedia seems to use &quot;MATLAB&quot;. [[User:Ahy1|Ahy1]] 18:02, 19 August 2006 (PDT)

:I agree that it's silly to have two categories. FWIW, the creators of MATLAB, The Mathworks, seem to prefer presenting the name as [http://www.mathworks.com/products/matlab/ MATLAB]. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 12:57, 20 August 2006 (PDT)

:: Ok, now [[:Category:Programming language:Matlab]] redirects here. I had to copy the old category, as I don't know of a way to move categories. Because of that, the history is still in the old category. [[User:Ahy1|Ahy1]] 10:05, 21 August 2006 (PDT)

== Namin conventions ==

Many articles in this category uses a different naming convention from the rest of LiteratePrograms. Is there a good reason for that? If not, I think they should be renamed. [[User:Ahy1|Ahy1]] 10:08, 21 August 2006 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Maple</title>
    <id>3321</id>
    <revision>
      <id>12539</id>
      <timestamp>2008-02-21T03:17:27Z</timestamp>
      <contributor>
        <ip>122.3.195.238</ip>
      </contributor>
      <text xml:space="preserve">hellow!</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Occam</title>
    <id>1395</id>
    <revision>
      <id>1661</id>
      <timestamp>2006-03-03T05:19:48Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>Category talk:Programming language:Occam moved to Category talk:Programming language:occam: new cat with correct name capitalization created</comment>
      <text xml:space="preserve">#redirect [[Category talk:Programming language:occam]]</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Oz</title>
    <id>3790</id>
    <revision>
      <id>15862</id>
      <timestamp>2009-01-09T07:50:01Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">-</text>
    </revision>
    <revision>
      <id>16220</id>
      <timestamp>2009-03-08T11:05:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Prolog</title>
    <id>3738</id>
    <revision>
      <id>15665</id>
      <timestamp>2008-12-21T17:51:07Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">You need to be logged in to edit this page as it is a spam target. Sorry. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 12:51, 21 December 2008 (EST)</text>
    </revision>
    <revision>
      <id>16196</id>
      <timestamp>2009-03-08T10:55:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Sed</title>
    <id>3132</id>
    <revision>
      <id>10102</id>
      <timestamp>2007-05-16T00:38:11Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>Duplicate category! should delete this one.</comment>
      <text xml:space="preserve">==Duplicate Category==

This is a dup of [[:Category:Programming Language:sed]] (note capitalization).  This one should be deleted. --[[User:IanOsgood|IanOsgood]] 17:38, 15 May 2007 (PDT)</text>
    </revision>
    <revision>
      <id>10103</id>
      <timestamp>2007-05-16T00:38:24Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">==Duplicate Category==

This is a dup of [[:Category:Programming language:sed]] (note capitalization).  This one should be deleted. --[[User:IanOsgood|IanOsgood]] 17:38, 15 May 2007 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Smalltalk</title>
    <id>3553</id>
    <revision>
      <id>14494</id>
      <timestamp>2008-08-27T20:34:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>created empty page</comment>
      <text xml:space="preserve">&lt;!-- empty --&gt;</text>
    </revision>
    <revision>
      <id>16213</id>
      <timestamp>2009-03-08T11:04:24Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:Visual Basic</title>
    <id>3644</id>
    <revision>
      <id>15197</id>
      <timestamp>2008-10-21T08:43:29Z</timestamp>
      <contributor>
        <ip>91.121.179.148</ip>
      </contributor>
      <comment>larelrelelro</comment>
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      <comment>ricbocleto</comment>
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      <id>15324</id>
      <timestamp>2008-10-27T18:44:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
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      <comment>revert spam</comment>
      <text xml:space="preserve">&lt;!-- blanked --&gt;</text>
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      <id>15337</id>
      <timestamp>2008-10-28T08:10:49Z</timestamp>
      <contributor>
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      <comment>dronrolro</comment>
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video&quot;:http://copyproductions.com/aplugin/images/topic-1187.html [cordless phone batteries|http://copyproductions.com/aplugin/images/topic-1806.html] [[http://copyproductions.com/aplugin/images/topic-1806.html cordless phone batteries]] [http://copyproductions.com/aplugin/images/topic-1806.html|cordless phone batteries] ((http://copyproductions.com/aplugin/images/topic-1806.html cordless phone batteries)) [[http://copyproductions.com/aplugin/images/topic-1806.html | cordless phone batteries]] &quot;cordless phone batteries&quot;:http://copyproductions.com/aplugin/images/topic-1806.html 
&lt;!-- blanked --&gt;</text>
    </revision>
    <revision>
      <id>15339</id>
      <timestamp>2008-10-28T08:11:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">&lt;!-- blanked --&gt;</text>
    </revision>
    <revision>
      <id>16215</id>
      <timestamp>2009-03-08T11:04:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Programming language:occam</title>
    <id>1389</id>
    <revision>
      <id>1648</id>
      <timestamp>2006-03-03T03:53:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Name casing */</comment>
      <text xml:space="preserve">== Name casing ==

You think we should move this to [[Category:Programming language:occam]]? I'm unsure. [[User:Deco|Deco]] 19:53, 2 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>1649</id>
      <timestamp>2006-03-03T03:54:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Syntax</comment>
      <text xml:space="preserve">== Name casing ==

You think we should move this to [[:Category:Programming language:occam]]? I'm unsure. [[User:Deco|Deco]] 19:53, 2 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>1653</id>
      <timestamp>2006-03-03T05:06:30Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>yeah</comment>
      <text xml:space="preserve">== Name casing ==

You think we should move this to [[:Category:Programming language:occam]]? I'm unsure. [[User:Deco|Deco]] 19:53, 2 March 2006 (PST)

:I'd originally used Occam because it looked like all of the language names were being capitalized. However, upon closer inspection I see that things like csh script have lower case names. That being the case, I'm going to move this to [[:Category:Programming language:occam]], since the official name is lower case. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 21:06, 2 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>1660</id>
      <timestamp>2006-03-03T05:19:48Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>Category talk:Programming language:Occam moved to Category talk:Programming language:occam</comment>
      <text xml:space="preserve">== Name casing ==

You think we should move this to [[:Category:Programming language:occam]]? I'm unsure. [[User:Deco|Deco]] 19:53, 2 March 2006 (PST)

:I'd originally used Occam because it looked like all of the language names were being capitalized. However, upon closer inspection I see that things like csh script have lower case names. That being the case, I'm going to move this to [[:Category:Programming language:occam]], since the official name is lower case. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 21:06, 2 March 2006 (PST)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Quantitative finance</title>
    <id>1737</id>
    <revision>
      <id>2969</id>
      <timestamp>2006-03-08T20:21:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tag from article</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;</text>
    </revision>
    <revision>
      <id>3034</id>
      <timestamp>2006-03-09T12:26:34Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article}}</text>
    </revision>
    <revision>
      <id>3036</id>
      <timestamp>2006-03-09T12:35:19Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
[[Image:Arrow.png]][[:Category:Quantitative finance|Go to the article]]</text>
    </revision>
    <revision>
      <id>3047</id>
      <timestamp>2006-03-09T19:29:18Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>+template</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article}}</text>
    </revision>
    <revision>
      <id>3052</id>
      <timestamp>2006-03-09T19:50:15Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>+namespace to template</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article|namespace=Category}}</text>
    </revision>
    <revision>
      <id>3054</id>
      <timestamp>2006-03-09T19:57:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>test</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article|Category}}</text>
    </revision>
    <revision>
      <id>3066</id>
      <timestamp>2006-03-09T20:10:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>workaround template issues for now</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
&lt;!-- {{Go to the article}} --&gt;
[[Image:Arrow.png|30px]] Go to [[:Category:{{PAGENAME}}|the article]]</text>
    </revision>
    <revision>
      <id>3082</id>
      <timestamp>2006-03-09T20:31:15Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix template usage to add category param</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article|Category}}</text>
    </revision>
    <revision>
      <id>7811</id>
      <timestamp>2006-10-13T15:06:50Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article|Category}}

take into account this remarks:

 main distinction in quantitative finance is between the two sub-categories below:
 
 1. sell-side/pricing, that lives in the risk-neutral measure and is concerned with calibration.
 
 2. buy-side/management, that lives in the real measure and is concerned with estimation.</text>
    </revision>
    <revision>
      <id>8356</id>
      <timestamp>2006-12-27T10:05:59Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>External links to explore</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;
{{Go to the article|Category}}

take into account this remarks:

 main distinction in quantitative finance is between the two sub-categories below:
 
 1. sell-side/pricing, that lives in the risk-neutral measure and is concerned with calibration.
 
 2. buy-side/management, that lives in the real measure and is concerned with estimation.

== External links to explore ==

*[http://www-math.bgsu.edu/~zirbel/sde/ Matlab program files for Stochastic Differential Equations] - Craig L. Zirbel</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Quine</title>
    <id>1706</id>
    <revision>
      <id>2785</id>
      <timestamp>2006-03-07T13:55:37Z</timestamp>
      <contributor>
        <username>Nikie</username>
        <id>22</id>
      </contributor>
      <text xml:space="preserve">I put this page in the &quot;Computer science theory&quot; category, but I'm not really sure if it fits in there. I just wanted it to be reachable from the main page. --[[User:Nikie|Nikie]] 05:55, 7 March 2006 (PST)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Software sharing</title>
    <id>3189</id>
    <revision>
      <id>10721</id>
      <timestamp>2007-07-20T20:10:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>delete?</comment>
      <text xml:space="preserve">I don't think a category for shareware is relevant in this wiki. Sharewareware is never released under the MIT/X11 license used here, so it can't be included. Should we just delet this? [[User:Ahy1|Ahy1]] 13:10, 20 July 2007 (PDT)</text>
    </revision>
    <revision>
      <id>10727</id>
      <timestamp>2007-07-22T05:24:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>agree</comment>
      <text xml:space="preserve">I don't think a category for shareware is relevant in this wiki. Sharewareware is never released under the MIT/X11 license used here, so it can't be included. Should we just delet this? [[User:Ahy1|Ahy1]] 13:10, 20 July 2007 (PDT)

:Agreed. The page largely seems to exist as an ad for a shareware site at this point. I will delete it. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 22:24, 21 July 2007 (PDT)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Topological sort</title>
    <id>3472</id>
    <revision>
      <id>13632</id>
      <timestamp>2008-06-06T05:07:53Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">Nothing to see here</text>
    </revision>
    <revision>
      <id>16207</id>
      <timestamp>2009-03-08T10:57:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Userboxes:Programming languages</title>
    <id>1486</id>
    <revision>
      <id>1959</id>
      <timestamp>2006-03-04T01:33:10Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>two small suggestions</comment>
      <text xml:space="preserve">Perhaps &quot;minimal&quot; could be changed to &quot;some&quot;, which sounds less negative. Also, the boxes could probably be shrunk a bit. [[User:Fredrik|Fredrik]] 17:33, 3 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>2035</id>
      <timestamp>2006-03-04T03:49:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Sure</comment>
      <text xml:space="preserve">Perhaps &quot;minimal&quot; could be changed to &quot;some&quot;, which sounds less negative. Also, the boxes could probably be shrunk a bit. [[User:Fredrik|Fredrik]] 17:33, 3 March 2006 (PST)
:Sure, sounds good. [[User:Deco|Deco]] 19:49, 3 March 2006 (PST)</text>
    </revision>
    <revision>
      <id>9092</id>
      <timestamp>2007-02-15T17:29:49Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>Improvement of userboxes</comment>
      <text xml:space="preserve">Perhaps &quot;minimal&quot; could be changed to &quot;some&quot;, which sounds less negative. Also, the boxes could probably be shrunk a bit. [[User:Fredrik|Fredrik]] 17:33, 3 March 2006 (PST)
:Sure, sounds good. [[User:Deco|Deco]] 19:49, 3 March 2006 (PST)

== Improvement of userboxes ==

Currently, for each userbox, in general the language has to be given three times, even if it is the same all three times, e.g (taken directly from the example) &lt;nowiki&gt;{{Userbox PL1|Haskell|Haskell|Haskell}}&lt;/nowiki&gt;.

However, this could be improved by allowing to omit the second and third option if it's the same as the first one. This should be possible by changing each &lt;nowiki&gt;{{{2}}}&lt;/nowiki&gt; and &lt;nowiki&gt;{{{3}}}&lt;/nowiki&gt; to &lt;nowiki&gt;{{{2|{{{1}}}}}}&lt;/nowiki&gt; resp. &lt;nowiki&gt;{{{3|{{{1}}}}}}&lt;/nowiki&gt; in the template definitions.</text>
    </revision>
    <revision>
      <id>9093</id>
      <timestamp>2007-02-15T17:30:43Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Improvement of userboxes */ forgot to sign</comment>
      <text xml:space="preserve">Perhaps &quot;minimal&quot; could be changed to &quot;some&quot;, which sounds less negative. Also, the boxes could probably be shrunk a bit. [[User:Fredrik|Fredrik]] 17:33, 3 March 2006 (PST)
:Sure, sounds good. [[User:Deco|Deco]] 19:49, 3 March 2006 (PST)

== Improvement of userboxes ==

Currently, for each userbox, in general the language has to be given three times, even if it is the same all three times, e.g (taken directly from the example) &lt;nowiki&gt;{{Userbox PL1|Haskell|Haskell|Haskell}}&lt;/nowiki&gt;.

However, this could be improved by allowing to omit the second and third option if it's the same as the first one. This should be possible by changing each &lt;nowiki&gt;{{{2}}}&lt;/nowiki&gt; and &lt;nowiki&gt;{{{3}}}&lt;/nowiki&gt; to &lt;nowiki&gt;{{{2|{{{1}}}}}}&lt;/nowiki&gt; resp. &lt;nowiki&gt;{{{3|{{{1}}}}}}&lt;/nowiki&gt; in the template definitions. --[[User:Ce|Ce]] 09:30, 15 February 2007 (PST)</text>
    </revision>
    <revision>
      <id>9102</id>
      <timestamp>2007-02-16T02:49:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Improvement of userboxes */ reply</comment>
      <text xml:space="preserve">Perhaps &quot;minimal&quot; could be changed to &quot;some&quot;, which sounds less negative. Also, the boxes could probably be shrunk a bit. [[User:Fredrik|Fredrik]] 17:33, 3 March 2006 (PST)
:Sure, sounds good. [[User:Deco|Deco]] 19:49, 3 March 2006 (PST)

== Improvement of userboxes ==

Currently, for each userbox, in general the language has to be given three times, even if it is the same all three times, e.g (taken directly from the example) &lt;nowiki&gt;{{Userbox PL1|Haskell|Haskell|Haskell}}&lt;/nowiki&gt;.

However, this could be improved by allowing to omit the second and third option if it's the same as the first one. This should be possible by changing each &lt;nowiki&gt;{{{2}}}&lt;/nowiki&gt; and &lt;nowiki&gt;{{{3}}}&lt;/nowiki&gt; to &lt;nowiki&gt;{{{2|{{{1}}}}}}&lt;/nowiki&gt; resp. &lt;nowiki&gt;{{{3|{{{1}}}}}}&lt;/nowiki&gt; in the template definitions. --[[User:Ce|Ce]] 09:30, 15 February 2007 (PST)

:Cool! That seems to work pretty well. I've gone ahead and implemented this change on all three PL userboxes. --[[User:Allan McInnes|Allan McInnes]] &lt;small&gt;([[User talk:Allan McInnes|talk]])&lt;/small&gt; 18:49, 15 February 2007 (PST)</text>
    </revision>
  </page>
  <page>
    <title>Category talk:Users:PHP:Knows</title>
    <id>3840</id>
    <revision>
      <id>16048</id>
      <timestamp>2009-01-27T08:16:56Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">This page can only be edited by registered users because it has been a spam target at some time in the past. Sorry. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 27 January 2009 (EST)</text>
    </revision>
    <revision>
      <id>16049</id>
      <timestamp>2009-01-27T08:17:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This page can only be edited by users who have logged in because it has been a spam target at some time in the past. Sorry. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 27 January 2009 (EST)</text>
    </revision>
    <revision>
      <id>16228</id>
      <timestamp>2009-03-08T11:07:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Users:PHP:Some</title>
    <id>2945</id>
    <revision>
      <id>8727</id>
      <timestamp>2007-01-27T12:28:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created blank page</comment>
      <text xml:space="preserve">&lt;!-- Protected --&gt;</text>
    </revision>
    <revision>
      <id>16212</id>
      <timestamp>2009-03-08T10:57:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category talk:Users:Tcl:Some</title>
    <id>3693</id>
    <revision>
      <id>15524</id>
      <timestamp>2008-12-01T14:53:27Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>antispam measure</comment>
      <text xml:space="preserve">anti-spam measure</text>
    </revision>
    <revision>
      <id>16199</id>
      <timestamp>2009-03-08T10:55:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:99 Bottles of Beer</title>
    <id>1413</id>
    <revision>
      <id>1735</id>
      <timestamp>2006-03-03T12:31:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Introductory examples]]</comment>
      <text xml:space="preserve">This category's articles describe programs that print out the lyrics to the drinking song &quot;99 Bottle of Beer on the Wall&quot;, in which each verse decreases the number of bottles by one until none are left. A program printing out these lyrics is an example often used to introduce looping. There are sites that list many hundreds of implementations of this example (but please don't copy content from them).

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>8319</id>
      <timestamp>2006-12-09T19:12:34Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>+link</comment>
      <text xml:space="preserve">This category's articles describe programs that print out the lyrics to the drinking song &quot;99 Bottle of Beer on the Wall&quot;, in which each verse decreases the number of bottles by one until none are left. A program printing out these lyrics is an example often used to introduce looping. There are [http://www.99-bottles-of-beer.net/ sites] that list many hundreds of implementations of this example (but please don't copy content from them).

[[Category:Introductory examples]]</text>
    </revision>
  </page>
  <page>
    <title>Category:A* search</title>
    <id>2166</id>
    <revision>
      <id>5152</id>
      <timestamp>2006-05-24T06:51:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link Wikipedia, [[Category:Graph search algorithms]]</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/A%2A_search_algorithm A&lt;sup&gt;*&lt;/sup&gt; search] is a graph search algorithm that finds a path to a goal node, given a distance metric that estimates the distance to the goal from any given node. A simple example is a graph where each point corresponds to a point on a map and the metric is the Euclidean distance from the given point to the goal.

[[Category:Graph search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:AVL tree</title>
    <id>1971</id>
    <revision>
      <id>4553</id>
      <timestamp>2006-05-11T12:34:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, Wikipedia link, category</comment>
      <text xml:space="preserve">The first invented balanced binary search tree, [http://en.wikipedia.org/wiki/AVL_tree AVL trees] yield worst-case O(log ''n'') time for insertion, deletion, and lookup operations.

[[Category:Balanced tree]]</text>
    </revision>
    <revision>
      <id>4562</id>
      <timestamp>2006-05-12T02:46:09Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>http://en.wikipedia.org/wiki/Big_O_notation</comment>
      <text xml:space="preserve">The first invented balanced binary search tree, [http://en.wikipedia.org/wiki/AVL_tree AVL trees] yield worst-case [http://en.wikipedia.org/wiki/Big_O_notation O(log ''n'')] time for insertion, deletion, and lookup operations.

[[Category:Balanced tree]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Abstract factory pattern</title>
    <id>1622</id>
    <revision>
      <id>2434</id>
      <timestamp>2006-03-06T01:41:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependet objects without specifying their concrete classes. 

[[Category:Design patterns]]</text>
    </revision>
    <revision>
      <id>13475</id>
      <timestamp>2008-05-25T02:29:25Z</timestamp>
      <contributor>
        <ip>65.96.207.226</ip>
      </contributor>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Abstract_factory_pattern abstract factory pattern] provides a client with an interface for creating related or dependent objects without specifying their concrete classes. 

[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Abstract machine generators and simulators</title>
    <id>2269</id>
    <revision>
      <id>5923</id>
      <timestamp>2006-06-05T10:50:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Content from old cat [[Category:Abstract machine simulators]]</comment>
      <text xml:space="preserve">This category contains articles describing simulators for [http://en.wikipedia.org/wiki/Abstract_machine abstract machines] from computer science theory such as automata and Turing machines.

[[Category:Computer science theory]]
[[Category:Simulators and emulators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Abstract machine simulators</title>
    <id>1311</id>
    <revision>
      <id>1366</id>
      <timestamp>2006-02-28T20:03:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Computer science theory]], [[Category:Simulators and emulators]]</comment>
      <text xml:space="preserve">This category contains articles describing simulators for [http://en.wikipedia.org/wiki/Abstract_machine abstract machines] from computer science theory such as automata and Turing machines.

[[Category:Computer science theory]]
[[Category:Simulators and emulators]]</text>
    </revision>
    <revision>
      <id>5922</id>
      <timestamp>2006-06-05T10:50:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Moving</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Ackermann</title>
    <id>3493</id>
    <revision>
      <id>13775</id>
      <timestamp>2008-06-25T00:03:18Z</timestamp>
      <contributor>
        <username>Ggrandits</username>
        <id>1693</id>
      </contributor>
      <text xml:space="preserve">The Ackermann function is ideal for representation in Haskell and an excellent
use of its '''pattern matching''' facility and specifically '''''n+k'' pattern matching'''.

The Ackermann function could also have been easily implemented in Haskell with ''conditional code'' or ''guards''.

With pattern matching you create multiple definitions of a function and specify patterns for the arguments.
Haskell will use its pattern matching facility to invoke the first definition that matches the pattern.

Haskell has extremely little Housekeeping code
&lt;codeblock language=haskell&gt;
module Ackermann
    where
&lt;/codeblock&gt;

The case that bottoms out the recursion uses simple pattern matching to match the first
argument to 0 and binds the second argument to the variable n
&lt;codeblock language=haskell&gt;
ackermann 0 n = n+1
&lt;/codeblock&gt;

The case that reduces the first argument with primitive recursion
uses what is called ''n+k pattern matching'', in an ''n+k pattern'' match '''n&gt;= k'''.
In this case the ''n+k pattern'' is m+1 therefore the first argument or ''m'' must be
greater than 1.

The case that uses multiple recursion also uses ''n+k pattern matching''.
Therefore both the first and second argument must be greater than 1

&lt;codeblock language=haskell&gt;
ackermann (m+1) 0 = ackermann m 1
ackermann (m+1) (n+1) = ackermann m (ackermann (m+1) n)
&lt;/codeblock&gt;

Finally a &quot;catch all&quot; definition that use the underscore, which are wildcards
that don't even bother to bind the values.
Note the pattern matching goes in order, so something like this should always
be last.  This is nice approach for eeking out every bit of efficiency because
catching invalid negative arguments doesn't affect performance of algorithm
with valid arguments.  I suppose I could have spit out an error message, but
I simply return 0.
&lt;codeblock language=haskell&gt;
ackermann _ _ = 0
&lt;/codeblock&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Ackermann function</title>
    <id>2401</id>
    <revision>
      <id>6610</id>
      <timestamp>2006-07-02T13:37:58Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{shared text box |
The '''Ackermann function''' or '''Ackermann-Péter function''' is defined recursively for non-negative integers ''m'' and ''n'' as follows:

: &lt;math&gt; A(m, n) =
 \begin{cases}
 n+1 &amp; \mbox{if } m = 0 \\
 A(m-1, 1) &amp; \mbox{if } m &gt; 0 \mbox{ and } n = 0 \\
 A(m-1, A(m, n-1)) &amp; \mbox{if } m &gt; 0 \mbox{ and } n &gt; 0.
 \end{cases}
&lt;/math&gt;
In the theory of computation, the [http://en.wikipedia.org/wiki/Ackermann_function Ackermann function] is a simple example of a [http://en.wikipedia.org/wiki/Recursive_function recursive function] that is not [http://en.wikipedia.org/wiki/Primitive_recursive_function primitively recursive]. Note that this function grows very quickly -- even &lt;code&gt;A(4, 3)&lt;/code&gt; cannot be feasibly computed on ordinary computers.
}}

&lt;noinclude&gt;
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Adapter pattern</title>
    <id>1676</id>
    <revision>
      <id>2682</id>
      <timestamp>2006-03-06T21:16:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Algorithms</title>
    <id>1306</id>
    <revision>
      <id>1358</id>
      <timestamp>2006-02-28T19:54:56Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms and data structures]]</comment>
      <text xml:space="preserve">This category contains implementations and use cases of specific algorithms.

[[Category:Algorithms and data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Algorithms and data structures</title>
    <id>1305</id>
    <revision>
      <id>1357</id>
      <timestamp>2006-02-28T19:54:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains programs providing implementations or use cases of specific algorithms and data structures.</text>
    </revision>
    <revision>
      <id>1515</id>
      <timestamp>2006-03-02T23:31:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains programs providing implementations or use cases of specific algorithms and data structures.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>15622</id>
      <timestamp>2008-12-17T17:18:28Z</timestamp>
      <contributor>
        <ip>211.136.253.234</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_acvimonric</text>
    </revision>
    <revision>
      <id>15637</id>
      <timestamp>2008-12-17T21:33:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">This category contains programs providing implementations or use cases of specific algorithms and data structures.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Approximation algorithms</title>
    <id>1313</id>
    <revision>
      <id>1368</id>
      <timestamp>2006-02-28T20:08:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">This category contains articles describing [http://en.wikipedia.org/wiki/Approximation_algorithm approximation algorithms], algorithms designed to approximately solve a difficult problem within a certain degree of error.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Arbitrary-precision arithmetic</title>
    <id>1366</id>
    <revision>
      <id>1589</id>
      <timestamp>2006-03-03T02:14:33Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>to do list</comment>
      <text xml:space="preserve">To do:
* Representation of large integers and floating-point numbers
* Karatsuba multiplication
* Toom-Cook multiplication
* Fast Fourier transform (FFT) multiplication
* Number-theoretic transform (NTT) multiplication
* Newton's method
* Binary splitting</text>
    </revision>
    <revision>
      <id>4356</id>
      <timestamp>2006-05-03T18:51:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Cat:Numerical computing</comment>
      <text xml:space="preserve">To do:
* Representation of large integers and floating-point numbers
* Karatsuba multiplication
* Toom-Cook multiplication
* Fast Fourier transform (FFT) multiplication
* Number-theoretic transform (NTT) multiplication
* Newton's method
* Binary splitting

[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Arbitrary-precision integer arithmetic</title>
    <id>3786</id>
    <revision>
      <id>15859</id>
      <timestamp>2009-01-09T01:07:00Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">-</text>
    </revision>
    <revision>
      <id>16219</id>
      <timestamp>2009-03-08T11:05:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
    <revision>
      <id>16761</id>
      <timestamp>2010-07-15T09:55:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ Category:Arbitrary-precision arithmetic</comment>
      <text xml:space="preserve">[[Category:Arbitrary-precision arithmetic]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Array list</title>
    <id>1817</id>
    <revision>
      <id>3511</id>
      <timestamp>2006-03-22T12:52:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>#REDIRECT[[:Category:Dynamic array]]</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Dynamic array]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Artificial intelligence</title>
    <id>1308</id>
    <revision>
      <id>1363</id>
      <timestamp>2006-02-28T19:57:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Copy description from misspelled [[:Category:Artifical intelligence]]</comment>
      <text xml:space="preserve">This category contains programs relating to the field of [http://en.wikipedia.org/wiki/Artificial_intelligence Artificial intelligence]. Most articles should go in a more specific subcategory.</text>
    </revision>
    <revision>
      <id>1516</id>
      <timestamp>2006-03-02T23:31:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains programs relating to the field of [http://en.wikipedia.org/wiki/Artificial_intelligence Artificial intelligence]. Most articles should go in a more specific subcategory.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Artificial neural networks</title>
    <id>2815</id>
    <revision>
      <id>8176</id>
      <timestamp>2006-11-26T03:07:47Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Artificial neural networks</comment>
      <text xml:space="preserve">Category for different kinds of [http://en.wikipedia.org/wiki/Artificial_neural_network artificial neural networks].

[[Category:Artificial intelligence]]</text>
    </revision>
  </page>
  <page>
    <title>Category:B-tree</title>
    <id>1536</id>
    <revision>
      <id>2062</id>
      <timestamp>2006-03-04T04:09:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Data structures]]</comment>
      <text xml:space="preserve">[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:BMP decoders and encoders</title>
    <id>1330</id>
    <revision>
      <id>1429</id>
      <timestamp>2006-03-01T10:58:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Graphics file formats]]</comment>
      <text xml:space="preserve">Articles in this category translate between BMP files and more natural memory-resident representations such as raw bitmaps.

[[Category:Graphics file formats]]</text>
    </revision>
    <revision>
      <id>1430</id>
      <timestamp>2006-03-01T10:59:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Wotsit's link</comment>
      <text xml:space="preserve">Articles in this category translate between BMP files and more natural memory-resident representations such as raw bitmaps. For a general description of the format, see [http://www.wotsit.org/download.asp?f=bmp BMP information at Wotsit's Format].

[[Category:Graphics file formats]]</text>
    </revision>
    <revision>
      <id>1431</id>
      <timestamp>2006-03-01T11:01:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix link - direct downloads blocked</comment>
      <text xml:space="preserve">Articles in this category translate between BMP files and more natural memory-resident representations such as raw bitmaps. For a general description of the format, see [http://www.wotsit.org/search.asp?s=graphics the Graphics Files section at Wotsit's Format].

[[Category:Graphics file formats]]</text>
    </revision>
    <revision>
      <id>1432</id>
      <timestamp>2006-03-01T20:36:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Some more resources</comment>
      <text xml:space="preserve">Articles in this category translate between BMP files and more natural memory-resident representations such as raw bitmaps. For a general description of the format, see one of the following resources:

* [http://astronomy.swin.edu.au/~pbourke/dataformats/bmp/ Paul Bourke: BMP Files]
* [http://atlc.sourceforge.net/bmp.html David Kirkby: bmp format]
* [http://www.wotsit.org/search.asp?s=graphics The Graphics Files section at Wotsit's Format (old)]

[[Category:Graphics file formats]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Balanced tree</title>
    <id>1534</id>
    <revision>
      <id>2059</id>
      <timestamp>2006-03-04T04:07:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Binary search tree]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Self-balancing_binary_search_tree balanced tree], in the sense we use it here, is a binary search tree where the operations are modified to ensure that the tree height is low (usually ''O''(log ''n'')) at all times (or on average). There are several, often complex implementations of balanced trees.

[[Category:Binary search tree]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Base64</title>
    <id>3175</id>
    <revision>
      <id>10649</id>
      <timestamp>2007-07-07T01:46:29Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Base64#MIME Base 64] algorithm for encoding binary data as safely transportable text.

[[Category:File processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Basic constructs</title>
    <id>2361</id>
    <revision>
      <id>6381</id>
      <timestamp>2006-06-21T12:19:36Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains aricles describing some basic constructs in different languages.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>11656</id>
      <timestamp>2007-11-19T21:08:51Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>describe scope</comment>
      <text xml:space="preserve">This category contains articles describing some basic constructs in different languages.  At a minimum, these examples should demonstrate:
* Iteration constructs (foreach, while, list comprehension, etc.)
* Conditional constructs (if-then-else, switch, pattern matching, polymorphism, etc.)
* Data types (integer, real, bignum, string, composites, etc.)
* Decomposition (functions, procedures, objects, macros, modules, etc.)
* Syntactic elements (comments, statements, declarations, keywords, operators, etc.)

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>11657</id>
      <timestamp>2007-11-19T21:09:33Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing some basic constructs in different languages.  At a minimum, these examples should demonstrate:
* Iteration constructs (foreach, while, list comprehension, etc.)
* Conditional constructs (if-then-else, switch, pattern matching, polymorphism, etc.)
* Data types (integer, real, bignum, string, composites, collections, etc.)
* Decomposition (functions, procedures, objects, macros, modules, etc.)
* Syntactic elements (comments, statements, declarations, keywords, operators, etc.)

[[Category:Introductory examples]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Bernoulli numbers</title>
    <id>1993</id>
    <revision>
      <id>4652</id>
      <timestamp>2006-05-13T12:29:55Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] are a sequence of rational numbers of great importance in number theory. Large Bernoulli numbers are relatively difficult to compute.

[[Category:Number theory]]</text>
    </revision>
    <revision>
      <id>4655</id>
      <timestamp>2006-05-13T17:53:58Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>prep for transclusion</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Bernoulli_number Bernoulli numbers] ''B''&lt;sub&gt;m&lt;/sub&gt; are a sequence of rational numbers defined by the identity

:&lt;math&gt;\sum_{j=0}^m {{m+1}\choose{j}} B_j = 0&lt;/math&gt; 

with the initial condition ''B''&lt;sub&gt;0&lt;/sub&gt; = 1. Here, &lt;math&gt;{{n}\choose{k}}&lt;/math&gt; denotes a [http://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficient]. The sequence, which continues -1/2, 1/6, 0, -1/30, 0, 1/42, ..., obeys no simple pattern, and computing ''B&lt;sub&gt;m&lt;/sub&gt;'' for ''m'' as small as a few hundred is a relatively time-consuming task.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Binary heap</title>
    <id>2379</id>
    <revision>
      <id>6473</id>
      <timestamp>2006-06-24T05:20:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, meant to put binary heap text here</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_heap binary heap] is a simple concrete heap data structure using a binary tree. Binary heaps perform all operations in O(log ''n'') time, except examining the root (minimum/maximum) element, which is constant time. They do not support a merge operation. They are often represented as complete binary trees stored implicitly in arrays; this representation is used in [[:Category:Heapsort|heapsort]], for example. 

[[Category:Heap]]</text>
    </revision>
    <revision>
      <id>15949</id>
      <timestamp>2009-01-13T05:59:34Z</timestamp>
      <contributor>
        <ip>209.139.208.194</ip>
      </contributor>
      <comment>peFIgvrMjXHGowaC</comment>
      <text xml:space="preserve">1WyCJL  &lt;a href=&quot;http://tjrsqqnsdmta.com/&quot;&gt;tjrsqqnsdmta&lt;/a&gt;, [url=http://fsrdvmnchryp.com/]fsrdvmnchryp[/url], [link=http://qoiodmkgnxdu.com/]qoiodmkgnxdu[/link], http://jqdmqalqrpnt.com/</text>
    </revision>
    <revision>
      <id>15950</id>
      <timestamp>2009-01-13T07:20:21Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/209.139.208.194|209.139.208.194]] ([[User_talk:209.139.208.194|209.139.208.194]]); changed back to last version by [[User:Deco|Deco]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_heap binary heap] is a simple concrete heap data structure using a binary tree. Binary heaps perform all operations in O(log ''n'') time, except examining the root (minimum/maximum) element, which is constant time. They do not support a merge operation. They are often represented as complete binary trees stored implicitly in arrays; this representation is used in [[:Category:Heapsort|heapsort]], for example. 

[[Category:Heap]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Binary search</title>
    <id>2271</id>
    <revision>
      <id>5936</id>
      <timestamp>2006-06-05T18:25:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Desc, link, cat</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Binary_search_algorithm Binary search] is an algorithm used to quickly locate a particular value in a sorted random-access container, such as a sorted array. It operates by repeatedly narrowing the range of possible locations by examining the element in the middle of this range.

&lt;noinclude&gt;
[[Category:Algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Binary search tree</title>
    <id>1422</id>
    <revision>
      <id>1746</id>
      <timestamp>2006-03-03T12:44:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Data structures]]</comment>
      <text xml:space="preserve">[[Category:Data structures]]</text>
    </revision>
    <revision>
      <id>4552</id>
      <timestamp>2006-05-11T03:20:56Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>description</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Binary_search_tree binary search trees].

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Binomial heap</title>
    <id>2378</id>
    <revision>
      <id>6472</id>
      <timestamp>2006-06-24T05:19:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category, link</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binary_heap binomial heap] is a simple concrete heap data structure using a binary tree. Binary heaps perform all operations in O(log ''n'') time, except examining the root (minimum/maximum) element, which is constant time. They do not support a merge operation. They are often represented as complete binary trees stored implicitly in arrays; this representation is used in [[:Category:Heapsort|heapsort]], for example. 

[[Category:Heap]]</text>
    </revision>
    <revision>
      <id>6474</id>
      <timestamp>2006-06-24T05:23:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix description, wrong heap</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Binomial_heap binomial heap] is a concrete heap data structure constructed using a forest of binomial trees. Binomial heaps perform all operations in O(log ''n'') time, and unlike binary heaps, support an O(log ''n'') operation to (destructively) merge two heaps into one.

[[Category:Heap]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Bloom filter</title>
    <id>1420</id>
    <revision>
      <id>1744</id>
      <timestamp>2006-03-03T12:43:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Data structures]]</comment>
      <text xml:space="preserve">[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Boolean logic</title>
    <id>2244</id>
    <revision>
      <id>5687</id>
      <timestamp>2006-06-02T03:51:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Discrete and symbolic mathematics]]</comment>
      <text xml:space="preserve">[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Box-Muller transform</title>
    <id>2172</id>
    <revision>
      <id>5198</id>
      <timestamp>2006-05-26T12:33:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, Wikipedia link, [[Category:Pseudorandom number generators]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Box-Muller_transform Box-Muller transform is a simple method for generating normally distributed random numbers from uniformally distributed random numbers. Since most pseudorandom number generators output uniformally or nearly-uniformally distributed values, it is commonly used in combination with these to create generators for normally distributed values, which are useful in simulating data sets with a known mean (average) and spread.

[[Category:Pseudorandom number generators]]</text>
    </revision>
    <revision>
      <id>5199</id>
      <timestamp>2006-05-26T12:33:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Syntax</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Box-Muller_transform Box-Muller transform] is a simple method for generating normally distributed random numbers from uniformally distributed random numbers. Since most pseudorandom number generators output uniformally or nearly-uniformally distributed values, it is commonly used in combination with these to create generators for normally distributed values, which are useful in simulating data sets with a known mean (average) and spread.

[[Category:Pseudorandom number generators]]</text>
    </revision>
    <revision>
      <id>5200</id>
      <timestamp>2006-05-26T12:34:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>&lt;noinclude&gt;</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Box-Muller_transform Box-Muller transform] is a simple method for generating normally distributed random numbers from uniformally distributed random numbers. Since most pseudorandom number generators output uniformally or nearly-uniformally distributed values, it is commonly used in combination with these to create generators for normally distributed values, which are useful in simulating data sets with a known mean (average) and spread.

&lt;noinclude&gt;
[[Category:Pseudorandom number generators]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5217</id>
      <timestamp>2006-05-26T20:01:16Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>spelling + box text</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Box-Muller_transform Box-Muller transform] is a simple method for generating normally distributed random numbers from uniformly distributed random numbers. Since most pseudorandom number generators output uniformly or nearly-uniformly distributed values, it is commonly used in combination with these to create generators for normally distributed values, which are useful in simulating data sets with a known mean (average) and spread.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Pseudorandom number generators]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5219</id>
      <timestamp>2006-05-26T20:10:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>switch to shared text box template</comment>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Box-Muller_transform Box-Muller transform] is a simple method for generating normally distributed random numbers from uniformly distributed random numbers. Since most pseudorandom number generators output uniformly or nearly-uniformly distributed values, it is commonly used in combination with these to create generators for normally distributed values, which are useful in simulating data sets with a known mean (average) and spread.
}}

&lt;noinclude&gt;
[[Category:Pseudorandom number generators]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Boyer-Moore string search algorithm</title>
    <id>3284</id>
    <revision>
      <id>12052</id>
      <timestamp>2008-01-12T03:17:54Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Boyer-Moore implementations</comment>
      <text xml:space="preserve">This category contains  implementations of the [http://en.wikipedia.org/wiki/Boyer-Moore_string_search_algorithm Boyer-Moore string search algorithm].

[[Category:String search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Breadth-first search</title>
    <id>1902</id>
    <revision>
      <id>4189</id>
      <timestamp>2006-04-20T00:23:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Breadth-first_search breadth-first search], a simple graph search algorithm. Compared to [[Category:Depth-first search|depth-first search]], it always finds the shortest path, but can require much more space.

[[Category:Graph search algorithms]]</text>
    </revision>
    <revision>
      <id>4190</id>
      <timestamp>2006-04-20T00:23:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Syntax</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Breadth-first_search breadth-first search], a simple graph search algorithm. Compared to [[:Category:Depth-first search|depth-first search]], it always finds the shortest path, but can require much more space.

[[Category:Graph search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Bridge pattern</title>
    <id>1677</id>
    <revision>
      <id>2683</id>
      <timestamp>2006-03-06T21:16:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Bubble sort</title>
    <id>1455</id>
    <revision>
      <id>1855</id>
      <timestamp>2006-03-03T20:10:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort], a slow but simple sorting algorithm sometimes used in teaching.

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>10655</id>
      <timestamp>2007-07-10T16:13:07Z</timestamp>
      <contributor>
        <ip>75.37.224.44</ip>
      </contributor>
      <comment>humor</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort], a slow but simple sorting algorithm sometimes used in teaching.

''([http://ansuz.sooke.bc.ca/bonobo-conspiracy/?i=139 lame attempt at bubble-sort humor])''

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>13142</id>
      <timestamp>2008-04-18T06:25:20Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>category</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort], a slow but simple sorting algorithm sometimes used in teaching.

''([http://ansuz.sooke.bc.ca/bonobo-conspiracy/?i=139 lame attempt at bubble-sort humor])''

[[Category:Sorting algorithms]]
[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13143</id>
      <timestamp>2008-04-18T06:27:28Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>-spam</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Bubble_sort bubble sort], a slow but simple sorting algorithm sometimes used in teaching.

[[Category:Sorting algorithms]]
[[Category:Introductory examples]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Bucket sort</title>
    <id>1460</id>
    <revision>
      <id>1863</id>
      <timestamp>2006-03-03T20:17:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Bucket_sort bucket sort], a specialized sorting algorithm for lists that are well-distributed (not too much clustering of values).

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Builder pattern</title>
    <id>1672</id>
    <revision>
      <id>2678</id>
      <timestamp>2006-03-06T21:14:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Cellular automata</title>
    <id>2913</id>
    <revision>
      <id>8553</id>
      <timestamp>2007-01-15T10:36:09Z</timestamp>
      <contributor>
        <ip>62.202.90.155</ip>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">[[Category:Computer science theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Chain of responsibility pattern</title>
    <id>1683</id>
    <revision>
      <id>2689</id>
      <timestamp>2006-03-06T21:18:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Ciphers</title>
    <id>2341</id>
    <revision>
      <id>6238</id>
      <timestamp>2006-06-13T15:38:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contain implementations of [http://en.wikipedia.org/wiki/Category:Ciphers cipher] algorithms.

[[Category:Cryptography]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Circularly linked list</title>
    <id>1417</id>
    <revision>
      <id>1739</id>
      <timestamp>2006-03-03T12:34:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Linked list]]</comment>
      <text xml:space="preserve">[[Category:Linked list]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Code dumps</title>
    <id>2242</id>
    <revision>
      <id>5675</id>
      <timestamp>2006-06-02T00:25:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link template</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>10993</id>
      <timestamp>2007-10-01T19:21:55Z</timestamp>
      <contributor>
        <ip>64.59.139.153</ip>
      </contributor>
      <text xml:space="preserve">bocroldron
This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>10995</id>
      <timestamp>2007-10-01T21:41:53Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/64.59.139.153|64.59.139.153]] ([[User_talk:64.59.139.153|64.59.139.153]]); changed back to last version by [[User:Deco|Deco]]</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11099</id>
      <timestamp>2007-10-08T18:38:17Z</timestamp>
      <contributor>
        <ip>64.34.180.180</ip>
      </contributor>
      <text xml:space="preserve">roouliboor
This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11113</id>
      <timestamp>2007-10-08T19:55:58Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11428</id>
      <timestamp>2007-10-31T02:16:38Z</timestamp>
      <contributor>
        <ip>62.245.111.83</ip>
      </contributor>
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This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11431</id>
      <timestamp>2007-10-31T04:59:07Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/62.245.111.83|62.245.111.83]] ([[User_talk:62.245.111.83|62.245.111.83]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11472</id>
      <timestamp>2007-11-06T10:56:36Z</timestamp>
      <contributor>
        <ip>67.52.10.178</ip>
      </contributor>
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This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11475</id>
      <timestamp>2007-11-06T17:10:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/67.52.10.178|67.52.10.178]] ([[User_talk:67.52.10.178|67.52.10.178]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11563</id>
      <timestamp>2007-11-13T05:23:41Z</timestamp>
      <contributor>
        <ip>207.234.145.43</ip>
      </contributor>
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This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11564</id>
      <timestamp>2007-11-13T05:55:01Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>11687</id>
      <timestamp>2007-11-20T07:16:25Z</timestamp>
      <contributor>
        <ip>67.192.37.34</ip>
      </contributor>
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Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
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      <id>11688</id>
      <timestamp>2007-11-20T08:58:09Z</timestamp>
      <contributor>
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      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
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      <timestamp>2008-01-09T22:42:34Z</timestamp>
      <contributor>
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[http://herlindaruyle.ifrance.com/data/pearl-river-piano.html|pearl river piano prices] ((http://herlindaruyle.ifrance.com/data/pearl-river-piano.html pearl river piano prices)) [[http://herlindaruyle.ifrance.com/data/pearl-river-piano.html | pearl river piano prices]] &quot;pearl river piano prices&quot;:http://herlindaruyle.ifrance.com/data/pearl-river-piano.html [les gourmettes cooking|http://olivehamburg.ifrance.com/les-gourmettes.html] [[http://olivehamburg.ifrance.com/les-gourmettes.html les gourmettes cooking]] [http://olivehamburg.ifrance.com/les-gourmettes.html|les gourmettes cooking] ((http://olivehamburg.ifrance.com/les-gourmettes.html les gourmettes cooking)) [[http://olivehamburg.ifrance.com/les-gourmettes.html | les gourmettes cooking]] &quot;les gourmettes cooking&quot;:http://olivehamburg.ifrance.com/les-gourmettes.html [oblivion|http://eleonorehartlin.ifrance.com/blog/oblivion.html] [[http://eleonorehartlin.ifrance.com/blog/oblivion.html oblivion]] [http://eleonorehartlin.ifrance.com/blog/oblivion.html|oblivion] ((http://eleonorehartlin.ifrance.com/blog/oblivion.html oblivion)) [[http://eleonorehartlin.ifrance.com/blog/oblivion.html | oblivion]] &quot;oblivion&quot;:http://eleonorehartlin.ifrance.com/blog/oblivion.html 
This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
    <revision>
      <id>12013</id>
      <timestamp>2008-01-09T23:46:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/210.238.206.94|210.238.206.94]] ([[User_talk:210.238.206.94|210.238.206.94]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">This category contains articles classified as ''code dumps'', which have little or no accompanying documentation or rearrangement of code. Although still useful, these are not literate programs, and comprehension can often be improved by converting them into literate programs by splitting them into chunks and rearranging and documenting them liberally. If the program contains comments, a good starting point is to convert these into article text, especially if the comments attempt to depict tables or diagrams.

Articles are added to this category using [[Template:Codedump]]. All articles in this category should also be found in [[:Category:Developing]].</text>
    </revision>
  </page>
  <page>
    <title>Category:Color quantization</title>
    <id>1937</id>
    <revision>
      <id>4341</id>
      <timestamp>2006-05-02T08:21:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, Wikipedia link, category</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Color_quantization Color quantization] is a process which reduces the number of colors in an image. Most bitmap editors perform color quantization when converting an image with many colors to an image format with less colors, such as Photoshop's Mode&amp;rarr;Indexed Color. Ideally, the palette of the new image should be chosen so that the new image is as visually similar as possible to the old image. The most popular algorithms are the median cut and octree algorithms. Color quantization is frequently combined with [[:Category:Dithering|dithering]], to hide artifacts such as banding that it causes.

[[Category:Image processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Color space conversion</title>
    <id>1974</id>
    <revision>
      <id>4557</id>
      <timestamp>2006-05-11T14:54:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains code to convert images and colors among various common color spaces, such as RGB, CYMK, and HSV.

[[Category:Image processing]]</text>
    </revision>
    <revision>
      <id>4563</id>
      <timestamp>2006-05-12T02:48:07Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>wikipedia links</comment>
      <text xml:space="preserve">This category contains code to convert images and colors among various common color spaces, such as [http://en.wikipedia.org/wiki/RGB_color_model RGB], [http://en.wikipedia.org/wiki/CMYK_color_model CYMK], and [http://en.wikipedia.org/wiki/HSV_color_space HSV].

[[Category:Image processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Combinatorics</title>
    <id>2840</id>
    <revision>
      <id>8219</id>
      <timestamp>2006-11-28T16:33:53Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Combinatorics</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Combinatorics combinatorics].

[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Command pattern</title>
    <id>1684</id>
    <revision>
      <id>2690</id>
      <timestamp>2006-03-06T21:18:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Communities</title>
    <id>1710</id>
    <revision>
      <id>2807</id>
      <timestamp>2006-03-07T17:25:24Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Comminuties of users...</text>
    </revision>
  </page>
  <page>
    <title>Category:Communities:Matlab Community for Quantitative Finance</title>
    <id>1713</id>
    <revision>
      <id>2820</id>
      <timestamp>2006-03-07T17:37:23Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of Matlab Community For Quantitative Finance is to share some best practices in Matlab dedicated to its use in Quantitative Finance.</text>
    </revision>
    <revision>
      <id>2821</id>
      <timestamp>2006-03-07T17:37:48Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.</text>
    </revision>
    <revision>
      <id>4175</id>
      <timestamp>2006-04-19T08:34:14Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put this template in the articles you create that are in the scope of using Matlab in [[Category:Quantitative finance|Quantitative finance]].</text>
    </revision>
    <revision>
      <id>4177</id>
      <timestamp>2006-04-19T08:54:57Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;</text>
    </revision>
    <revision>
      <id>4178</id>
      <timestamp>2006-04-19T08:55:41Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[:Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;</text>
    </revision>
    <revision>
      <id>4179</id>
      <timestamp>2006-04-19T08:56:09Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[:Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>4180</id>
      <timestamp>2006-04-19T15:46:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>subst template as a precursor to removing circular categorization</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #09891B 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 200px; background: #8BF49A;&quot;
| style=&quot;width: 35px; height: 35px; background: #13D42F; text-align: center; font-size: 14pt; color: #003D09;&quot;| 
'''MCQF'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This article is maintained by [[:Category:Communities:Matlab Community for Quantitative Finance|Matlab Community for Quantitative Finance]].&lt;/div&gt;
|}
&lt;/div&gt;&lt;includeonly&gt;[[Category:Communities:Matlab Community for Quantitative Finance]]&lt;/includeonly&gt;&lt;noinclude&gt;
For instructions on using these boxes, see [[:Category:Userboxes:Programming languages]].
[[Category:Userboxes:Programming languages]]&lt;/noinclude&gt;
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[:Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>4181</id>
      <timestamp>2006-04-19T15:47:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>eliminate circular category reference</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #09891B 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 200px; background: #8BF49A;&quot;
| style=&quot;width: 35px; height: 35px; background: #13D42F; text-align: center; font-size: 14pt; color: #003D09;&quot;| 
'''MCQF'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This article is maintained by [[:Category:Communities:Matlab Community for Quantitative Finance|Matlab Community for Quantitative Finance]].&lt;/div&gt;
|}
&lt;/div&gt;
|}
&lt;/div&gt;

The goal of '''the Matlab Community For Quantitative Finance''' is to share some best practices in Matlab dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[:Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

[[Category:Quantitative finance]]</text>
    </revision>
    <revision>
      <id>7499</id>
      <timestamp>2006-08-26T02:56:48Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #09891B 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 200px; background: #8BF49A;&quot;
| style=&quot;width: 35px; height: 35px; background: #13D42F; text-align: center; font-size: 14pt; color: #003D09;&quot;| 
'''MCQF'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This article is maintained by [[:Category:Communities:Matlab Community for Quantitative Finance|Matlab Community for Quantitative Finance]].&lt;/div&gt;
|}
&lt;/div&gt;
|}
&lt;/div&gt;

The goal of '''the MATLAB Community For Quantitative Finance''' is to share some best practices in MATLAB dedicated to its use in Quantitative Finance.


Any [[Category:Programming language:Matlab|Matlab]] user is welcome into this Community.

To contribute, just create a profile and put it the Community template:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 {{Community member|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

You can put the following template in the articles you create that are in the scope of using Matlab in [[:Category:Quantitative finance|Quantitative finance]]:

 &lt;nowiki&gt;&lt;div class=&quot;tright&quot;&gt;
 {|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
 |{{Community article|MCQF|Matlab Community for Quantitative Finance}}
 |}
 &lt;/div&gt;&lt;/nowiki&gt;

[[Category:Quantitative finance]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Compilers and programming languages</title>
    <id>2824</id>
    <revision>
      <id>8192</id>
      <timestamp>2006-11-27T05:25:55Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Compilers and programming languages</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Compiler compilers] and [http://en.wikipedia.org/wiki/Programming_languages programming languages].

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Complex numbers</title>
    <id>1794</id>
    <revision>
      <id>3316</id>
      <timestamp>2006-03-14T19:11:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Data structures]], [[Category:Numerical computing]]</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Complex_number complex numbers], including a number of basic operations. A number of languages have built-in support for complex numbers, but we may still show implementations for some of these for demonstration or specialized purposes.

[[Category:Data structures]]
[[Category:Numerical computing]]</text>
    </revision>
    <revision>
      <id>3317</id>
      <timestamp>2006-03-14T19:12:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+Introductory</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Complex_number complex numbers], including a number of basic operations. A number of languages have built-in support for complex numbers, but we may still show implementations for some of these for demonstration or specialized purposes. Implementing complex numbers with basic arithmetic operations is also a common introductory exercise in programming, especially object-oriented programming.

[[Category:Data structures]]
[[Category:Numerical computing]]</text>
    </revision>
    <revision>
      <id>4642</id>
      <timestamp>2006-05-13T03:00:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>I wouldn't call this a data structure</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Complex_number complex numbers], including a number of basic operations. A number of languages have built-in support for complex numbers, but we may still show implementations for some of these for demonstration or specialized purposes. Implementing complex numbers with basic arithmetic operations is also a common introductory exercise in programming, especially object-oriented programming.

[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Composite pattern</title>
    <id>1678</id>
    <revision>
      <id>2684</id>
      <timestamp>2006-03-06T21:17:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Computational geometry</title>
    <id>1327</id>
    <revision>
      <id>1413</id>
      <timestamp>2006-03-01T03:28:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Graphics]], [[Category:Algorithms and data structures]]</comment>
      <text xml:space="preserve">This category contains articles relating to [http://en.wikipedia.org/wiki/Computational_geometry computational geometry], algorithms that solve large-scale geometric problems. These often arise in graphics, but also in other contexts such as database queries and computer vision.

[[Category:Graphics]]
[[Category:Algorithms and data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Computer algebra systems</title>
    <id>2957</id>
    <revision>
      <id>8773</id>
      <timestamp>2007-02-01T11:12:02Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial cat</comment>
      <text xml:space="preserve">This category contains articles relating to computer algebra systems.  These may be educational, allowing a constructive exploration of algebraic topics, or practical, where letting the computer handle the ancillary &quot;plug and chug&quot; work frees mathematicians to concentrate on the more interesting aspects of their problems.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>15708</id>
      <timestamp>2008-12-29T05:58:11Z</timestamp>
      <contributor>
        <ip>72.23.19.139</ip>
      </contributor>
      <comment>Add Axiom (Tim Daly)</comment>
      <text xml:space="preserve">This category contains articles relating to computer algebra systems.  These may be educational, allowing a constructive exploration of algebraic topics, or practical, where letting the computer handle the ancillary &quot;plug and chug&quot; work frees mathematicians to concentrate on the more interesting aspects of their problems.

[[Category:Top-level subject areas]]

* [http://en.wikipedia.org/wiki/Axiom_computer_algebra_system Axiom]</text>
    </revision>
  </page>
  <page>
    <title>Category:Computer science theory</title>
    <id>1315</id>
    <revision>
      <id>1371</id>
      <timestamp>2006-02-28T20:12:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles relating to computer science theory. Every article is a real program, but programs are often useful in demonstrating concepts from theoretical computer science.</text>
    </revision>
    <revision>
      <id>1517</id>
      <timestamp>2006-03-02T23:31:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains articles relating to computer science theory. Every article is a real program, but programs are often useful in demonstrating concepts from theoretical computer science.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>15822</id>
      <timestamp>2009-01-08T00:37:16Z</timestamp>
      <contributor>
        <ip>66.201.219.17</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_trtrdro.com/</text>
    </revision>
    <revision>
      <id>15828</id>
      <timestamp>2009-01-08T06:49:01Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/66.201.219.17|66.201.219.17]] ([[User_talk:66.201.219.17|66.201.219.17]]); changed back to last version by [[User:Deco|Deco]]</comment>
      <text xml:space="preserve">This category contains articles relating to computer science theory. Every article is a real program, but programs are often useful in demonstrating concepts from theoretical computer science.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Computer vision</title>
    <id>1310</id>
    <revision>
      <id>1365</id>
      <timestamp>2006-02-28T19:59:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Artificial intelligence]]</comment>
      <text xml:space="preserve">This category contains articles related to [http://en.wikipedia.org/wiki/Computer_vision computer vision].

[[Category:Artificial intelligence]]</text>
    </revision>
    <revision>
      <id>2228</id>
      <timestamp>2006-03-04T22:07:58Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Image processing]]</comment>
      <text xml:space="preserve">This category contains articles related to [http://en.wikipedia.org/wiki/Computer_vision computer vision].

[[Category:Artificial intelligence]]
[[Category:Image processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Concurrent programming</title>
    <id>3923</id>
    <revision>
      <id>16571</id>
      <timestamp>2009-11-25T20:37:46Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">Scholars still argue on the difference between Concurrent programming and other related idioms.

Here however, we make a distinction in that Concurrent usually refers to running a single job that is split into multiple tasks on one processing unit (multi-tasking is the case when multiple jobs are involved) while Multi-core and Parallel usually refer to tightly coupled units (integrated on a chip in case of multi-core and on a system in a more general case of parallel) running a single job (but possibly several tasks/threads), Distributed refers to loosely coupled units (integrated on the net) that run multiple jobs/tasks.</text>
    </revision>
    <revision>
      <id>16584</id>
      <timestamp>2009-11-25T21:59:06Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">Scholars still argue on the difference between Concurrent programming and other related idioms.

Here however, we make a distinction in that Concurrent usually refers to running a single job that is split into multiple tasks to run on one processing unit (multi-tasking is the case when multiple jobs are involved).

Multi-core and Parallel on the other hand usually refer to tightly coupled units (integrated on a chip in case of Multi- and Many-core and on a system in a more general case of Parallel) running a single job (possibly split into several tasks/threads).

Finally, Distributed refers to loosely coupled units (integrated on the net) that run multiple jobs/tasks, a.k.a. clusters, grids and clouds (I don't make any distinction between these right here).

Note that High-Performance or High-Reliability (Security) can cover all of Concurrent, Multi- and Many-core, Parallel and Distributed domains.</text>
    </revision>
  </page>
  <page>
    <title>Category:Convert Integer to String</title>
    <id>2394</id>
    <revision>
      <id>6552</id>
      <timestamp>2006-06-30T11:18:36Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Added new category</comment>
      <text xml:space="preserve">This category's articles describe functions that take a integer argument and return a string. For example ''99'' becomes ''ninety-nine''. This is more challenging than it might at first appear, particular because of the internationalization and localization issues. For example 129 in German is ''Einhunderdneunundzwanzig'' and in French is ''cent vingt neuf'' and there are often lots of irregularites and special cases. Even in English, which is reasonably regular, there are suprising localization issues. For example, in the USA 129 is pronounced ''one hundred twenty-nine'', whereas in the UK it is said as ''one hundred and twenty-nine''. 

A library function that solves this problem in a given programming language would be useful in refining the solution of [[99 Bottles of Beer]]. 

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>8897</id>
      <timestamp>2007-02-08T18:57:05Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This category's articles describe functions that take a integer argument and return a string. For example ''99'' becomes ''ninety-nine''. This is more challenging than it might at first appear, particular because of the internationalization and localization issues. For example 129 in German is ''Einhunderdneunundzwanzig'' and in French is ''cent vingt neuf'' and there are often lots of irregularites and special cases. Even in English, which is reasonably regular, there are surprising localization issues. For example, in the USA 129 is pronounced ''one hundred twenty-nine'', whereas an English person would say ''one hundred and twenty-nine''. 

A library function that solves this problem in a given programming language would be useful in refining the solution of [[99 Bottles of Beer]]. 

[[Category:Introductory examples]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Convex hull</title>
    <id>2295</id>
    <revision>
      <id>6068</id>
      <timestamp>2006-06-09T11:13:41Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains articles on computing the [http://en.wikipedia.org/wiki/Convex_hull convex hull] for a set of points. 

[[Image:Scattered_Points.png|framed|Thirteen points in a 2-dimensional plane]]
[[Image:Convex hull.png|framed|A convex hull]]

[[Category:Computational geometry]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Cooley-Tukey FFT algorithm</title>
    <id>1891</id>
    <revision>
      <id>4124</id>
      <timestamp>2006-04-13T18:49:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Fast fourier transform]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm Cooley-Tukey FFT algorithm] is a popular fast Fourier transform algorithm for rapidly computing the discrete fourier transform of a sampled digital signal.

[[Category:Fast fourier transform]]</text>
    </revision>
    <revision>
      <id>4125</id>
      <timestamp>2006-04-13T23:48:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>A bit more info</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm Cooley-Tukey FFT algorithm] is a popular fast Fourier transform algorithm for rapidly computing the discrete fourier transform of a sampled digital signal. It applies best to signal vectors whose lengths are highly composite, usually a power of 2.

[[Category:Fast fourier transform]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Counting sort</title>
    <id>1461</id>
    <revision>
      <id>1864</id>
      <timestamp>2006-03-03T20:18:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Counting_sort counting sort], a very simple but efficient specialized sorting algorithm suitable for lists with a small number of possible element values.

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Cryptography</title>
    <id>1318</id>
    <revision>
      <id>1376</id>
      <timestamp>2006-02-28T20:24:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Security]]</comment>
      <text xml:space="preserve">This category contains articles giving implementations and use cases of cryptography algorithms and best practices.

[[Category:Security]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Data structures</title>
    <id>3809</id>
    <revision>
      <id>1609</id>
      <timestamp>2006-03-03T02:36:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Algorithms and data structures]]</comment>
      <text xml:space="preserve">[[Category:Algorithms and data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Data types</title>
    <id>2622</id>
    <revision>
      <id>7226</id>
      <timestamp>2006-08-11T19:15:38Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">[[Category:Algorithms and data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Databases</title>
    <id>2857</id>
    <revision>
      <id>8303</id>
      <timestamp>2006-12-03T10:12:52Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>create</comment>
      <text xml:space="preserve">:''Six thousand years ago, the Sumerians invented writing for transaction processing.  The earliest known writing is found on clay tablets recording the royal inventory of taxes, land, grain, cattle, slaves, and gold; scribes evidently kept records of each transaction.'' &amp;mdash; Gray &amp; Reuter</text>
    </revision>
    <revision>
      <id>8304</id>
      <timestamp>2006-12-03T10:17:57Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>box (and lengthen) quote</comment>
      <text xml:space="preserve">&lt;div style=&quot;border: 1px solid #ddf; background-color: #eef; margin: 0 auto 1em auto; padding: .2em&quot;&gt;
''Six thousand years ago, the Sumerians invented writing for transaction processing.  The earliest known writing is found on clay tablets recording the royal inventory of taxes, land, grain, cattle, slaves, and gold; scribes evidently kept records of each transaction. ... The Sumerians' approach allowed the scribes to easily ask questions about the current and past state, while providing a historical record of how the system got to the present state.'' &amp;mdash; Gray &amp; Reuter
&lt;/div&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Dates</title>
    <id>2620</id>
    <revision>
      <id>7224</id>
      <timestamp>2006-08-11T19:12:55Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">[[Category:Data Types]]</text>
    </revision>
    <revision>
      <id>7281</id>
      <timestamp>2006-08-13T23:12:21Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>case</comment>
      <text xml:space="preserve">[[Category:Data types]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Decorator pattern</title>
    <id>1679</id>
    <revision>
      <id>2685</id>
      <timestamp>2006-03-06T21:17:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Depth-first search</title>
    <id>1901</id>
    <revision>
      <id>4187</id>
      <timestamp>2006-04-20T00:21:58Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Depth-first_search depth-first search], a simple graph search algorithm. Compared to [[Category:Breadth-first search|breadth-first search]], it is more space efficient but doesn't always find the shortest path.

[[Category:Graph search algorithms]]</text>
    </revision>
    <revision>
      <id>4188</id>
      <timestamp>2006-04-20T00:22:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Syntax</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Depth-first_search depth-first search], a simple graph search algorithm. Compared to [[:Category:Breadth-first search|breadth-first search]], it is more space efficient but doesn't always find the shortest path.

[[Category:Graph search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Design Patterns</title>
    <id>1608</id>
    <revision>
      <id>2356</id>
      <timestamp>2006-03-05T14:19:48Z</timestamp>
      <contributor>
        <ip>85.164.8.153</ip>
      </contributor>
      <text xml:space="preserve">This category contains programs relating to the field of 
[http://en.wikipedia.org/wiki/Design_pattern_%28computer_science%29 Design Patterns].</text>
    </revision>
    <revision>
      <id>2382</id>
      <timestamp>2006-03-05T20:36:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Stick this in [[Category:Software engineering]]</comment>
      <text xml:space="preserve">This category contains programs relating to the field of 
[http://en.wikipedia.org/wiki/Design_pattern_%28computer_science%29 Design Patterns].

[[Category:Software engineering]]</text>
    </revision>
    <revision>
      <id>2384</id>
      <timestamp>2006-03-05T20:38:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Casing</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Design patterns</title>
    <id>1614</id>
    <revision>
      <id>2385</id>
      <timestamp>2006-03-05T20:39:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Copied from [[:Category:Design Patterns]]</comment>
      <text xml:space="preserve">This category contains programs relating to the field of 
[http://en.wikipedia.org/wiki/Design_pattern_%28computer_science%29 Design Patterns].

[[Category:Software engineering]]</text>
    </revision>
    <revision>
      <id>2392</id>
      <timestamp>2006-03-05T21:10:51Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>improve description</comment>
      <text xml:space="preserve">This category contains demonstrations of specific
[http://en.wikipedia.org/wiki/Design_pattern_%28computer_science%29 design patterns].

[[Category:Software engineering]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Developing</title>
    <id>1478</id>
    <revision>
      <id>1927</id>
      <timestamp>2006-03-04T00:17:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles currently under development and not yet ready to download, build, and run.</text>
    </revision>
    <revision>
      <id>1929</id>
      <timestamp>2006-03-04T00:18:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles currently under development and not yet ready to download, build, and run. Articles can be placed in this category by placing the template {{tl|Develop}} at the top of the article.</text>
    </revision>
    <revision>
      <id>11724</id>
      <timestamp>2007-11-25T13:17:49Z</timestamp>
      <contributor>
        <ip>194.69.1.23</ip>
      </contributor>
      <text xml:space="preserve">lichielc
This category contains articles currently under development and not yet ready to download, build, and run. Articles can be placed in this category by placing the template {{tl|Develop}} at the top of the article.</text>
    </revision>
    <revision>
      <id>11730</id>
      <timestamp>2007-11-25T14:01:22Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/194.69.1.23|194.69.1.23]] ([[User_talk:194.69.1.23|194.69.1.23]]); changed back to last version by [[User:Deco|Deco]]</comment>
      <text xml:space="preserve">This category contains articles currently under development and not yet ready to download, build, and run. Articles can be placed in this category by placing the template {{tl|Develop}} at the top of the article.</text>
    </revision>
    <revision>
      <id>11815</id>
      <timestamp>2007-12-11T00:33:55Z</timestamp>
      <contributor>
        <ip>203.147.0.30</ip>
      </contributor>
      <text xml:space="preserve">[professional web development|http://begin.servemp3.com/blog/professional-web.html] [[http://begin.servemp3.com/blog/professional-web.html professional web development]] [http://begin.servemp3.com/blog/professional-web.html|professional web development] ((http://begin.servemp3.com/blog/professional-web.html professional web development)) [[http://begin.servemp3.com/blog/professional-web.html | professional web development]] &quot;professional web development&quot;:http://begin.servemp3.com/blog/professional-web.html [web page promotion|http://aeolus.servemp3.com/web-page-promotion.html] [[http://aeolus.servemp3.com/web-page-promotion.html web page promotion]] [http://aeolus.servemp3.com/web-page-promotion.html|web page promotion] ((http://aeolus.servemp3.com/web-page-promotion.html web page promotion)) [[http://aeolus.servemp3.com/web-page-promotion.html | web page promotion]] &quot;web page promotion&quot;:http://aeolus.servemp3.com/web-page-promotion.html [brunei|http://nonino.servemp3.com/article/brunei.html] [[http://nonino.servemp3.com/article/brunei.html brunei]] [http://nonino.servemp3.com/article/brunei.html|brunei] ((http://nonino.servemp3.com/article/brunei.html brunei)) [[http://nonino.servemp3.com/article/brunei.html | brunei]] &quot;brunei&quot;:http://nonino.servemp3.com/article/brunei.html [sanandreas|http://copied.servemp3.com/text/sanandreas.html] [[http://copied.servemp3.com/text/sanandreas.html sanandreas]] [http://copied.servemp3.com/text/sanandreas.html|sanandreas] ((http://copied.servemp3.com/text/sanandreas.html sanandreas)) [[http://copied.servemp3.com/text/sanandreas.html | sanandreas]] &quot;sanandreas&quot;:http://copied.servemp3.com/text/sanandreas.html [organized living|http://wiving.servemp3.com/organized-living.htm] [[http://wiving.servemp3.com/organized-living.htm organized living]] [http://wiving.servemp3.com/organized-living.htm|organized 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This category contains articles currently under development and not yet ready to download, build, and run. Articles can be placed in this category by placing the template {{tl|Develop}} at the top of the article.</text>
    </revision>
    <revision>
      <id>11818</id>
      <timestamp>2007-12-11T05:55:41Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles currently under development and not yet ready to download, build, and run. Articles can be placed in this category by placing the template {{tl|Develop}} at the top of the article.</text>
    </revision>
  </page>
  <page>
    <title>Category:Digital signal processing</title>
    <id>3303</id>
    <revision>
      <id>12348</id>
      <timestamp>2008-01-28T15:12:53Z</timestamp>
      <contributor>
        <username>Kugland</username>
        <id>1618</id>
      </contributor>
      <text xml:space="preserve">Digital signal processing</text>
    </revision>
  </page>
  <page>
    <title>Category:Dijkstra's algorithm</title>
    <id>2245</id>
    <revision>
      <id>5695</id>
      <timestamp>2006-06-02T07:57:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, links, category</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Dijkstra's_algorithm Dijkstra's algorithm] is a [[:Category:Graph algorithms|graph algorithm]] that simultaneously finds the '''shortest path''' from a single vertex in a weighted graph to all other vertices in the graph, called the single-source shortest path problem. It works for directed and undirected graphs, but unlike the more sophisticated [[:Category:Bellman-Ford algorithm]], requires nonnegative edge weights.

&lt;noinclude&gt;
If the edge weights are all fixed and equal, a better solution is [[:Category:Breadth-first search]].

If the graph is embedded in the plane, as the roads on a map, and just a path between two points is desired, a better solution is [[:Category:A* search]].

[[Category:Shortest path algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5813</id>
      <timestamp>2006-06-03T21:18:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Dijkstra's_algorithm Dijkstra's algorithm] is a [[:Category:Graph algorithms|graph algorithm]] that simultaneously finds the '''shortest path''' from a single vertex in a weighted graph to all other vertices in the graph, called the single-source shortest path problem. It works for directed and undirected graphs, but unlike the more sophisticated [[:Category:Bellman-Ford algorithm|Bellman-Ford algorithm]], requires nonnegative edge weights.

&lt;noinclude&gt;
If the edge weights are all fixed and equal, a better solution is [[:Category:Breadth-first search]].

If the graph is embedded in the plane, as the roads on a map, and just a path between two points is desired, a better solution is [[:Category:A* search]].

[[Category:Shortest path algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>17080</id>
      <timestamp>2011-03-10T22:47:33Z</timestamp>
      <contributor>
        <username>Ruud Koot</username>
        <id>2228</id>
      </contributor>
      <comment>Bellman-Ford isn't &quot;more sophisticated&quot;</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Dijkstra's_algorithm Dijkstra's algorithm] is a [[:Category:Graph algorithms|graph algorithm]] that simultaneously finds the '''shortest path''' from a single vertex in a weighted graph to all other vertices in the graph, called the single-source shortest path problem. It works for directed and undirected graphs, but unlike the [[:Category:Bellman-Ford algorithm|Bellman-Ford algorithm]], requires nonnegative edge weights.

&lt;noinclude&gt;
If the edge weights are all fixed and equal, a better solution is [[:Category:Breadth-first search]].

If the graph is embedded in the plane, as the roads on a map, and just a path between two points is desired, a better solution is [[:Category:A* search]].

[[Category:Shortest path algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Discrete and symbolic mathematics</title>
    <id>1362</id>
    <revision>
      <id>1580</id>
      <timestamp>2006-03-03T01:41:57Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">* [[:Category:Number theory]]
* [[:Category:Symbolic mathematics]]</text>
    </revision>
    <revision>
      <id>1625</id>
      <timestamp>2006-03-03T03:04:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Eliminate links, now subcats</comment>
      <text xml:space="preserve" />
    </revision>
    <revision>
      <id>4352</id>
      <timestamp>2006-05-03T18:13:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Cat:Top-level subject areas</comment>
      <text xml:space="preserve">[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Discrete fourier transform</title>
    <id>1889</id>
    <revision>
      <id>4121</id>
      <timestamp>2006-04-13T18:34:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Discrete_Fourier_transform discrete fourier transform], a signal processing transformation used to decompose a signal into its component frequencies.

[[Category:Signal processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Disjoint set data structure</title>
    <id>1726</id>
    <revision>
      <id>2911</id>
      <timestamp>2006-03-08T07:04:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description and [[Category:Data structures]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Disjoint-set_data_structure disjoint set data structure], also known as a union-find set, is a data structure that keeps track of a partitioning of a set of elements over time as certain operations are done. The three main operations are:

* '''MakeSet''': Create a new partition containing a single given element.
* '''Find''': Figure out which partition a given element is in.
* '''Merge/Union''': Merge two partitions into a single partition.

There are several solutions to this problem. The most efficient known and most commonly used is disjoint set forests with path compression and the union rank heuristic, which has a performance of O(&amp;alpha;(''n'')) amortized time per operation, where &amp;alpha;(''n'') is a very slowly growing function that never for all practical purposes exceeds 5.

[[Category:Data structures]]</text>
    </revision>
    <revision>
      <id>2915</id>
      <timestamp>2006-03-08T08:07:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>noinclude</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Disjoint-set_data_structure disjoint set data structure], also known as a union-find set, is a data structure that keeps track of a partitioning of a set of elements over time as certain operations are done. The three main operations are:

* '''MakeSet''': Create a new partition containing a single given element.
* '''Find''': Figure out which partition a given element is in.
* '''Merge/Union''': Merge two partitions into a single partition.

There are several solutions to this problem. The most efficient known and most commonly used is disjoint set forests with path compression and the union rank heuristic, which has a performance of O(&amp;alpha;(''n'')) amortized time per operation, where &amp;alpha;(''n'') is a very slowly growing function that never for all practical purposes exceeds 5.

&lt;noinclude&gt;
[[Category:Data structures]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2916</id>
      <timestamp>2006-03-08T08:18:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>+never</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Disjoint-set_data_structure disjoint set data structure], also known as a union-find set, is a data structure that keeps track of a partitioning of a set of elements over time as certain operations are done. The three main operations are:

* '''MakeSet''': Create a new partition containing a single given element.
* '''Find''': Figure out which partition a given element is in.
* '''Merge/Union''': Merge two partitions into a single partition.

There are several solutions to this problem. The most efficient known and most commonly used is disjoint set forests with path compression and the union rank heuristic, which has a performance of O(&amp;alpha;(''n'')) amortized time per operation, where &amp;alpha;(''n'') is a very slowly growing function that never for all practical purposes never exceeds 5.

&lt;noinclude&gt;
[[Category:Data structures]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2933</id>
      <timestamp>2006-03-08T09:54:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Double never</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Disjoint-set_data_structure disjoint set data structure], also known as a union-find set, is a data structure that keeps track of a partitioning of a set of elements over time as certain operations are done. The three main operations are:

* '''MakeSet''': Create a new partition containing a single given element.
* '''Find''': Figure out which partition a given element is in.
* '''Merge/Union''': Merge two partitions into a single partition.

There are several solutions to this problem. The most efficient known and most commonly used is disjoint set forests with path compression and the union rank heuristic, which has a performance of O(&amp;alpha;(''n'')) amortized time per operation, where &amp;alpha;(''n'') is a very slowly growing function that for all practical purposes never exceeds 5.

&lt;noinclude&gt;
[[Category:Data structures]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Dithering</title>
    <id>1927</id>
    <revision>
      <id>4310</id>
      <timestamp>2006-04-28T22:15:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, Wikipedia link, category</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Dithering Dithering] is a technique that adds noise to an image to reduce artifacts such as color banding and create an impression of an image more similar to the original. It is often used, for example, when displaying photographs on 256-color devices. The most popular is [[Category:Floyd-Steinberg dithering|Floyd-Steinberg dithering]].

[[Category:Image processing]]</text>
    </revision>
    <revision>
      <id>4311</id>
      <timestamp>2006-04-28T22:15:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Colon</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Dithering Dithering] is a technique that adds noise to an image to reduce artifacts such as color banding and create an impression of an image more similar to the original. It is often used, for example, when displaying photographs on 256-color devices. The most popular is [[:Category:Floyd-Steinberg dithering|Floyd-Steinberg dithering]].

[[Category:Image processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Domain-specific</title>
    <id>3072</id>
    <revision>
      <id>9483</id>
      <timestamp>2007-03-15T08:15:01Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Domain-specific_programming_language domain-specific] language is a tool intended for, and tailored to, a specific use.</text>
    </revision>
  </page>
  <page>
    <title>Category:Double-ended dynamic array</title>
    <id>1813</id>
    <revision>
      <id>3505</id>
      <timestamp>2006-03-22T12:38:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Dynamic array]]</comment>
      <text xml:space="preserve">A double-ended dynamic array is a type of dynamic array in which the data is stored in the middle of the allocated array, with free space on both sides. This allows us to add and remove from either end in amortized constant time while preserving ordinary indexing (although unlike in an ordinary dynamic array, the base index changes over time).

[[Category:Dynamic array]]</text>
    </revision>
    <revision>
      <id>3506</id>
      <timestamp>2006-03-22T12:38:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>std::deque</comment>
      <text xml:space="preserve">A double-ended dynamic array is a type of dynamic array in which the data is stored in the middle of the allocated array, with free space on both sides. This allows us to add and remove from either end in amortized constant time while preserving ordinary indexing (although unlike in an ordinary dynamic array, the base index changes over time). The primary mainstream implementation is C++'s &lt;code&gt;std::deque&lt;/code&gt;.

[[Category:Dynamic array]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Doubly linked list</title>
    <id>1416</id>
    <revision>
      <id>1738</id>
      <timestamp>2006-03-03T12:33:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Linked list]]</comment>
      <text xml:space="preserve">[[Category:Linked list]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Dynamic array</title>
    <id>1812</id>
    <revision>
      <id>3504</id>
      <timestamp>2006-03-22T12:34:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Data structures]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Dynamic_array dynamic array] is a simple array data structure that automatically resizes to accomodate an unlimited number of elements. Insertions at the end require only amortized constant time, at the expense of worst-case linear reserved space being wasted. It is known by many names, including:
* dynamic array
* growable array
* resizable array
* dynamic table
* array list
* vector (as in C++'s std::vector)
* ArrayList (Java and .NET call it this)

See also [[:Category:Double-ended dynamic array|Double-ended dynamic array]].

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Dynamic programming</title>
    <id>2832</id>
    <revision>
      <id>8206</id>
      <timestamp>2006-11-28T03:16:14Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Dynamic programming</comment>
      <text xml:space="preserve">This category contains algorithms implemented using [http://en.wikipedia.org/wiki/Dynamic_programming dynamic programming].

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Educational</title>
    <id>2955</id>
    <revision>
      <id>8771</id>
      <timestamp>2007-02-01T11:03:39Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial cat</comment>
      <text xml:space="preserve">This category contains articles relating to educational software &amp;mdash; software aimed at students or novice computer users, where the main goal is teaching and self-education.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>8775</id>
      <timestamp>2007-02-01T18:02:56Z</timestamp>
      <contributor>
        <ip>168.156.170.61</ip>
      </contributor>
      <text xml:space="preserve">{{speedy}}
{{spam}}
{{junk}}
{{delete}}
{{copyvio}}

This category contains articles relating to educational software &amp;mdash; software aimed at students or novice computer users, where the main goal is teaching and self-education.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>8785</id>
      <timestamp>2007-02-01T19:31:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert lots of templates</comment>
      <text xml:space="preserve">This category contains articles relating to educational software &amp;mdash; software aimed at students or novice computer users, where the main goal is teaching and self-education.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Eight queens puzzle</title>
    <id>2915</id>
    <revision>
      <id>8569</id>
      <timestamp>2007-01-16T08:10:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Eight_queens_puzzle eight queens problem] is the problem of placing eight queens on an 8&amp;times;8 chessboard such that none of them attack one another (no two are in the same row, column, or diagonal). More generally, the ''n'' queens problem places ''n'' queens on an ''n''&amp;times;''n'' chessboard.&lt;noinclude&gt;
''This category not yet categorized.''
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>9662</id>
      <timestamp>2007-04-05T00:50:16Z</timestamp>
      <contributor>
        <ip>68.228.231.24</ip>
      </contributor>
      <comment>categorized</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Eight_queens_puzzle eight queens problem] is the problem of placing eight queens on an 8&amp;times;8 chessboard such that none of them attack one another (no two are in the same row, column, or diagonal). More generally, the ''n'' queens problem places ''n'' queens on an ''n''&amp;times;''n'' chessboard.&lt;noinclude&gt;
&lt;/noinclude&gt;

[[Category:Games and entertainment]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:.NET</title>
    <id>2159</id>
    <revision>
      <id>5093</id>
      <timestamp>2006-05-21T12:28:41Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/.NET_Framework .NET Framework].

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:All POSIX</title>
    <id>1768</id>
    <revision>
      <id>3154</id>
      <timestamp>2006-03-11T00:01:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written for [[http://en.wikipedia.org/wiki/Posix POSIX]] compatible systems.

[[Category:Environments]]</text>
    </revision>
    <revision>
      <id>15818</id>
      <timestamp>2009-01-07T20:53:21Z</timestamp>
      <contributor>
        <ip>66.201.219.17</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_casitmontrd.com/</text>
    </revision>
    <revision>
      <id>15819</id>
      <timestamp>2009-01-07T22:03:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/66.201.219.17|66.201.219.17]] ([[User_talk:66.201.219.17|66.201.219.17]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written for [[http://en.wikipedia.org/wiki/Posix POSIX]] compatible systems.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:DOS</title>
    <id>2612</id>
    <revision>
      <id>7174</id>
      <timestamp>2006-08-09T02:46:33Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>description</comment>
      <text xml:space="preserve">This category contains articles describing code written to run under the DOS environment. Since the Windows 2.x/3.x/95/98/ME environments are built on top of the DOS environment and the Windows NT/2000/XP environments contain a DOS compatible subsystem, it is fairly like that code in this category will also run on Windows.</text>
    </revision>
    <revision>
      <id>7175</id>
      <timestamp>2006-08-09T02:47:09Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">This category contains articles describing code written to run under the DOS environment. Since the Windows 2.x/3.x/95/98/ME environments are built on top of the DOS environment and the Windows NT/2000/XP environments contain a DOS compatible subsystem, it is fairly likely that code in this category will also run on Windows.</text>
    </revision>
    <revision>
      <id>7176</id>
      <timestamp>2006-08-09T02:48:50Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>clarify</comment>
      <text xml:space="preserve">This category contains articles describing code written to run under the DOS environment. Since the Windows 2.x/3.x/95/98/ME environments are built on top of the DOS environment and the Windows NT/2000/XP environments contain a DOS compatible subsystem, it is fairly likely that code in this category will also run on Windows although it should not make any use of Windows specific features.</text>
    </revision>
    <revision>
      <id>7459</id>
      <timestamp>2006-08-21T16:55:07Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Category:Environments]]</comment>
      <text xml:space="preserve">This category contains articles describing code written to run under the DOS environment. Since the Windows 2.x/3.x/95/98/ME environments are built on top of the DOS environment and the Windows NT/2000/XP environments contain a DOS compatible subsystem, it is fairly likely that code in this category will also run on Windows although it should not make any use of Windows specific features.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Linux</title>
    <id>1898</id>
    <revision>
      <id>4153</id>
      <timestamp>2006-04-15T19:27:25Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written for [http://en.wikipedia.org/wiki/Linux Linux] systems.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Mac OS X</title>
    <id>3269</id>
    <revision>
      <id>11934</id>
      <timestamp>2008-01-02T23:31:01Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category describes programs written to run under Apple Computer's Mac OS X. The primary programming language used is [[:Category:Programming language:Objective-C|Objective-C]] using the [[Cocoa]] application framework. There are also native [[Java]] interfaces to Cocoa. The operating system is built on [[FreeBSD]] running on top of the [[Mach]] microkernel, so [[POSIX]] compilant programs are also easy to port.
[[Category:Environments]]</text>
    </revision>
    <revision>
      <id>11938</id>
      <timestamp>2008-01-03T06:15:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>link categories</comment>
      <text xml:space="preserve">This category describes programs written to run under Apple Computer's Mac OS X. The primary programming language used is [[:Category:Programming language:Objective-C|Objective-C]] using the [[Cocoa]] application framework. There are also native [[:Category:Programming language:Java|Java]] interfaces to Cocoa. The operating system is built on [[:Category:Environment:FreeBSD|FreeBSD]] running on top of the [[Mach]] microkernel, so [[:Category:Environment:All POSIX|POSIX]] compilant programs are also easy to port.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:NetBSD</title>
    <id>1882</id>
    <revision>
      <id>4077</id>
      <timestamp>2006-04-10T20:12:44Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written for [http://en.wikipedia.org/wiki/NetBSD NetBSD] systems.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:OS independent</title>
    <id>3816</id>
    <revision>
      <id>6652</id>
      <timestamp>2006-07-09T20:43:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains implementations that can run on any operating system on which their language interpreter runs.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Platform independent</title>
    <id>2276</id>
    <revision>
      <id>5969</id>
      <timestamp>2006-06-06T03:51:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains implementations that can run on any platform on which their language interpreter runs, and applies to most implementations in interpreted languages that don't depend on platform-specific libraries.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Portable</title>
    <id>3508</id>
    <revision>
      <id>1309</id>
      <timestamp>2006-02-28T09:50:56Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Brief description</comment>
      <text xml:space="preserve">This category contains articles describing code written to be portable to many different environments.</text>
    </revision>
    <revision>
      <id>1507</id>
      <timestamp>2006-03-02T23:24:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Environments]]</comment>
      <text xml:space="preserve">This category contains articles describing code written to be portable to many different environments.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Windows</title>
    <id>1910</id>
    <revision>
      <id>4222</id>
      <timestamp>2006-04-21T20:09:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/Microsoft_Windows Microsoft Windows] family of operating systems.</text>
    </revision>
    <revision>
      <id>4231</id>
      <timestamp>2006-04-21T22:34:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Category:Environments</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/Microsoft_Windows Microsoft Windows] family of operating systems.

[[Category:Environments]]</text>
    </revision>
    <revision>
      <id>11935</id>
      <timestamp>2008-01-02T23:37:54Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>== Win32</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/Microsoft_Windows Microsoft Windows] family of operating systems. This interface is also known as '''Win32''', often programmed in [[C++]] or [[C]]. Microsoft has deprecated this interface in favor of [[.NET]] and the languages implemented for it, such as [[C#]].

[[Category:Environments]]</text>
    </revision>
    <revision>
      <id>11937</id>
      <timestamp>2008-01-03T06:13:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>link to categories</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/Microsoft_Windows Microsoft Windows] family of operating systems. This interface is also known as '''Win32''', often programmed in [[:Category:Programming language:C Plus Plus|C++]] or [[:Category:Programming language:C|C]]. Microsoft has deprecated this interface in favor of [[:Category:Environment:.NET|.NET]] and the languages implemented for it, such as [[:Category:Programming language:C Sharp|C#]].

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Windows 2000</title>
    <id>2948</id>
    <revision>
      <id>8737</id>
      <timestamp>2007-01-29T01:10:09Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>&quot;enabled&quot; page</comment>
      <text xml:space="preserve">This category contains articles describing programs running in the [http://en.wikipedia.org/wiki/Windows_2000 Microsoft Windows 2000] operating system.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:Windows XP</title>
    <id>2408</id>
    <revision>
      <id>6653</id>
      <timestamp>2006-07-09T20:46:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing programs running in the [http://en.wikipedia.org/wiki/Windows_XP Microsoft Windows XP] operating system.

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environment:X Window System</title>
    <id>1999</id>
    <revision>
      <id>4805</id>
      <timestamp>2006-05-16T19:49:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created, text</comment>
      <text xml:space="preserve">This category contains code written for [http://en.wikipedia.org/wiki/X_Window_System X Window System] (Also called ''X11'' or just ''X'').

[[Category:Environments]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Environments</title>
    <id>1348</id>
    <revision>
      <id>1508</id>
      <timestamp>2006-03-02T23:26:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains various environments (hardware platforms and/or operating systems) in which code can run. Everything listed here should also be listed in the template [[Template:List of environment categories]].</text>
    </revision>
  </page>
  <page>
    <title>Category:Euclidean algorithm</title>
    <id>1979</id>
    <revision>
      <id>4588</id>
      <timestamp>2006-05-12T15:57:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, cat</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] is an efficient method for computing the greatest common divisor of two natural numbers (or polynomials, or any other object with the necessary structure), and was one of the first known algorithms to be described formally. It is based on the two identities:

:''a'' &gt; ''b'' implies: gcd(''a'', ''b'') = \gcd(''b'', ''a'' \mbox{ mod } ''b'')
:gcd(''a'', 0) = ''a''

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>4589</id>
      <timestamp>2006-05-12T15:57:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Kill TeX markup</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] is an efficient method for computing the greatest common divisor of two natural numbers (or polynomials, or any other object with the necessary structure), and was one of the first known algorithms to be described formally. It is based on the two identities:

:''a'' &gt; ''b'' implies: gcd(''a'', ''b'') = gcd(''b'', ''a'' mod ''b'')
:gcd(''a'', 0) = ''a''

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>10762</id>
      <timestamp>2007-07-26T16:56:39Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>+cat:intro</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] is an efficient method for computing the greatest common divisor of two natural numbers (or polynomials, or any other object with the necessary structure), and was one of the first known algorithms to be described formally. It is based on the two identities:

:''a'' &gt; ''b'' implies: gcd(''a'', ''b'') = gcd(''b'', ''a'' mod ''b'')
:gcd(''a'', 0) = ''a''

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Exponential and logarithm functions</title>
    <id>2717</id>
    <revision>
      <id>7720</id>
      <timestamp>2006-10-03T06:23:02Z</timestamp>
      <contributor>
        <ip>211.28.126.76</ip>
      </contributor>
      <comment>Add entry for logarithm function</comment>
      <text xml:space="preserve">See also [http://en.wikipedia.org/wiki/Exponential_function Exponential functions] on Wikipedia.

* Logarithm Function (Python)

[[Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>7721</id>
      <timestamp>2006-10-03T06:23:52Z</timestamp>
      <contributor>
        <ip>211.28.126.76</ip>
      </contributor>
      <comment>oops forgot link</comment>
      <text xml:space="preserve">See also [http://en.wikipedia.org/wiki/Exponential_function Exponential functions] on Wikipedia.

* [[Logarithm Function (Python)]]

[[Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>8080</id>
      <timestamp>2006-11-16T22:11:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>don't need this link</comment>
      <text xml:space="preserve">See also [http://en.wikipedia.org/wiki/Exponential_function Exponential functions] on Wikipedia.

[[Category:Numerical special functions]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Exponentiation by squaring</title>
    <id>2732</id>
    <revision>
      <id>7826</id>
      <timestamp>2006-10-15T17:41:07Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>create per Special:WantedPages</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Exponentiation_by_squaring exponentiation by squaring], an algorithm used for the fast computation of large integer powers of a number.

It is also known as binary exponentiation, because it analyzes the exponent as a binary number, shifting bit by bit, instead of as a natural number, decrementing predecessor by predecessor.</text>
    </revision>
  </page>
  <page>
    <title>Category:Extended Euclidean algorithm</title>
    <id>2589</id>
    <revision>
      <id>7036</id>
      <timestamp>2006-07-18T11:07:23Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">The '''extended Euclidean algorithm''' is an algorithm used to calculate the greatest common divisor (gcd, or also highest common factor, HCF) of two integers ''a'' and ''b'', as well as integers ''x'' and ''y'' such that
:&lt;math&gt;ax + by = \gcd(a, b). \,&lt;/math&gt;
The algorithm is essentially the same as the Euclidean algorithm, but keeps track of the quotient during the computation in order to find ''x'' and ''y'' as above.

The extended Euclidean algorithm is particularly useful when ''a'' and ''b'' are coprime, since ''x'' is the multiplicative inverse of ''a'' modulo ''b''.

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>7037</id>
      <timestamp>2006-07-18T13:16:08Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{Shared text box |
The '''extended Euclidean algorithm''' is an algorithm used to calculate the greatest common divisor (gcd, or also highest common factor, HCF) of two integers ''a'' and ''b'', as well as integers ''x'' and ''y'' such that
:&lt;math&gt;ax + by = \gcd(a, b). \,&lt;/math&gt;
The algorithm is essentially the same as the Euclidean algorithm, but keeps track of the quotient during the computation in order to find ''x'' and ''y'' as above.

The extended Euclidean algorithm is particularly useful when ''a'' and ''b'' are coprime, since ''x'' is the multiplicative inverse of ''a'' modulo ''b''.
}}

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Facade pattern</title>
    <id>1680</id>
    <revision>
      <id>2686</id>
      <timestamp>2006-03-06T21:17:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Factorials with prime factorization</title>
    <id>1773</id>
    <revision>
      <id>3167</id>
      <timestamp>2006-03-11T07:06:39Z</timestamp>
      <contributor>
        <ip>131.107.0.84</ip>
      </contributor>
      <comment>Copied content from [[Factorials with prime factorization (Python)]]</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;
The ''n''th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

This implementation is based on the following references:

* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''
&lt;/div&gt;</text>
    </revision>
    <revision>
      <id>3175</id>
      <timestamp>2006-03-11T09:09:30Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Note that sum is finite</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;
The ''n''th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

Notice that this is actually a finite sum, since the floor is zero whenever &lt;math&gt;p^i &gt; n&lt;/math&gt;. This implementation is based on the following references:

* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''
&lt;/div&gt;</text>
    </revision>
    <revision>
      <id>4354</id>
      <timestamp>2006-05-03T18:37:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Cat:Number theory</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;
The ''n''th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

Notice that this is actually a finite sum, since the floor is zero whenever &lt;math&gt;p^i &gt; n&lt;/math&gt;. This implementation is based on the following references:

* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''
&lt;/div&gt;

[[Category:Number theory]]</text>
    </revision>
    <revision>
      <id>6208</id>
      <timestamp>2006-06-13T03:01:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>noinclude parent cat</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;
The ''n''th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

Notice that this is actually a finite sum, since the floor is zero whenever &lt;math&gt;p^i &gt; n&lt;/math&gt;. This implementation is based on the following references:

* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''
&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Factory method pattern</title>
    <id>1673</id>
    <revision>
      <id>2679</id>
      <timestamp>2006-03-06T21:15:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Fast fourier transform</title>
    <id>1890</id>
    <revision>
      <id>4122</id>
      <timestamp>2006-04-13T18:38:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Discrete fourier transform]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Fast_Fourier_transform fast Fourier transform] is a fast, typically O(''n'' log ''n'') algorithm for computing the discrete fourier transform of a signal.

[[Category:Discrete fourier transform]]</text>
    </revision>
    <revision>
      <id>4123</id>
      <timestamp>2006-04-13T18:47:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+The most common by far is the [[:Category:Cooley-Tukey FFT algorithm|Cooley-Tukey FFT algorithm]].</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Fast_Fourier_transform fast Fourier transform] (FFT) is a fast, typically O(''n'' log ''n'') algorithm for computing the discrete fourier transform of a signal. The most common by far is the [[:Category:Cooley-Tukey FFT algorithm|Cooley-Tukey FFT algorithm]].

[[Category:Discrete fourier transform]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Feed forward neural networks</title>
    <id>2814</id>
    <revision>
      <id>8175</id>
      <timestamp>2006-11-26T03:05:48Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Feed forward neural networks</comment>
      <text xml:space="preserve">A category for different kinds of [http://en.wikipedia.org/wiki/Feedforward_neural_networks feed-forward neural networks].

[[Category:Artificial neural networks]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Fibonacci heap</title>
    <id>2380</id>
    <revision>
      <id>6475</id>
      <timestamp>2006-06-24T05:27:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat, link</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Fibonacci_heap Fibonacci heap] is a concrete heap data structure that is efficient in practice and provides constant amortized time bounds for several important operations: it can insert a node, find the minimum value, decrease a node's key, and union two heaps in amortized constant time; deleting a key still requires O(log ''n'') time.

[[Category:Heap]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Fibonacci numbers</title>
    <id>1654</id>
    <revision>
      <id>2596</id>
      <timestamp>2006-03-06T17:05:02Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. They are often used as an introductory example of [http://en.wikipedia.org/wiki/Recursion recursion].

[[Category:Number theory]]
[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>2601</id>
      <timestamp>2006-03-06T17:10:48Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases}.
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

[[Category:Number theory]]
[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>2638</id>
      <timestamp>2006-03-06T20:24:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Mark categories noinclude</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases}.
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2746</id>
      <timestamp>2006-03-07T02:22:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>restyle content to match [[Category:Pi with Machin's formula]]</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Fibonacci numbers=

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases}.
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2748</id>
      <timestamp>2006-03-07T02:24:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>rm title (messes with TOC in implementation pages)</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases}.
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2754</id>
      <timestamp>2006-03-07T03:16:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Put border around math so it isn't so ugly</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:{{border|
&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases}.
&lt;/math&gt;}}

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>3729</id>
      <timestamp>2006-04-03T16:21:17Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>tweak page to force LaTeX re-render</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by

:{{border|
&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;}}

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>3731</id>
      <timestamp>2006-04-03T17:13:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak for math</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:{{border|
&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;}}

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5221</id>
      <timestamp>2006-05-26T20:13:37Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>switch to shared text box template</comment>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:{{border|
&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;}}

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5222</id>
      <timestamp>2006-05-26T20:18:41Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>switch to shared text box template</comment>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>11869</id>
      <timestamp>2007-12-29T21:45:35Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>erpasde</comment>
      <text xml:space="preserve">lialcouno
{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>11918</id>
      <timestamp>2007-12-31T03:10:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>11993</id>
      <timestamp>2008-01-09T15:36:22Z</timestamp>
      <contributor>
        <ip>80.250.210.12</ip>
      </contributor>
      <comment>ortazelvard</comment>
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{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>11996</id>
      <timestamp>2008-01-09T16:25:39Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/80.250.210.12|80.250.210.12]] ([[User_talk:80.250.210.12|80.250.210.12]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci numbers] are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined [http://en.wikipedia.org/wiki/Recursion recursively] by 

:&lt;math&gt;
 F(n) =
 \begin{cases}
   0             &amp; n = 0 \\
   1             &amp; n = 1 \\
   F(n-1)+F(n-2) &amp; n &gt; 1 \\
  \end{cases} .
&lt;/math&gt;

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist. 
}}

&lt;noinclude&gt;
[[Category:Number theory]]
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:File formats</title>
    <id>1316</id>
    <revision>
      <id>1372</id>
      <timestamp>2006-02-28T20:14:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Files and file systems]]</comment>
      <text xml:space="preserve">This category contains articles that load, save, or otherwise process specific persistent file formats.

[[Category:Files and file systems]]</text>
    </revision>
  </page>
  <page>
    <title>Category:File management tools</title>
    <id>1926</id>
    <revision>
      <id>4284</id>
      <timestamp>2006-04-25T19:51:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains implementations of file management tools.

[[Category:Files and file systems]]</text>
    </revision>
  </page>
  <page>
    <title>Category:File processing</title>
    <id>1930</id>
    <revision>
      <id>4316</id>
      <timestamp>2006-04-30T01:25:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code for processing files.

[[Category:Files and file systems]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Files and file systems</title>
    <id>1925</id>
    <revision>
      <id>4283</id>
      <timestamp>2006-04-25T19:47:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category is for articles describing code related to files and file systems.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Finite automaton generators and simulators</title>
    <id>2268</id>
    <revision>
      <id>5921</id>
      <timestamp>2006-06-05T10:49:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Desc, cat</comment>
      <text xml:space="preserve">This category contains machines that generate finite automata, a simple type of state machine that includes the deterministic finite automaton, nondeterministic finite automaton, and pushdown automaton.

[[Category:Abstract machine generators and simulators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Finite automaton string search algorithm</title>
    <id>2180</id>
    <revision>
      <id>5235</id>
      <timestamp>2006-05-27T22:24:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat, image, no link (no article on Wikipedia)</comment>
      <text xml:space="preserve">[[Image:DFA_search_mommy.svg|250px|thumb|DFA for searching for the string &quot;MOMMY&quot;. Each time the double-circled state is reached, a match has been found. All unspecified transitions return to the initial state in the upper left.]]
The finite automaton string search algorithm works by constructing a simple state machine associated with the string being searched for. As it consumes the string being searched, the current state indicates a set of possible positions in the string being searched for. It can be generalized to search for arbitrary regular expressions. For example, to the right is the state machine associated with the search word &quot;MOMMY&quot;. The procedure is a special case of the powerset construction procedure used to transform a nondeterministic finite automaton (NFA) into a deterministic finite automaton, since it is easy to create an NFA that recognizes a particular substring.

[[Category:String search algorithms]]</text>
    </revision>
    <revision>
      <id>5295</id>
      <timestamp>2006-05-28T23:22:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>&lt;noinclude&gt;</comment>
      <text xml:space="preserve">[[Image:DFA_search_mommy.svg|250px|thumb|DFA for searching for the string &quot;MOMMY&quot;. Each time the double-circled state is reached, a match has been found. All unspecified transitions return to the initial state in the upper left.]]
The finite automaton string search algorithm works by constructing a simple state machine associated with the string being searched for. As it consumes the string being searched, the current state indicates a set of possible positions in the string being searched for. It can be generalized to search for arbitrary regular expressions. For example, to the right is the state machine associated with the search word &quot;MOMMY&quot;. The procedure is a special case of the powerset construction procedure used to transform a nondeterministic finite automaton (NFA) into a deterministic finite automaton, since it is easy to create an NFA that recognizes a particular substring.

&lt;noinclude&gt;
[[Category:String search algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>5925</id>
      <timestamp>2006-06-05T10:51:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add to an additional cat</comment>
      <text xml:space="preserve">[[Image:DFA_search_mommy.svg|250px|thumb|DFA for searching for the string &quot;MOMMY&quot;. Each time the double-circled state is reached, a match has been found. All unspecified transitions return to the initial state in the upper left.]]
The finite automaton string search algorithm works by constructing a simple state machine associated with the string being searched for. As it consumes the string being searched, the current state indicates a set of possible positions in the string being searched for. It can be generalized to search for arbitrary regular expressions. For example, to the right is the state machine associated with the search word &quot;MOMMY&quot;. The procedure is a special case of the powerset construction procedure used to transform a nondeterministic finite automaton (NFA) into a deterministic finite automaton, since it is easy to create an NFA that recognizes a particular substring.

&lt;noinclude&gt;
[[Category:String search algorithms]]
[[Category:Finite automaton generators and simulators]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Fisher-Yates shuffle</title>
    <id>3374</id>
    <revision>
      <id>13182</id>
      <timestamp>2008-04-21T08:57:01Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">{{Shared text box|
The '''Fisher-Yates shuffle''' is a most used algorithm for shuffling lists or arrays. In its original wording, you should get a random element from the original list into an accumulator until the original list is empty. In practice, a more convoluted wording is commonly used, which shuffles a list in-place:
# Let &lt;tt&gt;'''A'''&lt;/tt&gt; be the list, &lt;tt&gt;'''N'''&lt;/tt&gt; be its length, &lt;tt&gt;'''A&lt;sub&gt;1&lt;/sub&gt;'''&lt;/tt&gt;&amp;ndash;&lt;tt&gt;'''A&lt;sub&gt;N&lt;/sub&gt;'''&lt;/tt&gt; be its elements. Let &lt;tt&gt;'''i'''&lt;/tt&gt; be &lt;tt&gt;'''N'''&lt;/tt&gt;.
# Let &lt;tt&gt;'''r'''&lt;/tt&gt; be random between 1 and &lt;tt&gt;'''i'''&lt;/tt&gt; (inclusive).
# If &lt;tt&gt;'''i'''&lt;/tt&gt; is not equal to &lt;tt&gt;'''r'''&lt;/tt&gt;, swap &lt;tt&gt;'''A&lt;sub&gt;r&lt;/sub&gt;'''&lt;/tt&gt; and &lt;tt&gt;'''A&lt;sub&gt;i&lt;/sub&gt;'''&lt;/tt&gt;.
# Decrease &lt;tt&gt;'''i'''&lt;/tt&gt; by one.
# Repeat steps 2 through 4 until &lt;tt&gt;'''i'''&lt;/tt&gt; equals 1.
}}</text>
    </revision>
    <revision>
      <id>13186</id>
      <timestamp>2008-04-21T09:21:18Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>category</comment>
      <text xml:space="preserve">{{Shared text box|
The '''Fisher-Yates shuffle''' is a most used algorithm for shuffling lists or arrays. In its original wording, you should get a random element from the original list into an accumulator until the original list is empty. In practice, a more convoluted wording is commonly used, which shuffles a list in-place:
# Let &lt;tt&gt;'''A'''&lt;/tt&gt; be the list, &lt;tt&gt;'''N'''&lt;/tt&gt; be its length, &lt;tt&gt;'''A&lt;sub&gt;1&lt;/sub&gt;'''&lt;/tt&gt;&amp;ndash;&lt;tt&gt;'''A&lt;sub&gt;N&lt;/sub&gt;'''&lt;/tt&gt; be its elements. Let &lt;tt&gt;'''i'''&lt;/tt&gt; be &lt;tt&gt;'''N'''&lt;/tt&gt;.
# Let &lt;tt&gt;'''r'''&lt;/tt&gt; be random between 1 and &lt;tt&gt;'''i'''&lt;/tt&gt; (inclusive).
# If &lt;tt&gt;'''i'''&lt;/tt&gt; is not equal to &lt;tt&gt;'''r'''&lt;/tt&gt;, swap &lt;tt&gt;'''A&lt;sub&gt;r&lt;/sub&gt;'''&lt;/tt&gt; and &lt;tt&gt;'''A&lt;sub&gt;i&lt;/sub&gt;'''&lt;/tt&gt;.
# Decrease &lt;tt&gt;'''i'''&lt;/tt&gt; by one.
# Repeat steps 2 through 4 until &lt;tt&gt;'''i'''&lt;/tt&gt; equals 1.
}}
[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>13187</id>
      <timestamp>2008-04-21T09:44:24Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>grammar</comment>
      <text xml:space="preserve">{{Shared text box|
The '''Fisher-Yates shuffle''' is the most used algorithm for shuffling lists or arrays. In its original wording, you should get a random element from the original list into an accumulator until the original list is empty. In practice, a more convoluted wording is commonly used, which shuffles a list in-place:
# Let &lt;tt&gt;'''A'''&lt;/tt&gt; be the list, &lt;tt&gt;'''N'''&lt;/tt&gt; be its length, &lt;tt&gt;'''A&lt;sub&gt;1&lt;/sub&gt;'''&lt;/tt&gt;&amp;ndash;&lt;tt&gt;'''A&lt;sub&gt;N&lt;/sub&gt;'''&lt;/tt&gt; be its elements. Let &lt;tt&gt;'''i'''&lt;/tt&gt; be &lt;tt&gt;'''N'''&lt;/tt&gt;.
# Let &lt;tt&gt;'''r'''&lt;/tt&gt; be random between 1 and &lt;tt&gt;'''i'''&lt;/tt&gt; (inclusive).
# If &lt;tt&gt;'''i'''&lt;/tt&gt; is not equal to &lt;tt&gt;'''r'''&lt;/tt&gt;, swap &lt;tt&gt;'''A&lt;sub&gt;r&lt;/sub&gt;'''&lt;/tt&gt; and &lt;tt&gt;'''A&lt;sub&gt;i&lt;/sub&gt;'''&lt;/tt&gt;.
# Decrease &lt;tt&gt;'''i'''&lt;/tt&gt; by one.
# Repeat steps 2 through 4 until &lt;tt&gt;'''i'''&lt;/tt&gt; equals 1.
}}
[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>13191</id>
      <timestamp>2008-04-21T17:08:22Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>noinclude cat</comment>
      <text xml:space="preserve">{{Shared text box|
The '''Fisher-Yates shuffle''' is the most used algorithm for shuffling lists or arrays. In its original wording, you should get a random element from the original list into an accumulator until the original list is empty. In practice, a more convoluted wording is commonly used, which shuffles a list in-place:
# Let &lt;tt&gt;'''A'''&lt;/tt&gt; be the list, &lt;tt&gt;'''N'''&lt;/tt&gt; be its length, &lt;tt&gt;'''A&lt;sub&gt;1&lt;/sub&gt;'''&lt;/tt&gt;&amp;ndash;&lt;tt&gt;'''A&lt;sub&gt;N&lt;/sub&gt;'''&lt;/tt&gt; be its elements. Let &lt;tt&gt;'''i'''&lt;/tt&gt; be &lt;tt&gt;'''N'''&lt;/tt&gt;.
# Let &lt;tt&gt;'''r'''&lt;/tt&gt; be random between 1 and &lt;tt&gt;'''i'''&lt;/tt&gt; (inclusive).
# If &lt;tt&gt;'''i'''&lt;/tt&gt; is not equal to &lt;tt&gt;'''r'''&lt;/tt&gt;, swap &lt;tt&gt;'''A&lt;sub&gt;r&lt;/sub&gt;'''&lt;/tt&gt; and &lt;tt&gt;'''A&lt;sub&gt;i&lt;/sub&gt;'''&lt;/tt&gt;.
# Decrease &lt;tt&gt;'''i'''&lt;/tt&gt; by one.
# Repeat steps 2 through 4 until &lt;tt&gt;'''i'''&lt;/tt&gt; equals 1.
}}
&lt;noinclude&gt;
[[Category:Algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>13204</id>
      <timestamp>2008-04-22T09:38:49Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>addition</comment>
      <text xml:space="preserve">{{Shared text box|
The '''Fisher-Yates shuffle''' is the most used algorithm for shuffling lists or arrays. In its original wording, you should get a random element from the original list into an accumulator until the original list is empty. In practice, a more convoluted wording is commonly used, which shuffles a list in-place:
# Let &lt;tt&gt;'''A'''&lt;/tt&gt; be the list, &lt;tt&gt;'''N'''&lt;/tt&gt; be its length, &lt;tt&gt;'''A&lt;sub&gt;1&lt;/sub&gt;'''&lt;/tt&gt;&amp;ndash;&lt;tt&gt;'''A&lt;sub&gt;N&lt;/sub&gt;'''&lt;/tt&gt; be its elements. Let &lt;tt&gt;'''i'''&lt;/tt&gt; be &lt;tt&gt;'''N'''&lt;/tt&gt;.
# Let &lt;tt&gt;'''r'''&lt;/tt&gt; be random between 1 and &lt;tt&gt;'''i'''&lt;/tt&gt; (inclusive).
# If &lt;tt&gt;'''i'''&lt;/tt&gt; is not equal to &lt;tt&gt;'''r'''&lt;/tt&gt;, swap &lt;tt&gt;'''A&lt;sub&gt;r&lt;/sub&gt;'''&lt;/tt&gt; and &lt;tt&gt;'''A&lt;sub&gt;i&lt;/sub&gt;'''&lt;/tt&gt;.
# Decrease &lt;tt&gt;'''i'''&lt;/tt&gt; by one.
# Repeat steps 2 through 4 until &lt;tt&gt;'''i'''&lt;/tt&gt; equals 1.
The algorithm complexity is O(n).
}}
&lt;noinclude&gt;
[[Category:Algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Fixed-point arithmetic</title>
    <id>2762</id>
    <revision>
      <id>8008</id>
      <timestamp>2006-11-14T10:06:00Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Wikipedia article: [http://en.wikipedia.org/wiki/Fixed-point_arithmetic]

[[Category:Numerical computing]]</text>
    </revision>
    <revision>
      <id>10782</id>
      <timestamp>2007-07-27T16:48:31Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>merge from article</comment>
      <text xml:space="preserve">Fixed point mathematics are mainly used on real-time systems, or on terminals with low CPU power. Main reason to this is that fixed point maths use INTEGER type for all calculations even divisions, cosines, sinus and square root. You'll never need FLOAT types or Math CPU. 

== Useful tools before start ==

*[[Cosine table (C)| Cosines tables - full 8 bit circle (0-255)]]
*[[Tangents tables - half 8 bit circle (0-127)]]
*[[Inverse cosines tables - range from -1 to 1]]

Wikipedia article: [http://en.wikipedia.org/wiki/Fixed-point_arithmetic]

[[Category:Numerical computing]]</text>
    </revision>
    <revision>
      <id>10783</id>
      <timestamp>2007-07-27T16:51:39Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">Fixed point mathematics are mainly used on real-time systems, for low-level graphics operations, or on terminals with low CPU power. Main reason to this is that fixed point maths use INTEGER type for all calculations even divisions, cosines, sinus and square root. You'll never need FLOAT types or Math CPU. 

== Useful tools before start ==

*[[Cosine table (C)| Cosines tables - full 8 bit circle (0-255)]]
*[[Tangents tables - half 8 bit circle (0-127)]]
*[[Inverse cosines tables - range from -1 to 1]]

Wikipedia article: [http://en.wikipedia.org/wiki/Fixed-point_arithmetic]

[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:FizzBuzz</title>
    <id>3366</id>
    <revision>
      <id>13126</id>
      <timestamp>2008-04-17T12:30:15Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <comment>new category</comment>
      <text xml:space="preserve">FizzBuzz is a common exercise program, such as [[:Category:Hello World|Hello, world!]] or [[:Category:99 Bottles of Beer|99 Bottles of Beer]]. It is based on a common game of the same name. The program prints some first natural numbers, substituting those divisible by 3 with &quot;Fizz&quot;, divisible by 5 with &quot;Buzz&quot; and divisible by both with &quot;FizzBuzz&quot;.</text>
    </revision>
    <revision>
      <id>13127</id>
      <timestamp>2008-04-17T12:41:58Z</timestamp>
      <contributor>
        <username>Codeholic</username>
        <id>1678</id>
      </contributor>
      <minor/>
      <comment>category</comment>
      <text xml:space="preserve">FizzBuzz is a common exercise program, such as [[:Category:Hello World|Hello, world!]] or [[:Category:99 Bottles of Beer|99 Bottles of Beer]]. It is based on a common game of the same name. The program prints some first natural numbers, substituting those divisible by 3 with &quot;Fizz&quot;, divisible by 5 with &quot;Buzz&quot; and divisible by both with &quot;FizzBuzz&quot;.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13137</id>
      <timestamp>2008-04-18T01:49:40Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>make shared text box</comment>
      <text xml:space="preserve">{{Shared text box |
FizzBuzz is a common exercise program, such as [[:Category:Hello World|Hello, world!]] or [[:Category:99 Bottles of Beer|99 Bottles of Beer]]. It is based on a common game of the same name. The program prints a series of natural numbers, substituting those divisible by 3 with &quot;Fizz&quot;, those divisible by 5 with &quot;Buzz&quot; and those divisible by both 3 and 5 with &quot;FizzBuzz&quot;.
}}

&lt;noinclude&gt;
[[Category:Introductory examples]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Floyd's cycle finding algorithm</title>
    <id>1586</id>
    <revision>
      <id>2267</id>
      <timestamp>2006-03-04T22:51:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">Floyd's cycle-finding algorithm finds a cycle in a list using two iterators moving through the list at different &quot;speeds&quot;.

[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>2347</id>
      <timestamp>2006-03-05T13:09:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link Wikipedia</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Cycle_detection Floyd's cycle-finding algorithm] finds a cycle in a list using two iterators moving through the list at different &quot;speeds&quot;.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Floyd-Steinberg dithering</title>
    <id>1928</id>
    <revision>
      <id>4312</id>
      <timestamp>2006-04-28T22:18:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Dithering]]</comment>
      <text xml:space="preserve">[http://www.visgraf.impa.br/Courses/ip00/proj/Dithering1/floyd_steinberg_dithering.html Floyd-Steinberg dithering] is an image dithering algorithm based on ''error distribution'', which distributes the error between a pixel's original and palletized value into neighboring pixels.

[[Category:Dithering]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Flyweight pattern</title>
    <id>1681</id>
    <revision>
      <id>2687</id>
      <timestamp>2006-03-06T21:17:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Formal specifications</title>
    <id>2350</id>
    <revision>
      <id>6329</id>
      <timestamp>2006-06-20T08:31:24Z</timestamp>
      <contributor>
        <username>GeorgesMariano</username>
        <id>68</id>
      </contributor>
      <text xml:space="preserve">
Literate programming is not so far from (formal) specification (or formal methods)

http://en.wikipedia.org/wiki/Formal_methods

Would be nice to have examples of &quot;Literate specifying&quot;...</text>
    </revision>
    <revision>
      <id>7047</id>
      <timestamp>2006-07-25T19:53:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Category:Top-level subject areas</comment>
      <text xml:space="preserve">Literate programming is not so far from (formal) specification (or formal methods)

http://en.wikipedia.org/wiki/Formal_methods

Would be nice to have examples of &quot;Literate specifying&quot;...

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>7058</id>
      <timestamp>2006-07-26T02:24:14Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rewrite cat description</comment>
      <text xml:space="preserve">Many [http://en.wikipedia.org/wiki/Formal_specification formal specification] techniques (or [http://en.wikipedia.org/wiki/Formal_methods formal methods]) encourage the creation of &quot;literate&quot; specifications that provide informal text intended to help the reader understand the formal text. This category contains examples of such literate specifications.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Fuzzy string search algorithms</title>
    <id>3281</id>
    <revision>
      <id>12044</id>
      <timestamp>2008-01-11T23:53:47Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Fuzzy string algorithms</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Fuzzy_string_searching fuzzy string search] algorithms, also known as inexact or approximate string matching.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Games and entertainment</title>
    <id>1483</id>
    <revision>
      <id>1946</id>
      <timestamp>2006-03-04T00:44:49Z</timestamp>
      <contributor>
        <ip>84.154.49.62</ip>
      </contributor>
      <text xml:space="preserve">This category contains game and entertainment programs.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>10756</id>
      <timestamp>2007-07-26T06:02:23Z</timestamp>
      <contributor>
        <username>Liyunwinny</username>
        <id>996</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This category contains game and entertainment programs.

[[Category:Top-level subject areas]]

===M===</text>
    </revision>
    <revision>
      <id>10757</id>
      <timestamp>2007-07-26T06:03:35Z</timestamp>
      <contributor>
        <username>Liyunwinny</username>
        <id>996</id>
      </contributor>
      <minor/>
      <comment>/* M */</comment>
      <text xml:space="preserve">This category contains game and entertainment programs.

[[Category:Top-level subject areas]]

===M===
[[Merry Motors|http://www.sharewaredown.com/Shareware/Games%20&amp;%20Entertainment/Kids/Merry_Motors_84665.html  Merry Motors]]</text>
    </revision>
    <revision>
      <id>10758</id>
      <timestamp>2007-07-26T06:06:30Z</timestamp>
      <contributor>
        <username>Liyunwinny</username>
        <id>996</id>
      </contributor>
      <minor/>
      <comment>/* M */</comment>
      <text xml:space="preserve">This category contains game and entertainment programs.

[[Category:Top-level subject areas]]

===M===
[http://www.sharewaredown.com/Shareware/Games%20&amp;%20Entertainment/Kids/Merry_Motors_84665.html  Merry Motors]</text>
    </revision>
    <revision>
      <id>10759</id>
      <timestamp>2007-07-26T10:01:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert shareware link</comment>
      <text xml:space="preserve">This category contains game and entertainment programs.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Gamma function with the Lanczos approximation</title>
    <id>1792</id>
    <revision>
      <id>3295</id>
      <timestamp>2006-03-13T23:22:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Text from [[Category:Gamma function with the Lanczos approximation (Python)]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Lanczos_approximation Lanczos approximation] offers a relatively simple way to calculate the gamma function of a complex argument to any desired precision. The precision is determined by a free constant ''g'' and a series whose coefficients depend on ''g'' and may be computed in advanced if a fixed precision is desired. The following implementation uses the same coefficients as the GNU Scientific Library's gamma function. The typical relative error is about 10&lt;sup&gt;-15&lt;/sup&gt; (nearly full double precision accuracy).

Lanczos' series is only valid for numbers in the right half complex plane, so the reflection formula for the gamma function is employed for negative arguments (and also arguments in (0, 0.5), since this should increase accuracy near the singularity at zero.)

&lt;noinclude&gt;
[[Category:Numerical special functions]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Generic tree</title>
    <id>3268</id>
    <revision>
      <id>11881</id>
      <timestamp>2007-12-31T02:51:13Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Generic tree implementations</comment>
      <text xml:space="preserve">This category contains implementations of generic [http://en.wikipedia.org/wiki/Tree_%28data_structure%29 trees].

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graph algorithms</title>
    <id>1475</id>
    <revision>
      <id>1915</id>
      <timestamp>2006-03-03T23:29:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, 2 cats</comment>
      <text xml:space="preserve">This category contains articles that solve computational [http://en.wikipedia.org/wiki/Graph_theory graph theory] problems for [http://en.wikipedia.org/wiki/Graph_%28mathematics%29 graph]s.

[[Category:Algorithms]]
[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
    <revision>
      <id>2443</id>
      <timestamp>2006-03-06T02:34:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>minor readability fix</comment>
      <text xml:space="preserve">This category contains articles that solve computational [http://en.wikipedia.org/wiki/Graph_theory graph theory] problems for [http://en.wikipedia.org/wiki/Graph_%28mathematics%29 graphs].

[[Category:Algorithms]]
[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graph coloring algorithms</title>
    <id>2614</id>
    <revision>
      <id>7194</id>
      <timestamp>2006-08-10T23:48:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Graph algorithms]]</comment>
      <text xml:space="preserve">This category contains algorithms for [http://en.wikipedia.org/wiki/Graph_coloring graph coloring]. Because graph coloring is an NP-complete problem, the algorithms here are either slow, restricted to special cases, or do not find optimal solutions.

[[Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graph search algorithms</title>
    <id>1900</id>
    <revision>
      <id>4186</id>
      <timestamp>2006-04-20T00:15:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Graph algorithms]]</comment>
      <text xml:space="preserve">Graph search algorithms attempt to locate a node or path in a graph, generally by traversing edges  to visit graph nodes in a particular formally specified order. Some of these are listed at Wikipedia's [http://en.wikipedia.org/wiki/Tree_traversal tree traversal] article.

[[Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graph theory</title>
    <id>4000</id>
    <revision>
      <id>17061</id>
      <timestamp>2011-02-19T18:44:19Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">[[Category:Graph algorithms]]</text>
    </revision>
    <revision>
      <id>17062</id>
      <timestamp>2011-02-19T18:48:23Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">[[Category:Discrete and symbolic mathematics:Graph algorithms]]</text>
    </revision>
    <revision>
      <id>17063</id>
      <timestamp>2011-02-19T18:48:51Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">[[Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graph theory algorithms</title>
    <id>1312</id>
    <revision>
      <id>1367</id>
      <timestamp>2006-02-28T20:06:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">This category contains articles for solving computational problems in the mathematical field of [http://en.wikipedia.org/wiki/Graph_theory graph theory].

[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>2438</id>
      <timestamp>2006-03-06T01:48:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Revert to more conventional name</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graphics</title>
    <id>1326</id>
    <revision>
      <id>1412</id>
      <timestamp>2006-03-01T03:25:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles relating to computer graphics, including software and hardware rendering algorithms, manipulation of 3D objects and scenes, geometric problems, virtual reality, and so on.</text>
    </revision>
    <revision>
      <id>1518</id>
      <timestamp>2006-03-02T23:31:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains articles relating to computer graphics, including software and hardware rendering algorithms, manipulation of 3D objects and scenes, geometric problems, virtual reality, and so on.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Graphics file formats</title>
    <id>1329</id>
    <revision>
      <id>1428</id>
      <timestamp>2006-03-01T10:53:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>This category contains articles that load, save, or otherwise process file formats describing graphical images.

Description, [[Category:File formats]]</comment>
      <text xml:space="preserve">This category contains articles that load, save, or otherwise process file formats describing graphical images.

[[Category:File formats]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Group theory</title>
    <id>4003</id>
    <revision>
      <id>17074</id>
      <timestamp>2011-02-19T19:22:25Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">Algorithms for Abstract Algebra. So Groups, Rings, and Fields.</text>
    </revision>
  </page>
  <page>
    <title>Category:Growable array</title>
    <id>1816</id>
    <revision>
      <id>3510</id>
      <timestamp>2006-03-22T12:51:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Another name</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Dynamic array]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Hash table</title>
    <id>1421</id>
    <revision>
      <id>1745</id>
      <timestamp>2006-03-03T12:43:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Data structures]]</comment>
      <text xml:space="preserve">[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Heap</title>
    <id>2377</id>
    <revision>
      <id>6471</id>
      <timestamp>2006-06-24T05:14:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Heap_%28data_structure%29 heap] is an abstract tree data structure in which each node contains a larger (for max-heaps) or smaller (for min-heaps) value than its childrens' values. They are often used to efficiently implement priority queues, graph algorithms, and sorting/selection algorithms. Although heaps are abstract, the subcategories contain implementations for specific heap data structures.

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Heapsort</title>
    <id>1458</id>
    <revision>
      <id>1861</id>
      <timestamp>2006-03-03T20:14:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Heapsort heapsort], an efficient in-place sorting algorithm based on [[Category:Selection sort|selection sort]].

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>2495</id>
      <timestamp>2006-03-06T07:35:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix link</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Heapsort heapsort], an efficient in-place sorting algorithm based on [[:Category:Selection sort|selection sort]].

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Hello World</title>
    <id>1355</id>
    <revision>
      <id>1541</id>
      <timestamp>2006-03-03T00:20:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Describe, [[Category:Introductory examples]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>5266</id>
      <timestamp>2006-05-28T13:43:27Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to this subject.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>5267</id>
      <timestamp>2006-05-28T13:45:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Added link to ACM hellow world catalogue</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>12204</id>
      <timestamp>2008-01-23T07:04:24Z</timestamp>
      <contributor>
        <ip>217.20.138.129</ip>
      </contributor>
      <comment>trocmontrc</comment>
      <text xml:space="preserve">lilido
This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>12270</id>
      <timestamp>2008-01-23T07:21:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/217.20.138.129|217.20.138.129]] ([[User_talk:217.20.138.129|217.20.138.129]]); changed back to last version by [[User:Cpjobling|Cpjobling]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>12698</id>
      <timestamp>2008-03-05T20:56:26Z</timestamp>
      <contributor>
        <ip>61.235.114.169</ip>
      </contributor>
      <comment>basrol</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>12700</id>
      <timestamp>2008-03-06T00:16:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.235.114.169|61.235.114.169]] ([[User_talk:61.235.114.169|61.235.114.169]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13003</id>
      <timestamp>2008-04-07T22:41:33Z</timestamp>
      <contributor>
        <ip>61.132.89.130</ip>
      </contributor>
      <comment>oloaceldelbo</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13007</id>
      <timestamp>2008-04-08T01:55:01Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.132.89.130|61.132.89.130]] ([[User_talk:61.132.89.130|61.132.89.130]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13825</id>
      <timestamp>2008-07-01T12:58:30Z</timestamp>
      <contributor>
        <ip>203.177.74.137</ip>
      </contributor>
      <comment>monouca</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>13828</id>
      <timestamp>2008-07-01T16:33:29Z</timestamp>
      <contributor>
        <ip>88.88.245.234</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14222</id>
      <timestamp>2008-08-09T09:52:17Z</timestamp>
      <contributor>
        <ip>213.231.132.107</ip>
      </contributor>
      <comment>domlierlet</comment>
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[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14227</id>
      <timestamp>2008-08-09T13:46:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14423</id>
      <timestamp>2008-08-21T14:55:09Z</timestamp>
      <contributor>
        <ip>121.14.139.147</ip>
      </contributor>
      <comment>cnadoml</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14426</id>
      <timestamp>2008-08-21T18:37:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14623</id>
      <timestamp>2008-09-15T04:32:45Z</timestamp>
      <contributor>
        <ip>222.134.69.179</ip>
      </contributor>
      <comment>libocboroelt</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14626</id>
      <timestamp>2008-09-15T04:41:30Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/222.134.69.179|222.134.69.179]] ([[User_talk:222.134.69.179|222.134.69.179]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14689</id>
      <timestamp>2008-09-21T19:36:51Z</timestamp>
      <contributor>
        <ip>61.190.67.238</ip>
      </contributor>
      <comment>trocchierer</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14690</id>
      <timestamp>2008-09-21T19:46:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.190.67.238|61.190.67.238]] ([[User_talk:61.190.67.238|61.190.67.238]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14843</id>
      <timestamp>2008-10-07T00:01:45Z</timestamp>
      <contributor>
        <ip>216.155.133.68</ip>
      </contributor>
      <comment>tatralolo</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>14852</id>
      <timestamp>2008-10-07T05:45:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>15118</id>
      <timestamp>2008-10-19T04:45:21Z</timestamp>
      <contributor>
        <ip>122.169.111.25</ip>
      </contributor>
      <comment>olovilamo</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>15124</id>
      <timestamp>2008-10-19T05:39:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>15274</id>
      <timestamp>2008-10-24T19:15:08Z</timestamp>
      <contributor>
        <ip>198.83.124.250</ip>
      </contributor>
      <comment>oudarc</comment>
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This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>15276</id>
      <timestamp>2008-10-24T19:30:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/198.83.124.250|198.83.124.250]] ([[User_talk:198.83.124.250|198.83.124.250]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles exhibiting simple programs that perform a simple interactive task such as print the phrase &quot;Hello World&quot; to the screen. This is a canonical example for introducing beginners to a new programming language or other technology. There is also an [http://www2.latech.edu/~acm/HelloWorld.shtml ACM website] devoted to cataloguing hello world examples.

[[Category:Introductory examples]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Hidden Markov model</title>
    <id>2828</id>
    <revision>
      <id>8201</id>
      <timestamp>2006-11-28T02:59:48Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Hidden Markov model</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Hidden_Markov_Models hidden Markov models].

[[Category:Statistics]]
[[Category:Machine learning]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Homology</title>
    <id>4001</id>
    <revision>
      <id>17071</id>
      <timestamp>2011-02-19T19:16:26Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">Homology related algorithms</text>
    </revision>
  </page>
  <page>
    <title>Category:Image processing</title>
    <id>1572</id>
    <revision>
      <id>2225</id>
      <timestamp>2006-03-04T22:02:48Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new cat</comment>
      <text xml:space="preserve">
[[Category:Graphics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Incomplete</title>
    <id>3163</id>
    <revision>
      <id>10519</id>
      <timestamp>2007-06-16T21:52:20Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>create</comment>
      <text xml:space="preserve">This category contains articles that have incomplete programs, i.e. programs that are missing key definitions, or are otherwise uncompilable or impossible to run.</text>
    </revision>
  </page>
  <page>
    <title>Category:Input</title>
    <id>2636</id>
    <revision>
      <id>7283</id>
      <timestamp>2006-08-14T06:20:37Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">[[Category:User interface design]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Insertion sort</title>
    <id>1302</id>
    <revision>
      <id>1350</id>
      <timestamp>2006-02-28T19:32:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description,  [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Insertion_sort insertion sort] sorting algorithm.

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>1351</id>
      <timestamp>2006-02-28T19:33:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Insertion_sort insertion sort] sorting algorithm.

[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>1352</id>
      <timestamp>2006-02-28T19:34:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, wrong window</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Insertion_sort insertion sort] sorting algorithm.

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Integer factorization</title>
    <id>2671</id>
    <revision>
      <id>7521</id>
      <timestamp>2006-08-29T22:03:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Shorter name, cat, description</comment>
      <text xml:space="preserve">This category contains implementations of various algorithms for [http://en.wikipedia.org/wiki/Integer_factorization integer factorization], locating a number which evenly divides a larger given number. See also [[:Category:Primality testing]].

[[Category:Number theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Integer factorization algorithms</title>
    <id>2669</id>
    <revision>
      <id>7517</id>
      <timestamp>2006-08-29T21:57:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Number theory]]</comment>
      <text xml:space="preserve">This category contains implementations of various algorithms for [http://en.wikipedia.org/wiki/Integer_factorization integer factorization].

[[Category:Number theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Interpreter pattern</title>
    <id>1685</id>
    <revision>
      <id>2691</id>
      <timestamp>2006-03-06T21:20:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Introductory Examples</title>
    <id>3035</id>
    <revision>
      <id>9279</id>
      <timestamp>2007-02-22T18:35:38Z</timestamp>
      <contributor>
        <ip>72.2.18.35</ip>
      </contributor>
      <comment>None</comment>
      <text xml:space="preserve">Hello, very nice site! Please also visit my homepages:
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    </revision>
    <revision>
      <id>9281</id>
      <timestamp>2007-02-22T18:51:47Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rm links, short intro</comment>
      <text xml:space="preserve">This category contains articles with elementary/introductory programs.</text>
    </revision>
  </page>
  <page>
    <title>Category:Introductory examples</title>
    <id>1354</id>
    <revision>
      <id>1538</id>
      <timestamp>2006-03-03T00:17:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains articles describing introductory code that presents programming language features or programming techniques to beginners in a simple, often contrived way.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Iterator pattern</title>
    <id>1686</id>
    <revision>
      <id>2692</id>
      <timestamp>2006-03-06T21:20:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Knot theory</title>
    <id>4002</id>
    <revision>
      <id>17072</id>
      <timestamp>2011-02-19T19:19:53Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">Knot theory related algorithms

* [[:Category:Knot Coloring]]
* [[:Category:Gauss Codes]]
* [[:Category:Braid Group]]
* [[:Category:Knot Polynomials]]</text>
    </revision>
    <revision>
      <id>17073</id>
      <timestamp>2011-02-19T19:20:20Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">Knot theory related algorithms

* [[:Category:Knot coloring]]
* [[:Category:Gauss codes]]
* [[:Category:Braid group]]
* [[:Category:Knot polynomials]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Kruskal's algorithm</title>
    <id>1473</id>
    <revision>
      <id>1911</id>
      <timestamp>2006-03-03T23:26:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Minimum spanning tree algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Kruskal%27s_algorithm Kruskal's algorithm] for finding minimum spanning trees in a weighted, undirected graph.

[[Category:Minimum spanning tree algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:LU decomposition</title>
    <id>1986</id>
    <revision>
      <id>4635</id>
      <timestamp>2006-05-13T02:46:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/LU_decomposition LU decomposition] is a matrix decomposition that writes a matrix as the product of a lower triangular matrix and an upper triangular matrix, sometimes also including a permutation matrix.

&lt;noinclude&gt;
[[Category:Matrix algebra]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Law, ethics, and psychology</title>
    <id>2956</id>
    <revision>
      <id>8772</id>
      <timestamp>2007-02-01T11:05:42Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial cat</comment>
      <text xml:space="preserve">This category contains articles relating to law, ethics, and psychology.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Levenshtein distance</title>
    <id>3286</id>
    <revision>
      <id>12055</id>
      <timestamp>2008-01-12T03:58:59Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Levenshtein implementations</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Levenshtein_distance Levenshtein distance] computation, also known as edit distance.

[[Category:Fuzzy string search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Libraries</title>
    <id>2365</id>
    <revision>
      <id>6399</id>
      <timestamp>2006-06-21T23:01:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This is the top level category for library dependencies.</text>
    </revision>
  </page>
  <page>
    <title>Category:Linguistics</title>
    <id>2889</id>
    <revision>
      <id>8465</id>
      <timestamp>2007-01-03T23:52:21Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>Created</comment>
      <text xml:space="preserve">Programs related to the study of languages, both natural and artificial.</text>
    </revision>
  </page>
  <page>
    <title>Category:Linked list</title>
    <id>1414</id>
    <revision>
      <id>1736</id>
      <timestamp>2006-03-03T12:32:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Data structures]]</comment>
      <text xml:space="preserve">[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Literate Programming</title>
    <id>3942</id>
    <revision>
      <id>16715</id>
      <timestamp>2010-05-03T17:19:52Z</timestamp>
      <contributor>
        <username>EdK</username>
        <id>1039</id>
      </contributor>
      <text xml:space="preserve">Programs to aid in writing literate programs.</text>
    </revision>
  </page>
  <page>
    <title>Category:LiteratePrograms help</title>
    <id>1591</id>
    <revision>
      <id>2282</id>
      <timestamp>2006-03-04T23:53:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new cat</comment>
      <text xml:space="preserve">Browse this category for [[Help:Contents|help]] and tips on contributing to LiteratePrograms.</text>
    </revision>
  </page>
  <page>
    <title>Category:Longest common extension</title>
    <id>2807</id>
    <revision>
      <id>8163</id>
      <timestamp>2006-11-25T17:41:24Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Longest_common_extension</comment>
      <text xml:space="preserve">This category contains implementations of ''longest common extension'' computation.

[[Category:String search algorithms]]</text>
    </revision>
    <revision>
      <id>12047</id>
      <timestamp>2008-01-12T00:10:55Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains implementations of ''longest common extension'' computation.</text>
    </revision>
  </page>
  <page>
    <title>Category:Look and say sequence</title>
    <id>3251</id>
    <revision>
      <id>11661</id>
      <timestamp>2007-11-19T21:27:06Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">Generate [http://en.wikipedia.org/wiki/Look_and_say_sequence look-and-say sequences] such as the [http://en.wikipedia.org/wiki/Conway_sequence Conway sequence].

[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Lucas-Lehmer test for Mersenne numbers</title>
    <id>3259</id>
    <revision>
      <id>11800</id>
      <timestamp>2007-12-08T16:26:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing implementations of [http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_test_for_Mersenne_numbers Lucas-Lehmer test for Mersenne numbers].

[[Category:Primality testing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Machine learning</title>
    <id>2829</id>
    <revision>
      <id>8202</id>
      <timestamp>2006-11-28T03:01:28Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Machine learning</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Machine_learning machine learning].

[[Category:Artificial intelligence]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Mathematical constants</title>
    <id>3265</id>
    <revision>
      <id>11806</id>
      <timestamp>2007-12-08T16:34:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains sub-categories with articles about mathematical constants.</text>
    </revision>
  </page>
  <page>
    <title>Category:Mathematics</title>
    <id>3078</id>
    <revision>
      <id>9531</id>
      <timestamp>2007-03-21T07:31:41Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">A lot of mathematical questions can be studied numerically or using symbolic computations.</text>
    </revision>
    <revision>
      <id>17036</id>
      <timestamp>2011-02-02T01:08:17Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <minor/>
      <comment>added number theory as a subcategory</comment>
      <text xml:space="preserve">A lot of mathematical questions can be studied numerically or using symbolic computations.

* [[:Category:Number theory]]</text>
    </revision>
    <revision>
      <id>17057</id>
      <timestamp>2011-02-19T18:31:49Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">A lot of mathematical questions can be studied numerically or using symbolic computations.

* [[:Category:Number theory]]
* [[:Category:Group theory]]
* [[:Category:Knot theory]]
* [[:Category:Graph Theory]]
* [[:Category:Combinatorics]]</text>
    </revision>
    <revision>
      <id>17058</id>
      <timestamp>2011-02-19T18:37:18Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">A lot of mathematical questions can be studied numerically or using symbolic computations.

* [[:Category:Number theory]]
* [[:Category:Group theory]]
* [[:Category:Knot theory]]
* [[:Category:Graph Theory]]
* [[:Category:Combinatorics]]
* [[:Category:Probability]]
* [[:Category:Topology]]
* [[:Category:Homology]]
* [[:Category:Geometry]]
* [[:Category:Linear Algebra]]
* [[:Category:Analysis]]
* [[:Category:Logic]]</text>
    </revision>
    <revision>
      <id>17059</id>
      <timestamp>2011-02-19T18:41:04Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">A lot of mathematical questions can be studied numerically or using symbolic computations.

* [[:Category:Number theory]]
* [[:Category:Group theory]]
* [[:Category:Knot theory]]
* [[:Category:Graph theory]]
* [[:Category:Combinatorics]]
* [[:Category:Probability]]
* [[:Category:Topology]]
* [[:Category:Homology]]
* [[:Category:Geometry]]
* [[:Category:Linear algebra]]
* [[:Category:Analysis]]
* [[:Category:Logic]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Matrix algebra</title>
    <id>1959</id>
    <revision>
      <id>4449</id>
      <timestamp>2006-05-07T08:53:57Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Matrix_algebra matrix algebra].

[[Category:Numerical computing]]
[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Matrix product verification</title>
    <id>1803</id>
    <revision>
      <id>3379</id>
      <timestamp>2006-03-17T16:51:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Introduction and references</comment>
      <text xml:space="preserve">A frequently used introductory example of randomized algorithms is matrix product verification, where we are given two matrices '''A''' and '''B''' and a matrix '''C''' and asked whether '''AB''' = '''C'''. With currently known matrix multiplication algorithms, the obvious approach of multiplying out '''AB''' takes &amp;Omega;(''n''&lt;sup&gt;2.37&lt;/sup&gt;) time.

However, suppose that the matrices are over the finite field &lt;math&gt;\mathbb{Z}_p&lt;/math&gt;. In this case, we can prove that a randomly chosen vector ''x'' with satisfy A(Bx) = Cx with bounded probability 

These implementations are based primarily on R. Frievald's 1979 paper &quot;Fast probabilistic algorithms&quot; as surveyed in Tracy Kimbel and Rakesh Sinha's [http://citeseer.ifi.unizh.ch/kimbrel91probabilistic.htm A Probabilistic Algorithm for Verifying Matrix Products Using &lt;math&gt;O(n^2)&lt;/math&gt; Time and &lt;math&gt;\log_2 n + O(1)&lt;/math&gt; Random Bits].

[[Category:Randomized algorithms]]</text>
    </revision>
    <revision>
      <id>3381</id>
      <timestamp>2006-03-17T16:54:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Clean up</comment>
      <text xml:space="preserve">A frequently used introductory example of randomized algorithms is matrix product verification, where we are given two matrices '''A''' and '''B''' and a matrix '''C''' and asked whether '''AB''' = '''C'''. With currently known matrix multiplication algorithms, the obvious approach of multiplying out '''AB''' takes &amp;Omega;(''n''&lt;sup&gt;2.37&lt;/sup&gt;) time. Simple randomized algorithms that instead compute '''A'''('''B'''x) and compare it to '''C'''x can show equality with high probability in only &lt;math&gt;O(n^2)&lt;/math&gt; time.

These implementations are based primarily on R. Frievald's 1979 paper &quot;Fast probabilistic algorithms&quot; as surveyed in Tracy Kimbel and Rakesh Sinha's [http://citeseer.ifi.unizh.ch/kimbrel91probabilistic.htm A Probabilistic Algorithm for Verifying Matrix Products Using &lt;math&gt;O(n^2)&lt;/math&gt; Time and &lt;math&gt;\log_2 n + O(1)&lt;/math&gt; Random Bits].

[[Category:Randomized algorithms]]</text>
    </revision>
    <revision>
      <id>3382</id>
      <timestamp>2006-03-17T16:54:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Clarify</comment>
      <text xml:space="preserve">A frequently used introductory example of randomized algorithms is matrix product verification, where we are given two matrices '''A''' and '''B''' and a matrix '''C''' and asked whether '''AB''' = '''C'''. With currently known matrix multiplication algorithms, the obvious approach of multiplying out '''AB''' takes &amp;Omega;(''n''&lt;sup&gt;2.37&lt;/sup&gt;) time. Simple randomized algorithms that instead compute '''A'''('''B'''x) and compare it to '''C'''x for certain randomly chosen vectors ''x'' can show equality with high probability in only &lt;math&gt;O(n^2)&lt;/math&gt; time.

These implementations are based primarily on R. Frievald's 1979 paper &quot;Fast probabilistic algorithms&quot; as surveyed in Tracy Kimbel and Rakesh Sinha's [http://citeseer.ifi.unizh.ch/kimbrel91probabilistic.htm A Probabilistic Algorithm for Verifying Matrix Products Using &lt;math&gt;O(n^2)&lt;/math&gt; Time and &lt;math&gt;\log_2 n + O(1)&lt;/math&gt; Random Bits].

[[Category:Randomized algorithms]]</text>
    </revision>
    <revision>
      <id>3385</id>
      <timestamp>2006-03-17T17:27:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Noinclude category</comment>
      <text xml:space="preserve">A frequently used introductory example of randomized algorithms is matrix product verification, where we are given two matrices '''A''' and '''B''' and a matrix '''C''' and asked whether '''AB''' = '''C'''. With currently known matrix multiplication algorithms, the obvious approach of multiplying out '''AB''' takes &amp;Omega;(''n''&lt;sup&gt;2.37&lt;/sup&gt;) time. Simple randomized algorithms that instead compute '''A'''('''B'''x) and compare it to '''C'''x for certain randomly chosen vectors ''x'' can show equality with high probability in only &lt;math&gt;O(n^2)&lt;/math&gt; time.

These implementations are based primarily on R. Frievald's 1979 paper &quot;Fast probabilistic algorithms&quot; as surveyed in Tracy Kimbel and Rakesh Sinha's [http://citeseer.ifi.unizh.ch/kimbrel91probabilistic.htm A Probabilistic Algorithm for Verifying Matrix Products Using &lt;math&gt;O(n^2)&lt;/math&gt; Time and &lt;math&gt;\log_2 n + O(1)&lt;/math&gt; Random Bits].

&lt;noinclude&gt;
[[Category:Randomized algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Median cut algorithm</title>
    <id>1938</id>
    <revision>
      <id>4342</id>
      <timestamp>2006-05-03T05:05:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, a couple categories</comment>
      <text xml:space="preserve">The median cut algorithm is a popular algorithm for [[:Category:Color quantization|color quantization]], but can be applied to virtually any point clustering problem. In outline, it works as follows:

&lt;pre&gt;
let B be a set of boxes containing points, initially
   containing only a single box containing all points
while number of boxes in B is less than desired number of clusters
    find the largest side length of any side of any box
    cut the box into two boxes along the largest side in such a way
        that half the contained points fall into each new box
    shrink the two new boxes so that they are just large enough to
        contain their points
&lt;/pre&gt;

[[Category:Color quantization]]
[[Category:Clustering]]</text>
    </revision>
    <revision>
      <id>4343</id>
      <timestamp>2006-05-03T05:06:30Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Better as bullets</comment>
      <text xml:space="preserve">The median cut algorithm is a popular algorithm for [[:Category:Color quantization|color quantization]], but can be applied to virtually any point clustering problem. In outline, it works as follows:

* Let B be a set of boxes containing points, initially containing only a single box containing all points.
* While the number of boxes in B is less than desired number of clusters...
** Find the largest side length of any side of any box.
** Cut that box into two boxes along its largest side in such a way that half the contained points fall into each new box.
** Shrink the two new boxes so that they are just large enough to contain their points.

[[Category:Color quantization]]
[[Category:Clustering]]</text>
    </revision>
    <revision>
      <id>4344</id>
      <timestamp>2006-05-03T05:18:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Noinclude cats</comment>
      <text xml:space="preserve">The median cut algorithm is a popular algorithm for [[:Category:Color quantization|color quantization]], but can be applied to virtually any point clustering problem. In outline, it works as follows:

* Let B be a set of boxes containing points, initially containing only a single box containing all points.
* While the number of boxes in B is less than desired number of clusters...
** Find the largest side length of any side of any box.
** Cut that box into two boxes along its largest side in such a way that half the contained points fall into each new box.
** Shrink the two new boxes so that they are just large enough to contain their points.

&lt;noinclude&gt;
[[Category:Color quantization]]
[[Category:Clustering]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Median filter</title>
    <id>1587</id>
    <revision>
      <id>2269</id>
      <timestamp>2006-03-04T22:53:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Image processing]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of the [http://en.wikipedia.org/wiki/Median_filter Median filter] image processing algorithm.

[[Category:Image processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:MedianFilter</title>
    <id>1590</id>
    <revision>
      <id>2274</id>
      <timestamp>2006-03-04T22:54:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>#REDIRECT[[:Category:Median filter]]</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Median filter]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Mediator pattern</title>
    <id>1687</id>
    <revision>
      <id>2693</id>
      <timestamp>2006-03-06T21:20:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Memento pattern</title>
    <id>1688</id>
    <revision>
      <id>2694</id>
      <timestamp>2006-03-06T21:20:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Merge sort</title>
    <id>1453</id>
    <revision>
      <id>1852</id>
      <timestamp>2006-03-03T20:02:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of the [http://en.wikipedia.org/wiki/Merge_sort merge sort] sorting algorithm.

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Mergesort</title>
    <id>1452</id>
    <revision>
      <id>1851</id>
      <timestamp>2006-03-03T20:01:30Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Redirect</comment>
      <text xml:space="preserve">#REDIRECT[[Category:Merge sort]]</text>
    </revision>
    <revision>
      <id>2276</id>
      <timestamp>2006-03-04T22:56:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix link to not make this a subcat</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Merge sort]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Mersenne twister</title>
    <id>1919</id>
    <revision>
      <id>4264</id>
      <timestamp>2006-04-24T09:25:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Pseudorandom number generators]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Mersenne_twister Mersenne twister] is a highly random pseudorandom number generator algorithm invented by Makoto Matsumoto in 1998, suitable for large-dimensional Monte Carlo simulations and having period 2&lt;sup&gt;19937&lt;/sup&gt;&amp;minus;1. See [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html the official page], [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf the original paper (PDF)].

[[Category:Pseudorandom number generators]]</text>
    </revision>
    <revision>
      <id>4277</id>
      <timestamp>2006-04-24T10:54:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Not sticking</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Mersenne_twister Mersenne twister] is a highly random pseudorandom number generator algorithm invented by Makoto Matsumoto in 1998, suitable for large-dimensional Monte Carlo simulations and having period 2&lt;sup&gt;19937&lt;/sup&gt;&amp;minus;1. See [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html the official page], [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf the original paper (PDF)].
 
[[Category:Pseudorandom number generators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Miller-Rabin primality test</title>
    <id>2289</id>
    <revision>
      <id>6032</id>
      <timestamp>2006-06-08T21:36:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, cat</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Miller-Rabin_primality_test Miller-Rabin primality test] is a simple probabilistic algorithm for determining whether a number is prime  or composite that is easy to implement. It proves compositeness of a number using the following formulas:

Suppose 0 &lt; ''a'' &lt; ''n'' is coprime to ''n'' (this is easy to test using the GCD). Write the number ''n''&amp;minus;1 as &lt;math&gt;2^s \cdot d&lt;/math&gt;, where ''d'' is odd. Then, provided that all of the following formulas hold, ''n'' is composite:

:&lt;math&gt;
a^{d} \not\equiv 1\pmod{n}
&lt;/math&gt;
:&lt;math&gt;
a^{2^rd} \not\equiv -1\pmod{n}&lt;/math&gt; for all &lt;math&gt;0 \le r \le s-1
&lt;/math&gt;

If ''a'' is chosen uniformly at random and ''n'' is prime, these formulas hold with probability 1/4. Thus, repeating the test for ''k'' random choices of ''a'' gives a probability of &lt;math&gt;1 - 1/4^k&lt;/math&gt; that the number is prime. Moreover, Gerhard Jaeschke showed that any 32-bit number can be deterministically tested for primality by trying only ''a''=2, 7, and 61.

[[Category:Primality testing]]</text>
    </revision>
    <revision>
      <id>6033</id>
      <timestamp>2006-06-08T22:57:24Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>noinclude</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Miller-Rabin_primality_test Miller-Rabin primality test] is a simple probabilistic algorithm for determining whether a number is prime  or composite that is easy to implement. It proves compositeness of a number using the following formulas:

Suppose 0 &lt; ''a'' &lt; ''n'' is coprime to ''n'' (this is easy to test using the GCD). Write the number ''n''&amp;minus;1 as &lt;math&gt;2^s \cdot d&lt;/math&gt;, where ''d'' is odd. Then, provided that all of the following formulas hold, ''n'' is composite:

:&lt;math&gt;
a^{d} \not\equiv 1\pmod{n}
&lt;/math&gt;
:&lt;math&gt;
a^{2^rd} \not\equiv -1\pmod{n}&lt;/math&gt; for all &lt;math&gt;0 \le r \le s-1
&lt;/math&gt;

If ''a'' is chosen uniformly at random and ''n'' is prime, these formulas hold with probability 1/4. Thus, repeating the test for ''k'' random choices of ''a'' gives a probability of &lt;math&gt;1 - 1/4^k&lt;/math&gt; that the number is prime. Moreover, Gerhard Jaeschke showed that any 32-bit number can be deterministically tested for primality by trying only ''a''=2, 7, and 61.

&lt;noinclude&gt;
[[Category:Primality testing]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Minimum spanning tree algorithms</title>
    <id>1474</id>
    <revision>
      <id>1912</id>
      <timestamp>2006-03-03T23:27:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Graph algorithms]]</comment>
      <text xml:space="preserve">This category's articles implement algorithms that find a [http://en.wikipedia.org/wiki/Minimum_spanning_tree minimum spanning tree] of a graph.

[[Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Mismatch</title>
    <id>2811</id>
    <revision>
      <id>8170</id>
      <timestamp>2006-11-25T20:50:34Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Mismatch</comment>
      <text xml:space="preserve">This category contains implementations of string matching algorithms that match with a defined number of mismatches, also known as the ''k-mismatch'' problem.

[[Category:String search algorithms]]</text>
    </revision>
    <revision>
      <id>12046</id>
      <timestamp>2008-01-12T00:10:39Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains implementations of string matching algorithms that match with a defined number of mismatches, also known as the ''k-mismatch'' problem.</text>
    </revision>
  </page>
  <page>
    <title>Category:Modular Division</title>
    <id>3983</id>
    <revision>
      <id>16986</id>
      <timestamp>2010-12-19T09:45:04Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <text xml:space="preserve">{{Shared text box | text=
'''Modular division''' is a division operation performed in modular arithmetic. Specifically, given two integers ''a'' and ''b'' and a modulo ''m'', the result of the modular division of a by b is a number ''z'' such that:

:&lt;math&gt;z * b \equiv a \pmod{m}.&lt;/math&gt;

For example:

:&lt;math&gt;2 / 3 \equiv 6 \pmod{8}.&lt;/math&gt;

since

:&lt;math&gt;6 * 3 = 18 \equiv 2 \pmod{8}.&lt;/math&gt;

Unlike the other three arithmetic operators, the result of a division may not always exist. For example: &lt;math&gt;1 / 2 \pmod{8}&lt;/math&gt; does not exist, since there is no integer z such that: &lt;math&gt;z * 2 \equiv 1 \pmod{8}&lt;/math&gt;.

A necessary and sufficient condition for the result to exist is that the GCD (greatest common divisor) of b and m divides a:

:&lt;math&gt;gcd(b,m) | a&lt;/math&gt;

In the above example, gcd(2,8) = 2, and 1 is not a multiple of 2, so the division is not defined.


Unlike the other three arithmetic operators, the result of a division is not always unique. For example:

:&lt;math&gt;2 / 6 \equiv 3 \pmod{8}&lt;/math&gt;

but it is also true that:

:&lt;math&gt;2 / 6 \equiv 7 \pmod{8}&lt;/math&gt;

since:

:&lt;math&gt;6 * 7 = 42 \equiv 2 \pmod{8}.&lt;/math&gt;

In general, if:

:&lt;math&gt;z \equiv a / b \pmod{m}&lt;/math&gt;

Then for each integer k:

:&lt;math&gt;z + k * m/gcd(b,m) \equiv a / b \pmod{m}&lt;/math&gt;

Since for each such k:

:&lt;math&gt;b * (z + k * m/gcd(b,m)) \equiv b * z + k * [b/gcd(b,m)] * m \equiv b * z \equiv a \pmod{m}&lt;/math&gt;

The result of the division is unique modulu m/gcd(b,m).


The modular division may be calculated using the [[:Category:Extended Euclidean algorithm|Extended Euclidean algorithm]]. The latter algorithm finds the GCD of two given numbers (in this case: ''b'' and ''m''), and additionally calculates numbers ''x'', ''y'' such that:

:&lt;math&gt;bx + my = \gcd(b,m)\,&lt;/math&gt;

The result of the division can be calculated if and only if a is a multiple of gcd(b,m), i.e. there exists an integer q such that:

:&lt;math&gt;a = q * gcd(b,m)&lt;/math&gt;

In this case we can multiple the previous equation by q, and get:

:&lt;math&gt;bqx + mqy = q * gcd(b,m) = a&lt;/math&gt;

Therefore. by the definition of modulus:

:&lt;math&gt;bqx \equiv a \pmod{m}.&lt;/math&gt;

so '''''qx''''' is the result of the division.
}}

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Monte Carlo simulation</title>
    <id>2369</id>
    <revision>
      <id>6427</id>
      <timestamp>2006-06-22T01:08:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Edited text written by [[User:Lehalle]]</comment>
      <text xml:space="preserve">A Monte Carlo simulation is an algorithm commonly used to obtain estimations of the expectation of a random variable. It is widely used in [[:Category:Quantitative finance|quantitative finance]] to estimate the payoff of an option.

The principal is very simple:
# simulate a lot of realizations of the random variable;
# the empirical mean is a good estimator of the expectation of the random variable.

The difficult points are:
* to generate [[pseudo random numbers]]
* to quantify the accuracy of the obtained estimation

==External links==
* The en.wikipedia article about the [http://en.wikipedia.org/wiki/Monte_Carlo_method Monte Carlo method].
* [http://home.online.no/~pjacklam/notes/invnorm/index.html An algorithm for computing the inverse normal cumulative distribution function], by Peter J. Acklam.</text>
    </revision>
    <revision>
      <id>7048</id>
      <timestamp>2006-07-25T19:54:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ [[Category:Quantitative finance]]</comment>
      <text xml:space="preserve">A Monte Carlo simulation is an algorithm commonly used to obtain estimations of the expectation of a random variable. It is widely used in [[:Category:Quantitative finance|quantitative finance]] to estimate the payoff of an option.

The principal is very simple:
# simulate a lot of realizations of the random variable;
# the empirical mean is a good estimator of the expectation of the random variable.

The difficult points are:
* to generate [[pseudo random numbers]]
* to quantify the accuracy of the obtained estimation

==External links==
* The en.wikipedia article about the [http://en.wikipedia.org/wiki/Monte_Carlo_method Monte Carlo method].
* [http://home.online.no/~pjacklam/notes/invnorm/index.html An algorithm for computing the inverse normal cumulative distribution function], by Peter J. Acklam.

[[Category:Quantitative finance]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Natural language processing</title>
    <id>2823</id>
    <revision>
      <id>8191</id>
      <timestamp>2006-11-27T05:22:20Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Natural language processing</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Natural_language_processing natural language processing].

[[Category:Artificial intelligence]]
[[Category:Linguistics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Networking</title>
    <id>1769</id>
    <revision>
      <id>3155</id>
      <timestamp>2006-03-11T00:04:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">This category is for articles describing code related to computer networking.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11136</id>
      <timestamp>2007-10-12T04:45:42Z</timestamp>
      <contributor>
        <ip>217.171.176.46</ip>
      </contributor>
      <text xml:space="preserve">bodomdelnosi
This category is for articles describing code related to computer networking.

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11138</id>
      <timestamp>2007-10-12T14:53:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category is for articles describing code related to computer networking.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:New</title>
    <id>3665</id>
    <revision>
      <id>15405</id>
      <timestamp>2008-11-07T11:30:31Z</timestamp>
      <contributor>
        <ip>24.191.242.44</ip>
      </contributor>
      <comment>cuszesyv</comment>
      <text xml:space="preserve"> htuhlmia http://ebilpfcg.com tmzqejfu jqawnoth  &lt;a href=&quot;http://wgmicama.com&quot;&gt;tptywiny&lt;/a&gt;  [URL=http://exglmvxv.com]igmyhmvf[/URL]</text>
    </revision>
    <revision>
      <id>15406</id>
      <timestamp>2008-11-07T15:31:24Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">&lt;!-- empty --&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Number theory</title>
    <id>1382</id>
    <revision>
      <id>1623</id>
      <timestamp>2006-03-03T03:03:58Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Discrete and symbolic mathematics]]</comment>
      <text xml:space="preserve">[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Numerical computing</title>
    <id>1360</id>
    <revision>
      <id>1560</id>
      <timestamp>2006-03-03T01:13:52Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>list of important topics (creating site structure with category pages is backwards though)</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>1581</id>
      <timestamp>2006-03-03T01:43:23Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>4351</id>
      <timestamp>2006-05-03T18:11:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Cat:Top-level subject areas</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>7697</id>
      <timestamp>2006-10-02T03:12:29Z</timestamp>
      <contributor>
        <ip>202.168.50.40</ip>
      </contributor>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>7718</id>
      <timestamp>2006-10-03T06:19:05Z</timestamp>
      <contributor>
        <ip>211.28.126.76</ip>
      </contributor>
      <comment>Add Exponential and logarithm functions</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>7719</id>
      <timestamp>2006-10-03T06:19:36Z</timestamp>
      <contributor>
        <ip>211.28.126.76</ip>
      </contributor>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11223</id>
      <timestamp>2007-10-15T09:08:46Z</timestamp>
      <contributor>
        <ip>201.12.178.33</ip>
      </contributor>
      <text xml:space="preserve">ricorc4
Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11225</id>
      <timestamp>2007-10-15T14:07:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11492</id>
      <timestamp>2007-11-08T21:24:11Z</timestamp>
      <contributor>
        <ip>195.8.8.1</ip>
      </contributor>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11496</id>
      <timestamp>2007-11-09T00:24:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/195.8.8.1|195.8.8.1]] ([[User_talk:195.8.8.1|195.8.8.1]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11739</id>
      <timestamp>2007-11-26T11:03:33Z</timestamp>
      <contributor>
        <ip>209.194.182.18</ip>
      </contributor>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11740</id>
      <timestamp>2007-11-26T11:44:35Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11760</id>
      <timestamp>2007-12-01T11:57:41Z</timestamp>
      <contributor>
        <ip>66.193.117.70</ip>
      </contributor>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11761</id>
      <timestamp>2007-12-01T13:06:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11790</id>
      <timestamp>2007-12-08T01:35:23Z</timestamp>
      <contributor>
        <ip>195.229.242.57</ip>
      </contributor>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>11791</id>
      <timestamp>2007-12-08T01:46:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>12573</id>
      <timestamp>2008-02-22T22:26:25Z</timestamp>
      <contributor>
        <ip>222.82.226.145</ip>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>12579</id>
      <timestamp>2008-02-22T23:41:14Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/222.82.226.145|222.82.226.145]] ([[User_talk:222.82.226.145|222.82.226.145]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>13011</id>
      <timestamp>2008-04-08T23:47:32Z</timestamp>
      <contributor>
        <ip>202.142.26.248</ip>
      </contributor>
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Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>13012</id>
      <timestamp>2008-04-09T04:40:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.142.26.248|202.142.26.248]] ([[User_talk:202.142.26.248|202.142.26.248]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">Important topics in numerical computing:
* [[:Category:Floating-point arithmetic]]
* [[:Category:Arbitrary-precision arithmetic]]
* [[:Category:Exponential and logarithm functions]]
* [[:Category:Numerical differentiation]]
* [[:Category:Numerical integration]]
* [[:Category:Numerical ordinary differential equations]]
* [[:Category:Numerical partial differential equations]]
* [[:Category:Numerical optimization]]
* [[:Category:Numerical interpolation]]
* [[:Category:Numerical special functions]]
* [[:Category:Trigonometric functions]]

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Numerical interpolation</title>
    <id>2908</id>
    <revision>
      <id>8537</id>
      <timestamp>2007-01-13T20:21:23Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Numerical ordinary differential equations</title>
    <id>3781</id>
    <revision>
      <id>15849</id>
      <timestamp>2009-01-08T17:45:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">-</text>
    </revision>
    <revision>
      <id>16217</id>
      <timestamp>2009-03-08T11:05:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Numerical special functions</title>
    <id>1781</id>
    <revision>
      <id>3200</id>
      <timestamp>2006-03-11T23:17:45Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">[[Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>3202</id>
      <timestamp>2006-03-11T23:20:03Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>er</comment>
      <text xml:space="preserve">[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Observer pattern</title>
    <id>1689</id>
    <revision>
      <id>2695</id>
      <timestamp>2006-03-06T21:21:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Operating systems</title>
    <id>3697</id>
    <revision>
      <id>15544</id>
      <timestamp>2008-12-09T15:53:06Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>instantiate cat</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Operating_system OS] related articles.</text>
    </revision>
  </page>
  <page>
    <title>Category:Order statistic algorithms</title>
    <id>1814</id>
    <revision>
      <id>3507</id>
      <timestamp>2006-03-22T12:44:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">Order statistic problems include finding the minimum, maximum, median, and, most importantly, the ''n''th largest (or smallest) element of a list. There are worst-case linear algorithms for finding each of these, which is ideal, but in practice expected linear-time algorithms for finding the median and ''n''th largest or smallest element outperform the known worst-case linear algorithms. Related problems include finding the ''k'' largest (or smallest) elements of a list and [[:Category:Sorting algorithms|sorting a list]].

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:POS tagging</title>
    <id>2827</id>
    <revision>
      <id>8200</id>
      <timestamp>2006-11-28T02:56:40Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:POS tagging</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Part-of-speech_tagging part of speech tagging].

[[Category:Natural language processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Parser</title>
    <id>2822</id>
    <revision>
      <id>8190</id>
      <timestamp>2006-11-27T05:19:42Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Parser</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Parsing parsers].


[[Category:Natural language processing]]
[[Category:Compilers and programming languages]]</text>
    </revision>
    <revision>
      <id>9025</id>
      <timestamp>2007-02-11T22:01:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>#redirect [[:Category:Parsers]]</comment>
      <text xml:space="preserve">#redirect [[:Category:Parsers]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Parsers</title>
    <id>3011</id>
    <revision>
      <id>9022</id>
      <timestamp>2007-02-11T21:58:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing parsing algorithms.

[[Category:Algorithms]]
[[Category:Compilers and programming languages]]</text>
    </revision>
    <revision>
      <id>9024</id>
      <timestamp>2007-02-11T22:01:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>link wp</comment>
      <text xml:space="preserve">This category contains articles describing [http://en.wikipedia.org/wiki/Parsing parsing] algorithms.

[[Category:Algorithms]]
[[Category:Compilers and programming languages]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Pascal's triangle</title>
    <id>3900</id>
    <revision>
      <id>16439</id>
      <timestamp>2009-05-18T11:44:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>create cat page</comment>
      <text xml:space="preserve">See [http://en.wikipedia.org/wiki/Pascal's_triangle Pascal's triangle].

[[Category:Mathematics]]</text>
    </revision>
    <revision>
      <id>17070</id>
      <timestamp>2011-02-19T19:09:35Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">See [http://en.wikipedia.org/wiki/Pascal's_triangle Pascal's triangle].

[[Category:Mathematics]]
[[Category:Combinatorics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Perceptron</title>
    <id>2813</id>
    <revision>
      <id>8174</id>
      <timestamp>2006-11-26T03:03:54Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Perceptron</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Perceptron perceptrons].

[[Category:Feed forward neural networks]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Permutations</title>
    <id>2839</id>
    <revision>
      <id>8218</id>
      <timestamp>2006-11-28T16:32:11Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Permutations</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Permutation permutations].

[[Category:Combinatorics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Pi with Machin's formula</title>
    <id>1566</id>
    <revision>
      <id>2179</id>
      <timestamp>2006-03-04T15:36:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, categories</comment>
      <text xml:space="preserve">This category's articles describe how to compute decimals of the mathematical constant ''&amp;pi;'' using a formula of Machin based on the arctangent.

[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]</text>
    </revision>
    <revision>
      <id>2469</id>
      <timestamp>2006-03-06T04:17:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Content from [[Template:Pi with Machin's formula language-independent summary]]</comment>
      <text xml:space="preserve">A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt; 

which he used along with the Taylor series expansion of the arc cotangent function,

:&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]</text>
    </revision>
    <revision>
      <id>2470</id>
      <timestamp>2006-03-06T04:17:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Table stuff</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt; 

which he used along with the Taylor series expansion of the arc cotangent function,

:&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;

[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]</text>
    </revision>
    <revision>
      <id>2644</id>
      <timestamp>2006-03-06T20:26:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Mark cats noinclude</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt; 

which he used along with the Taylor series expansion of the arc cotangent function,

:&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>2755</id>
      <timestamp>2006-03-07T03:16:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Border math to avoid ugly background clash</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:{{border|&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt;}}

which he used along with the Taylor series expansion of the arc cotangent function,

:{{border|&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;}}

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>9973</id>
      <timestamp>2007-05-09T03:14:43Z</timestamp>
      <contributor>
        <ip>68.228.231.24</ip>
      </contributor>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:{{border|&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt;}}

which he used along with the Taylor series expansion of the arc cotangent function,

:{{border|&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;}}

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;

&lt;noinclude&gt;
[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]
[[Category:Mathematics]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>9979</id>
      <timestamp>2007-05-09T14:03:10Z</timestamp>
      <contributor>
        <username>Phil Boswell</username>
        <id>529</id>
      </contributor>
      <minor/>
      <comment>move the TOC down when this is transcluded</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:{{border|&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt;}}

which he used along with the Taylor series expansion of the arc cotangent function,

:{{border|&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;}}

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;
&lt;includeonly&gt;__TOC__&lt;/includeonly&gt;
&lt;noinclude&gt;
[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]
[[Category:Mathematics]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>15523</id>
      <timestamp>2008-12-01T14:05:20Z</timestamp>
      <contributor>
        <ip>24.111.93.209</ip>
      </contributor>
      <comment>/* Machin's formula */</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

rrOFoc  &lt;a href=&quot;http://fdsnorzyjjmu.com/&quot;&gt;fdsnorzyjjmu&lt;/a&gt;, [url=http://kjlyalpmtmmc.com/]kjlyalpmtmmc[/url], [link=http://rraeonowigse.com/]rraeonowigse[/link], http://oifqtwomijyt.com/</text>
    </revision>
    <revision>
      <id>15525</id>
      <timestamp>2008-12-01T14:54:30Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/24.111.93.209|24.111.93.209]] ([[User_talk:24.111.93.209|24.111.93.209]]); changed back to last version by [[User:Phil Boswell|Phil Boswell]]</comment>
      <text xml:space="preserve">&lt;div style=&quot;background-color: #f8f8f8; border: 1px solid #aaaaaa; padding:0.5em&quot;&gt;

=Machin's formula=

A simple way to compute the mathematical constant &amp;pi; &amp;asymp; 3.14159 with any desired precision is due to [http://en.wikipedia.org/wiki/John_Machin John Machin]. In 1706, he found the formula

:{{border|&lt;math&gt;\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239&lt;/math&gt;}}

which he used along with the Taylor series expansion of the arc cotangent function,

:{{border|&lt;math&gt;\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots&lt;/math&gt;}}

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute &amp;pi; with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

&lt;/div&gt;
&lt;includeonly&gt;__TOC__&lt;/includeonly&gt;
&lt;noinclude&gt;
[[Category:Mathematical constants]]
[[Category:Arbitrary-precision arithmetic]]
[[Category:Mathematics]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Pi with the BBP formula</title>
    <id>2780</id>
    <revision>
      <id>8078</id>
      <timestamp>2006-11-16T22:05:25Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>created - no text</comment>
      <text xml:space="preserve">[[Category:Mathematical constants]]</text>
    </revision>
    <revision>
      <id>9974</id>
      <timestamp>2007-05-09T03:15:16Z</timestamp>
      <contributor>
        <ip>68.228.231.24</ip>
      </contributor>
      <text xml:space="preserve">[[Category:Mathematical constants]]
[[Category:Mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Possible copyright violations</title>
    <id>2980</id>
    <revision>
      <id>8825</id>
      <timestamp>2007-02-03T19:53:58Z</timestamp>
      <contributor>
        <ip>71.217.192.176</ip>
      </contributor>
      <text xml:space="preserve">pages flagged as potentially containing copyright violations.</text>
    </revision>
  </page>
  <page>
    <title>Category:Primality testing</title>
    <id>2288</id>
    <revision>
      <id>6031</id>
      <timestamp>2006-06-08T21:23:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, cat</comment>
      <text xml:space="preserve">This category contains algorithms designed to test whether a number is prime or composite; see [http://en.wikipedia.org/wiki/Primality_test primality test on Wikipedia].

[[Category:Number theory]]</text>
    </revision>
    <revision>
      <id>7518</id>
      <timestamp>2006-08-29T21:59:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link [[:Category:Integer factorization algorithms]]</comment>
      <text xml:space="preserve">This category contains algorithms designed to test whether a number is prime or composite; see [http://en.wikipedia.org/wiki/Primality_test primality test on Wikipedia]. See also [[:Category:Integer factorization algorithms]].

[[Category:Number theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Probability</title>
    <id>4004</id>
    <revision>
      <id>17075</id>
      <timestamp>2011-02-19T19:23:54Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">Probability.</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:ACL2</title>
    <id>2371</id>
    <revision>
      <id>6431</id>
      <timestamp>2006-06-22T01:23:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">[http://www.cs.utexas.edu/users/moore/acl2/ ACL2] is a programming language and automatic theorem prover/proof assistant system designed by researchers of formal hardware and software models. Articles in this category contain programs written in ACL2 which, where possible, are accompanied by proofs of their correctness or other important properties.</text>
    </revision>
    <revision>
      <id>6479</id>
      <timestamp>2006-06-24T20:57:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Category:Programming languages</comment>
      <text xml:space="preserve">[http://www.cs.utexas.edu/users/moore/acl2/ ACL2] is a programming language and automatic theorem prover/proof assistant system designed by researchers of formal hardware and software models. Articles in this category contain programs written in ACL2 which, where possible, are accompanied by proofs of their correctness or other important properties.

[[Category:Programming languages|ACL2]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:ALGOL 68</title>
    <id>3603</id>
    <revision>
      <id>14925</id>
      <timestamp>2008-10-10T13:31:10Z</timestamp>
      <contributor>
        <username>NevilleDNZ</username>
        <id>1731</id>
      </contributor>
      <comment>first try</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ALGOL_68 ALGOL 68 programming language]. {{languageuserhelp|ALGOL 68|ALGOL 68}}

Unless otherwise specified, ALGOL 68 code in this category is assumed to be as per the &quot;Revised Report on the Algorithmic Language Algol 68&quot;.

If you are unsure on how to compile and run ALGOL 68 programs, you might visit [[Help:Building and running/ALGOL 68]] for some help.

[[Category:Programming languages|ALGOL 68]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:APL</title>
    <id>3124</id>
    <revision>
      <id>9987</id>
      <timestamp>2007-05-09T22:48:01Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10005</id>
      <timestamp>2007-05-11T10:58:35Z</timestamp>
      <contributor>
        <ip>203.145.131.158</ip>
      </contributor>
      <comment>Unknown</comment>
      <text xml:space="preserve">&lt;a href= http://cesta-regalo.suphost.info &gt;cesta regalo&lt;/a&gt;   &lt;a href= http://regalo-fai-te-festa-papa.suphost.info &gt;regalo fai te festa papa&lt;/a&gt;   &lt;a href= http://mutuo-regionale-prima-casa.suphost.info &gt;mutuo regionale prima casa&lt;/a&gt;   &lt;a href= http://hardcore-fiesta-video-porno-gratis.suphost.info &gt;hardcore fiesta video porno gratis&lt;/a&gt;   &lt;a href= http://regalo-matrimonio.suphost.info &gt;regalo matrimonio&lt;/a&gt;   &lt;a href= http://figa-gratis.suphost.info &gt;figa gratis&lt;/a&gt;   &lt;a href= http://giochi-cellulare-gratis.suphost.info &gt;giochi cellulare gratis&lt;/a&gt;   &lt;a href= http://accessorio-cellulare-auto.suphost.info &gt;accessorio cellulare auto&lt;/a&gt;   &lt;a href= http://sigla-cartoni-animati.suphost.info &gt;sigla cartoni animati&lt;/a&gt;   &lt;a href= http://regalo-laurea.suphost.info &gt;regalo laurea&lt;/a&gt;</text>
    </revision>
    <revision>
      <id>10007</id>
      <timestamp>2007-05-11T11:07:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10024</id>
      <timestamp>2007-05-13T19:09:37Z</timestamp>
      <contributor>
        <ip>85.8.98.248</ip>
      </contributor>
      <comment>123456</comment>
      <text xml:space="preserve">&lt;a href= http://tuttosesso.free-spase.info &gt;tuttosesso&lt;/a&gt;   &lt;a href= http://risultato-serie-b.free-spase.info &gt;risultato serie b&lt;/a&gt;   &lt;a href= http://carta-moneta.free-spase.info &gt;carta moneta&lt;/a&gt;   &lt;a href= http://viaggi-turismo.free-spase.info &gt;viaggi turismo&lt;/a&gt;   &lt;a href= http://regalo-fai-te-festa-papa.free-spase.info &gt;regalo fai te festa papa&lt;/a&gt;   &lt;a href= http://sesso-con-animali.free-spase.info &gt;sesso con animali&lt;/a&gt;   &lt;a href= http://sesso-gay.free-spase.info &gt;sesso gay&lt;/a&gt;   &lt;a href= http://giochi-online-carta.free-spase.info &gt;giochi online carta&lt;/a&gt;   &lt;a href= http://melita-grande-fratello.free-spase.info &gt;melita grande fratello&lt;/a&gt;   &lt;a href= http://carta-credito-revolving.free-spase.info &gt;carta credito revolving&lt;/a&gt;</text>
    </revision>
    <revision>
      <id>10025</id>
      <timestamp>2007-05-13T19:32:34Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10033</id>
      <timestamp>2007-05-14T00:27:22Z</timestamp>
      <contributor>
        <ip>66.111.105.143</ip>
      </contributor>
      <comment>Unknown</comment>
      <text xml:space="preserve">&lt;a href= http://locandina-dei-film.seeyo.info &gt;locandina dei film&lt;/a&gt;   &lt;a href= http://cerca-base-agli-interesse.seeyo.info &gt;cerca base agli interesse&lt;/a&gt;   &lt;a href= http://rosa-rossa.seeyo.info &gt;rosa rossa&lt;/a&gt;   &lt;a href= http://polizza-auto-preventivi.seeyo.info &gt;polizza auto preventivi&lt;/a&gt;   &lt;a href= http://villa-vacanza-toscana.seeyo.info &gt;villa vacanza toscana&lt;/a&gt;   &lt;a href= http://assicurazione-auto-telefonica.seeyo.info &gt;assicurazione auto telefonica&lt;/a&gt;   &lt;a href= http://trucchi-gran-turismo-4.seeyo.info &gt;trucchi gran turismo 4&lt;/a&gt;   &lt;a href= http://affitto-barche.seeyo.info &gt;affitto barche&lt;/a&gt;   &lt;a href= http://vendita-barche.seeyo.info &gt;vendita barche&lt;/a&gt;   &lt;a href= http://noleggio-auto-malpensa.seeyo.info &gt;noleggio auto malpensa&lt;/a&gt;</text>
    </revision>
    <revision>
      <id>10036</id>
      <timestamp>2007-05-14T04:48:38Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/66.111.105.143|66.111.105.143]] ([[User_talk:66.111.105.143|66.111.105.143]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10236</id>
      <timestamp>2007-05-17T22:26:56Z</timestamp>
      <contributor>
        <ip>211.75.111.33</ip>
      </contributor>
      <comment>Unknown</comment>
      <text xml:space="preserve">&lt;a href= http://mutuo-casa.freehostss.info &gt;mutuo casa&lt;/a&gt;   &lt;a href= http://mutuo-conveniente.hostzz.info &gt;mutuo conveniente&lt;/a&gt;   &lt;a href= http://decorazioni-pasqua.freespase.info &gt;decorazioni pasqua&lt;/a&gt;   &lt;a href= http://scambio-coppia.freespase.info &gt;scambio coppia&lt;/a&gt;   &lt;a href= http://acquisto-dvd-vergini.hostzz.info &gt;acquisto dvd vergini&lt;/a&gt;   &lt;a href= http://isole-vergini.hostzz.info &gt;isole vergini&lt;/a&gt;   &lt;a href= http://racconto-porno.freespase.info &gt;racconto porno&lt;/a&gt;   &lt;a href= http://albergo-barcellona.freehostss.info &gt;albergo barcellona&lt;/a&gt;   &lt;a href= http://appunto-or-tesina.hostzz.info &gt;appunto or tesina&lt;/a&gt;   &lt;a href= http://viaggi-londra.19mb.info &gt;viaggi londra&lt;/a&gt;</text>
    </revision>
    <revision>
      <id>10237</id>
      <timestamp>2007-05-17T22:30:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10279</id>
      <timestamp>2007-05-19T08:08:37Z</timestamp>
      <contributor>
        <ip>190.51.21.69</ip>
      </contributor>
      <comment>Unknown</comment>
      <text xml:space="preserve">&lt;a href= http://crea-stampa-biglietto.freespase.info
 &gt;&lt;/a&gt;   &lt;a href= http://giochi-psp.19mb.info
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 &gt;&lt;/a&gt;   &lt;a href= http://clipart-pasqua.freespase.info
 &gt;&lt;/a&gt;   &lt;a href= http://spazio-web-pagamento.hostzz.info
 &gt;&lt;/a&gt;</text>
    </revision>
    <revision>
      <id>10280</id>
      <timestamp>2007-05-19T08:55:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
    <revision>
      <id>10284</id>
      <timestamp>2007-05-19T20:39:18Z</timestamp>
      <contributor>
        <ip>203.223.159.130</ip>
      </contributor>
      <comment>Unknown</comment>
      <text xml:space="preserve">Hi! Excellent site, I really like your stuff.
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Good luck.</text>
    </revision>
    <revision>
      <id>10285</id>
      <timestamp>2007-05-19T20:56:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category is for articles describing code written in [http://en.wikipedia.org/wiki/APL_%28programming_language%29 APL].</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:AWK</title>
    <id>2305</id>
    <revision>
      <id>6152</id>
      <timestamp>2006-06-11T17:58:57Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing programs written in [http://en.wikipedia.org/wiki/AWK_programming_language AWK]. {{languageuserhelp|AWK|AWK}}

[[Category:Programming languages|AWK]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Ada</title>
    <id>1346</id>
    <revision>
      <id>1495</id>
      <timestamp>2006-03-02T22:13:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ADA_programming_language Ada programming language].</text>
    </revision>
    <revision>
      <id>1502</id>
      <timestamp>2006-03-02T23:20:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ADA_programming_language Ada programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2007</id>
      <timestamp>2006-03-04T02:21:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{languageuserhelp|Ada|Ada}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ADA_programming_language Ada programming language]. {{languageuserhelp|Ada|Ada}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5519</id>
      <timestamp>2006-06-01T04:43:52Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ADA_programming_language Ada programming language]. {{languageuserhelp|Ada|Ada}}

[[Category:Programming languages|Ada]]</text>
    </revision>
    <revision>
      <id>15644</id>
      <timestamp>2008-12-18T00:47:18Z</timestamp>
      <contributor>
        <ip>221.13.32.99</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_ermonpa</text>
    </revision>
    <revision>
      <id>15648</id>
      <timestamp>2008-12-18T03:54:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.13.32.99|221.13.32.99]] ([[User_talk:221.13.32.99|221.13.32.99]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/ADA_programming_language Ada programming language]. {{languageuserhelp|Ada|Ada}}

[[Category:Programming languages|Ada]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Aldor</title>
    <id>2375</id>
    <revision>
      <id>6455</id>
      <timestamp>2006-06-22T23:19:51Z</timestamp>
      <contributor>
        <ip>66.161.54.196</ip>
      </contributor>
      <text xml:space="preserve">solve([y1=0.5+k*cos(pi*(x1-w*(1-a))/(2*w*a)),y2=0.5+k*cos(pi*(x2-w*(1-a))/(2*w*a)),y3=0.5+k*cos(pi*(x3-w*(1-a))/(2*w*a))],[k,w,a]);</text>
    </revision>
    <revision>
      <id>6480</id>
      <timestamp>2006-06-24T20:58:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ Category:Programming languages</comment>
      <text xml:space="preserve">solve([y1=0.5+k*cos(pi*(x1-w*(1-a))/(2*w*a)),y2=0.5+k*cos(pi*(x2-w*(1-a))/(2*w*a)),y3=0.5+k*cos(pi*(x3-w*(1-a))/(2*w*a))],[k,w,a]);

[[Category:Programming languages|Aldor]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Alice ML</title>
    <id>1859</id>
    <revision>
      <id>3847</id>
      <timestamp>2006-04-05T21:01:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.ps.uni-sb.de/alice/ Alice] dialect of ML. Alice ML is an extension of Standard ML which adds support for lazy functions, lightweight concurrency, distributed programming, and constraint programming. Alice ML builds on the experience of the  [[:Category:Programming language:Oz|Oz programming language]]. 

{{languageuserhelp|Alice ML|Alice ML}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>3928</id>
      <timestamp>2006-04-06T22:43:48Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>recat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.ps.uni-sb.de/alice/ Alice] dialect of ML. Alice ML is an extension of Standard ML which adds support for lazy functions, lightweight concurrency, distributed programming, and constraint programming. Alice ML builds on the experience of the  [[:Category:Programming language:Oz|Oz programming language]]. 

{{languageuserhelp|Alice ML|Alice ML}}

[[Category:Programming languages:ML]]</text>
    </revision>
    <revision>
      <id>3929</id>
      <timestamp>2006-04-06T22:44:11Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sp</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.ps.uni-sb.de/alice/ Alice] dialect of ML. Alice ML is an extension of Standard ML which adds support for lazy functions, lightweight concurrency, distributed programming, and constraint programming. Alice ML builds on the experience of the  [[:Category:Programming language:Oz|Oz programming language]]. 

{{languageuserhelp|Alice ML|Alice ML}}

[[Category:Programming language:ML]]</text>
    </revision>
    <revision>
      <id>5573</id>
      <timestamp>2006-06-01T19:29:33Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.ps.uni-sb.de/alice/ Alice] dialect of ML. Alice ML is an extension of Standard ML which adds support for lazy functions, lightweight concurrency, distributed programming, and constraint programming. Alice ML builds on the experience of the  [[:Category:Programming language:Oz|Oz programming language]]. 

{{languageuserhelp|Alice ML|Alice ML}}

[[Category:Programming language:ML|Alice ML]]</text>
    </revision>
    <revision>
      <id>15624</id>
      <timestamp>2008-12-17T18:52:12Z</timestamp>
      <contributor>
        <ip>194.204.64.75</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_zelpasleto</text>
    </revision>
    <revision>
      <id>15639</id>
      <timestamp>2008-12-17T21:34:06Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.ps.uni-sb.de/alice/ Alice] dialect of ML. Alice ML is an extension of Standard ML which adds support for lazy functions, lightweight concurrency, distributed programming, and constraint programming. Alice ML builds on the experience of the  [[:Category:Programming language:Oz|Oz programming language]]. 

{{languageuserhelp|Alice ML|Alice ML}}

[[Category:Programming language:ML|Alice ML]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Amiga E</title>
    <id>1666</id>
    <revision>
      <id>2656</id>
      <timestamp>2006-03-06T20:34:18Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Amiga_E Amiga E programming language]. {{languageuserhelp|Amiga E|Amiga E}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5520</id>
      <timestamp>2006-06-01T04:44:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Amiga_E Amiga E programming language]. {{languageuserhelp|Amiga E|Amiga E}}

[[Category:Programming languages|Amiga E]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:AppleScript</title>
    <id>2872</id>
    <revision>
      <id>8378</id>
      <timestamp>2007-01-01T14:37:01Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written in the AppleScript programming language. If you need help from other users with a program written in AppleScript, take a look at [[:Category:Users:AppleScript:Experts]], [[:Category:Users:AppleScript:Knows]], and possibly [[:Category:Users:AppleScript:Some]].

[[Category:Programming languages|AppleScript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Applescript</title>
    <id>2870</id>
    <revision>
      <id>8372</id>
      <timestamp>2007-01-01T14:30:10Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written in the AppleScript programming language. If you need help from other users with a program written in AppleScript, take a look at [[:Category:Users:AppleScript:Experts]], [[Category:Users:AppleScript:Knows]], and possibly [[Category:Users:AppleScript:Some]].

Unless otherwise specified, AppleScript code in this category is assumed to be in standard ANSI/ISO C89.</text>
    </revision>
    <revision>
      <id>8373</id>
      <timestamp>2007-01-01T14:30:36Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>category corrections</comment>
      <text xml:space="preserve">This category contains articles describing code written in the AppleScript programming language. If you need help from other users with a program written in AppleScript, take a look at [[:Category:Users:AppleScript:Experts]], [[:Category:Users:AppleScript:Knows]], and possibly [[:Category:Users:AppleScript:Some]].

Unless otherwise specified, AppleScript code in this category is assumed to be in standard ANSI/ISO C89.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>8376</id>
      <timestamp>2007-01-01T14:33:00Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This category contains articles describing code written in the AppleScript programming language. If you need help from other users with a program written in AppleScript, take a look at [[:Category:Users:AppleScript:Experts]], [[:Category:Users:AppleScript:Knows]], and possibly [[:Category:Users:AppleScript:Some]].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>8379</id>
      <timestamp>2007-01-01T14:39:18Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>emptied</comment>
      <text xml:space="preserve" />
    </revision>
    <revision>
      <id>8432</id>
      <timestamp>2007-01-02T22:50:21Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>#REDIRECT [[:Category:Programming language:AppleScript]]</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Programming language:AppleScript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:AspectJ</title>
    <id>1895</id>
    <revision>
      <id>4139</id>
      <timestamp>2006-04-15T00:56:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/AspectJ AspectJ].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5521</id>
      <timestamp>2006-06-01T04:44:29Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/AspectJ AspectJ].

[[Category:Programming languages|AspectJ]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Assembly</title>
    <id>1694</id>
    <revision>
      <id>2717</id>
      <timestamp>2006-03-06T22:55:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles written in various [http://en.wikipedia.org/wiki/Assembly_language assembly languages], primitive machine-specific languages designed to correspond directly to certain instruction sets.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5522</id>
      <timestamp>2006-06-01T04:44:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles written in various [http://en.wikipedia.org/wiki/Assembly_language assembly languages], primitive machine-specific languages designed to correspond directly to certain instruction sets.

[[Category:Programming languages|Assembly]]</text>
    </revision>
    <revision>
      <id>15763</id>
      <timestamp>2009-01-04T06:39:42Z</timestamp>
      <contributor>
        <ip>61.166.155.83</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_eldelcacacca.com/</text>
    </revision>
    <revision>
      <id>15764</id>
      <timestamp>2009-01-04T07:06:42Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.166.155.83|61.166.155.83]] ([[User_talk:61.166.155.83|61.166.155.83]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles written in various [http://en.wikipedia.org/wiki/Assembly_language assembly languages], primitive machine-specific languages designed to correspond directly to certain instruction sets.

[[Category:Programming languages|Assembly]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Assembly Intel x86</title>
    <id>1670</id>
    <revision>
      <id>2675</id>
      <timestamp>2006-03-06T21:12:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming language:Assembly]]</comment>
      <text xml:space="preserve">[[Category:Programming language:Assembly]]</text>
    </revision>
    <revision>
      <id>6124</id>
      <timestamp>2006-06-10T09:21:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming language:Assembly|Intel x86]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Assembly Motorola MC68K</title>
    <id>1671</id>
    <revision>
      <id>2676</id>
      <timestamp>2006-03-06T21:12:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming language:Assembly]]</comment>
      <text xml:space="preserve">[[Category:Programming language:Assembly]]</text>
    </revision>
    <revision>
      <id>6125</id>
      <timestamp>2006-06-10T09:22:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming language:Assembly|Motorola MC68K]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Assembly Parrot</title>
    <id>2297</id>
    <revision>
      <id>6126</id>
      <timestamp>2006-06-10T09:25:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written for the [http://en.wikipedia.org/wiki/Parrot_virtual_machine Parrot] virtual machine.

[[Category:Programming language:Assembly|Parrot]]</text>
    </revision>
    <revision>
      <id>6127</id>
      <timestamp>2006-06-10T09:37:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ assembly</comment>
      <text xml:space="preserve">This category contains articles describing code written in assembly languages for the [http://en.wikipedia.org/wiki/Parrot_virtual_machine Parrot virtual machine]. 

[[Category:Programming language:Assembly|Parrot]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:BASIC</title>
    <id>2606</id>
    <revision>
      <id>7130</id>
      <timestamp>2006-08-07T07:03:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Add missing cat page</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/BASIC BASIC programming language]. {{languageuserhelp|BASIC|BASIC}}

[[Category:Programming languages|BASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Batch files</title>
    <id>1833</id>
    <revision>
      <id>3632</id>
      <timestamp>2006-03-26T22:52:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming language:Shell script]]</comment>
      <text xml:space="preserve">Batch (.bat) files or command (.cmd) files are scripts written for DOS's COMMAND.COM or Windows' CMD.EXE command-line interpreter.

[[Category:Programming language:Shell script]]</text>
    </revision>
    <revision>
      <id>5623</id>
      <timestamp>2006-06-01T21:25:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">Batch (.bat) files or command (.cmd) files are scripts written for DOS's COMMAND.COM or Windows' CMD.EXE command-line interpreter.

[[Category:Programming language:Shell script|Batch files]]</text>
    </revision>
    <revision>
      <id>8517</id>
      <timestamp>2007-01-09T00:39:17Z</timestamp>
      <contributor>
        <username>Purodha</username>
        <id>129</id>
      </contributor>
      <text xml:space="preserve">Batch (.bat) files or command (.cmd) files are scripts written for DOS's COMMAND.COM or Windows' CMD.EXE command-line interpreter.
{{languageuserhelp|Batch files|Batch files}}

[[Category:Programming language:Shell script|Batch files]]</text>
    </revision>
    <revision>
      <id>15620</id>
      <timestamp>2008-12-17T15:14:42Z</timestamp>
      <contributor>
        <ip>69.114.77.249</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_eldelbopasl</text>
    </revision>
    <revision>
      <id>15635</id>
      <timestamp>2008-12-17T21:33:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">Batch (.bat) files or command (.cmd) files are scripts written for DOS's COMMAND.COM or Windows' CMD.EXE command-line interpreter.
{{languageuserhelp|Batch files|Batch files}}

[[Category:Programming language:Shell script|Batch files]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:C</title>
    <id>1290</id>
    <revision>
      <id>1308</id>
      <timestamp>2006-02-28T09:50:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Brief description</comment>
      <text xml:space="preserve">This article is about articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language].</text>
    </revision>
    <revision>
      <id>1310</id>
      <timestamp>2006-02-28T09:51:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Wording</comment>
      <text xml:space="preserve">This category contains about articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language].</text>
    </revision>
    <revision>
      <id>1348</id>
      <timestamp>2006-02-28T19:30:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Typo</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language].</text>
    </revision>
    <revision>
      <id>1504</id>
      <timestamp>2006-03-02T23:21:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>1978</id>
      <timestamp>2006-03-04T01:51:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{languageuserhelp|C}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>1981</id>
      <timestamp>2006-03-04T01:54:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add template parameter</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2389</id>
      <timestamp>2006-03-05T20:43:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5524</id>
      <timestamp>2006-06-01T04:45:23Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>6311</id>
      <timestamp>2006-06-17T23:29:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Added link to Help:Building_and_running/C</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building_and_running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>6312</id>
      <timestamp>2006-06-17T23:30:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>fix link</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11229</id>
      <timestamp>2007-10-18T01:39:50Z</timestamp>
      <contributor>
        <ip>201.12.178.33</ip>
      </contributor>
      <text xml:space="preserve">corolbocou
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11234</id>
      <timestamp>2007-10-18T05:11:36Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11460</id>
      <timestamp>2007-11-03T23:35:04Z</timestamp>
      <contributor>
        <ip>218.58.136.4</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11461</id>
      <timestamp>2007-11-04T01:10:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/218.58.136.4|218.58.136.4]] ([[User_talk:218.58.136.4|218.58.136.4]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11556</id>
      <timestamp>2007-11-12T18:46:43Z</timestamp>
      <contributor>
        <ip>208.78.99.157</ip>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11558</id>
      <timestamp>2007-11-12T18:56:15Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/208.78.99.157|208.78.99.157]] ([[User_talk:208.78.99.157|208.78.99.157]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11569</id>
      <timestamp>2007-11-14T11:16:54Z</timestamp>
      <contributor>
        <ip>62.220.12.98</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>11570</id>
      <timestamp>2007-11-14T11:38:36Z</timestamp>
      <contributor>
        <ip>89.139.124.74</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>12478</id>
      <timestamp>2008-02-07T10:13:58Z</timestamp>
      <contributor>
        <ip>66.216.91.200</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>12481</id>
      <timestamp>2008-02-07T11:12:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>15412</id>
      <timestamp>2008-11-08T00:13:27Z</timestamp>
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      <timestamp>2008-11-08T12:25:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
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      <timestamp>2008-11-09T18:44:20Z</timestamp>
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      <timestamp>2008-11-09T18:52:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>15482</id>
      <timestamp>2008-11-24T20:02:38Z</timestamp>
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      <id>15483</id>
      <timestamp>2008-11-24T21:35:43Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/91.192.189.165|91.192.189.165]] ([[User_talk:91.192.189.165|91.192.189.165]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
    <revision>
      <id>15485</id>
      <timestamp>2008-11-25T20:29:15Z</timestamp>
      <contributor>
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      <comment>gIwxQlpIcOicM</comment>
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    <revision>
      <id>15486</id>
      <timestamp>2008-11-25T20:33:17Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.130.193.14|221.130.193.14]] ([[User_talk:221.130.193.14|221.130.193.14]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_programming_language C programming language]. {{languageuserhelp|C|C}}

Unless otherwise specified, C code in this category is assumed to be in standard ANSI/ISO C89.

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/C]] for some help.

[[Category:Programming languages|C]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:C Plus Plus</title>
    <id>1411</id>
    <revision>
      <id>1708</id>
      <timestamp>2006-03-03T11:34:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2008</id>
      <timestamp>2006-03-04T02:22:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{languageuserhelp|C++|C Plus Plus}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>3658</id>
      <timestamp>2006-03-31T03:54:22Z</timestamp>
      <contributor>
        <ip>81.84.103.213</ip>
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      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5525</id>
      <timestamp>2006-06-01T04:45:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11073</id>
      <timestamp>2007-10-08T15:34:58Z</timestamp>
      <contributor>
        <ip>85.17.186.161</ip>
      </contributor>
      <text xml:space="preserve">zelricdomlil
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
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    <revision>
      <id>11090</id>
      <timestamp>2007-10-08T16:56:16Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
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      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11163</id>
      <timestamp>2007-10-12T20:08:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11508</id>
      <timestamp>2007-11-09T17:19:51Z</timestamp>
      <contributor>
        <ip>74.208.11.169</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11512</id>
      <timestamp>2007-11-09T20:19:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/74.208.11.169|74.208.11.169]] ([[User_talk:74.208.11.169|74.208.11.169]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11703</id>
      <timestamp>2007-11-24T14:54:52Z</timestamp>
      <contributor>
        <ip>210.22.158.132</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11705</id>
      <timestamp>2007-11-24T15:27:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>14344</id>
      <timestamp>2008-08-18T21:45:56Z</timestamp>
      <contributor>
        <ip>195.188.174.221</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
    <revision>
      <id>14353</id>
      <timestamp>2008-08-19T05:05:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C++ C++ programming language]. {{languageuserhelp|C++|C Plus Plus}} if you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/C%2B%2B_Programming C++ Programming] wikibook.

[[Category:Programming languages|C Plus Plus]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:C Sharp</title>
    <id>1515</id>
    <revision>
      <id>2009</id>
      <timestamp>2006-03-04T02:22:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, languageuserhelp, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_Sharp C#]. {{languageuserhelp|C#|C Sharp}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2011</id>
      <timestamp>2006-03-04T02:23:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+words</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_Sharp C#] programming language. {{languageuserhelp|C#|C Sharp}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5526</id>
      <timestamp>2006-06-01T04:46:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/C_Sharp C#] programming language. {{languageuserhelp|C#|C Sharp}}

[[Category:Programming languages|C Sharp]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:CSP</title>
    <id>2703</id>
    <revision>
      <id>7649</id>
      <timestamp>2006-09-16T06:13:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>init category</comment>
      <text xml:space="preserve">This category contains articles describing scripts written in the machine-readable version of [http://en.wikipedia.org/wiki/Communicating_sequential_processes CSP]. CSP is a process algebra intended for formal specification and verification of concurrent systems. The machine-readable version includes an embedded functional language. {{languageuserhelp|CSP|CSP}}

[[Category:Programming languages|CSP]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:CSS</title>
    <id>3797</id>
    <revision>
      <id>15903</id>
      <timestamp>2009-01-09T16:27:55Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">-</text>
    </revision>
    <revision>
      <id>16221</id>
      <timestamp>2009-03-08T11:05:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Candle</title>
    <id>4032</id>
    <revision>
      <id>17202</id>
      <timestamp>2011-07-28T09:43:40Z</timestamp>
      <contributor>
        <username>Henryluo</username>
        <id>2340</id>
      </contributor>
      <text xml:space="preserve">'''Candle''' ('''C'''ommon '''A'''pplicatio'''N''' '''D'''evelopment '''L'''anguag'''E''') is designed to be a new general-purpose scripting language capable of developing both desktop and Internet applications.

Besides the common features found in many scripting languages, like cross-platform, interpreted execution, auto garbage collection, dynamic typed, built-in list and map support, Candle also supports some unique features that are not common in today's general-purpose programming languages:

&lt;ul&gt;
&lt;li&gt;'''Built-in hierarchical data processing''': hierarchical data (whether from XML, HTML, XHTML, JSON, CSV, RDB or MIME Message) can be as easily constructed, selected, queries, transformed and serialized as any primitive data in Candle.&lt;/li&gt;
&lt;li&gt;'''Set-oriented expressions''': the expressions in Candle can handle not only a single item, but also a sequence of items - making the language more expressive and convenient.&lt;/li&gt;
&lt;li&gt;'''Unified pattern language''': Candle unifies several pattern related DSLs (including RegEx, BNF, RELAX NG, XQuery Sequence Type) into one consistent pattern language that can apply to sequence of items, nodes and strings.&lt;/li&gt;
&lt;li&gt;'''Unification of functional and procedural programming''': Some multi-paradigm programming languages, like Python, already have a mixture of features from both worlds. But by introducing a mechanism, I called separation-of-side-effects, Candle unifies two worlds in a more orderly manner. In Candle, routines are divided into functions and methods. Functions are routines without side-effects and methods are routines with side-effects. The rule of separation-of-side-effects is that methods can call functions, but not vice versa. In this way, pure functional islands are well-preserved in the vast sea of procedural program.&lt;/li&gt;
&lt;/ul&gt;

A hello-world program in Candle can be as simple as:
&lt;codeblock&gt;
&lt;?csp1.0?&gt;
function main() {
  &quot;Hello world from Candle!&quot;
}
&lt;/codeblock&gt;

For more information on Candle, you can visit [http://www.candlescript.org Candle website] or the [http://sourceforge.net/projects/candleapp/ SourceForge Project].</text>
    </revision>
    <revision>
      <id>17204</id>
      <timestamp>2011-07-28T09:54:50Z</timestamp>
      <contributor>
        <username>Henryluo</username>
        <id>2340</id>
      </contributor>
      <text xml:space="preserve">'''Candle''' ('''C'''ommon '''A'''pplicatio'''N''' '''D'''evelopment '''L'''anguag'''E''') is designed to be a new general-purpose scripting language capable of developing both desktop and Internet applications.

Besides the common features found in many scripting languages, like cross-platform, interpreted execution, auto garbage collection, dynamic typed, built-in list and map support, Candle also supports some unique features that are not common in today's general-purpose programming languages:

&lt;ul&gt;
&lt;li&gt;'''Built-in hierarchical data processing''': hierarchical data (whether from XML, HTML, XHTML, JSON, CSV, RDB or MIME Message) can be as easily constructed, selected, queries, transformed and serialized as any primitive data in Candle.&lt;/li&gt;
&lt;li&gt;'''Set-oriented expressions''': the expressions in Candle can handle not only a single item, but also a sequence of items - making the language more expressive and convenient.&lt;/li&gt;
&lt;li&gt;'''Unified pattern language''': Candle unifies several pattern related DSLs (including RegEx, BNF, RELAX NG, XQuery Sequence Type) into one consistent pattern language that can apply to sequence of items, nodes and strings.&lt;/li&gt;
&lt;li&gt;'''Unification of functional and procedural programming''': Some multi-paradigm programming languages, like Python, already have a mixture of features from both worlds. But by introducing a mechanism, I called separation-of-side-effects, Candle unifies two worlds in a more orderly manner. In Candle, routines are divided into functions and methods. Functions are routines without side-effects and methods are routines with side-effects. The rule of separation-of-side-effects is that methods can call functions, but not vice versa. In this way, pure functional islands are well-preserved in the vast sea of procedural program.&lt;/li&gt;
&lt;/ul&gt;

For more information on Candle, you can visit [http://www.candlescript.org Candle website] or the [http://sourceforge.net/projects/candleapp/ SourceForge Project].</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Classic BASIC</title>
    <id>2628</id>
    <revision>
      <id>7261</id>
      <timestamp>2006-08-13T19:46:58Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>description</comment>
      <text xml:space="preserve">The '''Classic BASIC''' category contains BASIC dialects based on version 6 or earlier of [http://en.wikipedia.org/wiki/Dartmouth_BASIC Dartmouth BASIC]</text>
    </revision>
    <revision>
      <id>7264</id>
      <timestamp>2006-08-13T20:00:28Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">The '''Classic BASIC''' category contains BASIC dialects based on version 6 or earlier of [http://en.wikipedia.org/wiki/Dartmouth_BASIC Dartmouth BASIC]

[[Category:Programming language:BASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Clojure</title>
    <id>3855</id>
    <revision>
      <id>16158</id>
      <timestamp>2009-02-07T09:49:26Z</timestamp>
      <contributor>
        <username>Stephenarneil</username>
        <id>1775</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Clojure Clojure]. {{languageuserhelp|Clojure|Clojure}}

[[Category:Programming languages|Clojure]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:D</title>
    <id>3114</id>
    <revision>
      <id>9875</id>
      <timestamp>2007-04-27T19:52:10Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>Lang. D categ.</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/D_(programming_language) D] is a systems programming language. Its focus is on combining the power and high performance of C and C++ with the programmer productivity of modern languages like Ruby and Python. Special attention is given to the needs of quality assurance, documentation, management, portability and reliability.

The D language is statically typed and compiles directly to machine code. It's multiparadigm, supporting many programming styles: imperative, object oriented, and metaprogramming. It's a member of the C syntax family, and its appearance is very similar to that of C++. For a quick comparison of the features, see this comparison of D with C, C++, C# and Java.

{{languageuserhelp|D|D}}

[[Category:Programming languages|D]]</text>
    </revision>
    <revision>
      <id>9879</id>
      <timestamp>2007-04-27T22:13:50Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>missing link</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/D_(programming_language) D] is a systems programming language. Its focus is on combining the power and high performance of C and C++ with the programmer productivity of modern languages like Ruby and Python. Special attention is given to the needs of quality assurance, documentation, management, portability and reliability.

The D language is statically typed and compiles directly to machine code. It's multiparadigm, supporting many programming styles: imperative, object oriented, and metaprogramming. It's a member of the C syntax family, and its appearance is very similar to that of C++. For a quick comparison of the features, see this [http://www.digitalmars.com/d/comparison.html comparison] of D with C, C++, C# and Java.

{{languageuserhelp|D|D}}

[[Category:Programming languages|D]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Delphi</title>
    <id>1719</id>
    <revision>
      <id>2860</id>
      <timestamp>2006-03-07T21:38:30Z</timestamp>
      <contributor>
        <ip>195.160.220.30</ip>
      </contributor>
      <comment>Hello World, console</comment>
      <text xml:space="preserve">begin
  WriteLn ('Hello, World!');
end.</text>
    </revision>
    <revision>
      <id>2862</id>
      <timestamp>2006-03-07T21:41:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move content to [[Hello World (Delphi)]]</comment>
      <text xml:space="preserve">[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5528</id>
      <timestamp>2006-06-01T04:46:33Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming languages|Delphi]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Dylan</title>
    <id>1394</id>
    <revision>
      <id>1659</id>
      <timestamp>2006-03-03T05:18:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Dylan_programming_language Dylan programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5529</id>
      <timestamp>2006-06-01T04:46:58Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Dylan_programming_language Dylan programming language].

[[Category:Programming languages|Dylan]]</text>
    </revision>
    <revision>
      <id>15802</id>
      <timestamp>2009-01-06T13:11:14Z</timestamp>
      <contributor>
        <ip>221.224.108.85</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_cnarel.com/</text>
    </revision>
    <revision>
      <id>15805</id>
      <timestamp>2009-01-06T15:40:09Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.224.108.85|221.224.108.85]] ([[User_talk:221.224.108.85|221.224.108.85]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Dylan_programming_language Dylan programming language].

[[Category:Programming languages|Dylan]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:E</title>
    <id>1655</id>
    <revision>
      <id>2602</id>
      <timestamp>2006-03-06T17:10:51Z</timestamp>
      <contributor>
        <ip>80.213.176.201</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Amiga_E E programming language]. {{languageuserhelp|E|E}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2604</id>
      <timestamp>2006-03-06T17:13:42Z</timestamp>
      <contributor>
        <ip>80.213.176.201</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Amiga_E E programming language]. {{languageuserhelp|E|E}}

[[Category:Programming languages]]

This is how hello world looks in E

  PROC main()
     WriteF('Hello, World!')
  ENDPROC</text>
    </revision>
    <revision>
      <id>2639</id>
      <timestamp>2006-03-06T20:24:17Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>move hello world program to [[Hello World (E)]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Amiga_E E programming language]. {{languageuserhelp|E|E}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2653</id>
      <timestamp>2006-03-06T20:32:56Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>make this the cat for http://en.wikipedia.org/wiki/E_programming_language - we'll create another category for Amiga E</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/E_programming_language E programming language]. {{languageuserhelp|E|E}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5530</id>
      <timestamp>2006-06-01T04:47:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/E_programming_language E programming language]. {{languageuserhelp|E|E}}

[[Category:Programming languages|E]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Eiffel</title>
    <id>1537</id>
    <revision>
      <id>2076</id>
      <timestamp>2006-03-04T07:46:53Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Eiffel_programming_language Eiffel programming language]. {{languageuserhelp|Eiffel|Eiffel}}</text>
    </revision>
    <revision>
      <id>4136</id>
      <timestamp>2006-04-15T00:43:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Cat:Programming languages</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Eiffel_programming_language Eiffel programming language]. {{languageuserhelp|Eiffel|Eiffel}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5531</id>
      <timestamp>2006-06-01T04:47:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Eiffel_programming_language Eiffel programming language]. {{languageuserhelp|Eiffel|Eiffel}}

[[Category:Programming languages|Eiffel]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Erlang</title>
    <id>1373</id>
    <revision>
      <id>1598</id>
      <timestamp>2006-03-03T02:23:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>category description</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Erlang_programming_language Erlang programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2077</id>
      <timestamp>2006-03-04T07:47:32Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+languageuserhelp</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Erlang_programming_language Erlang programming language]. {{languageuserhelp|Erlang|Erlang}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5532</id>
      <timestamp>2006-06-01T04:47:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Erlang_programming_language Erlang programming language]. {{languageuserhelp|Erlang|Erlang}}

[[Category:Programming languages|Erlang]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Excelsior</title>
    <id>3250</id>
    <revision>
      <id>11622</id>
      <timestamp>2007-11-18T20:48:55Z</timestamp>
      <contributor>
        <username>Popx</username>
        <id>1548</id>
      </contributor>
      <text xml:space="preserve">This page is for [http://www.j-paine.org/ Jocelyn Paine]'s Excelsior programming language. This is a functional language from which spreadsheets can be generated. Please see [[http://www.j-paine.org/excelsior/repository/ www.j-paine.org/excelsior/repository/]] for info, including sample programs.</text>
    </revision>
    <revision>
      <id>11629</id>
      <timestamp>2007-11-19T10:39:11Z</timestamp>
      <contributor>
        <username>Popx</username>
        <id>1548</id>
      </contributor>
      <text xml:space="preserve">This page is for [http://www.j-paine.org/ Jocelyn Paine]'s Excelsior programming language. This is an equational language from which spreadsheets can be generated. Please see [[http://www.j-paine.org/excelsior/repository/ www.j-paine.org/excelsior/repository/]] for info, including sample programs.</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:F Sharp</title>
    <id>1583</id>
    <revision>
      <id>2259</id>
      <timestamp>2006-03-04T22:40:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Usual stuff</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5533</id>
      <timestamp>2006-06-01T04:48:09Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
    <revision>
      <id>13961</id>
      <timestamp>2008-07-15T04:31:48Z</timestamp>
      <contributor>
        <ip>89.76.213.253</ip>
      </contributor>
      <comment>zeldronbocel</comment>
      <text xml:space="preserve">eltcolale
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
    <revision>
      <id>13962</id>
      <timestamp>2008-07-15T05:45:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
    <revision>
      <id>14302</id>
      <timestamp>2008-08-16T00:40:55Z</timestamp>
      <contributor>
        <ip>119.177.63.151</ip>
      </contributor>
      <comment>http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html</comment>
      <text xml:space="preserve">[respirate definition|http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html] [[http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html respirate definition]] [http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html|respirate definition] ((http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html respirate definition)) [[http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html | respirate definition]] &quot;respirate definition&quot;:http://nicolamenicacci.com/board/wp-content/uploads/media/1850.html [athleta|http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm] [[http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm athleta]] [http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm|athleta] ((http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm athleta)) [[http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm | athleta]] &quot;athleta&quot;:http://favoritethingsstudio.com/shopfts/images/icons/resource629.htm [bizarre love triangle|http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm] [[http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm bizarre love triangle]] [http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm|bizarre love triangle] ((http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm bizarre love triangle)) [[http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm | bizarre love triangle]] &quot;bizarre love triangle&quot;:http://favoritethingsstudio.com/shopfts/images/icons/resource2257.htm [hornyhousewives|http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html] [[http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html hornyhousewives]] [http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html|hornyhousewives] ((http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html hornyhousewives)) [[http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html | hornyhousewives]] &quot;hornyhousewives&quot;:http://nicolamenicacci.com/board/wp-content/uploads/media/1687.html [abuse drug prescription rehabilitation treatment|http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm] [[http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm abuse drug prescription rehabilitation treatment]] [http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm|abuse drug prescription rehabilitation treatment] ((http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm abuse drug prescription rehabilitation treatment)) [[http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm | abuse drug prescription rehabilitation treatment]] &quot;abuse drug prescription rehabilitation treatment&quot;:http://favoritethingsstudio.com/shopfts/images/icons/resource1535.htm 
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
    <revision>
      <id>14307</id>
      <timestamp>2008-08-16T10:49:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
    <revision>
      <id>14518</id>
      <timestamp>2008-08-29T15:44:12Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>external link fixed</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/F_Sharp_(programming_language) F# programming language]. {{languageuserhelp|F#|F Sharp}}

[[Category:Programming languages|F Sharp]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Forth</title>
    <id>2858</id>
    <revision>
      <id>8316</id>
      <timestamp>2006-12-09T17:36:14Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>+cat:Forth</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Forth_%28programming_language%29 Forth programming language].

[[Category:Programming languages|Forth]]</text>
    </revision>
    <revision>
      <id>12975</id>
      <timestamp>2008-04-04T23:06:10Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <comment>Jones Forth == literate Forth implementation</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Forth_%28programming_language%29 Forth programming language].

In addition, there is an i386 Linux implementation of Forth, [http://www.annexia.org/forth Jones Forth], which is itself a literate assembly/Forth program.

[[Category:Programming languages|Forth]]</text>
    </revision>
    <revision>
      <id>12978</id>
      <timestamp>2008-04-05T18:35:05Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>This category is for programs written in Forth, not implementations of Forth</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Forth_%28programming_language%29 Forth programming language].

[[Category:Programming languages|Forth]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Fortran</title>
    <id>2193</id>
    <revision>
      <id>5278</id>
      <timestamp>2006-05-28T14:30:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Fortran_programming_language Ruby programming language]. {{languageuserhelp|Fortran|Fortran}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5281</id>
      <timestamp>2006-05-28T14:32:05Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Fortran_programming_language Fortran programming language]. {{languageuserhelp|Fortran|Fortran}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5534</id>
      <timestamp>2006-06-01T04:48:27Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Fortran_programming_language Fortran programming language]. {{languageuserhelp|Fortran|Fortran}}

[[Category:Programming languages|Fortran]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Fortress</title>
    <id>3085</id>
    <revision>
      <id>9646</id>
      <timestamp>2007-04-04T07:07:37Z</timestamp>
      <contributor>
        <ip>80.34.137.78</ip>
      </contributor>
      <comment>Hello World in Fortress</comment>
      <text xml:space="preserve">&lt;h1&gt;Hello World in Fortress&lt;/h1&gt;
In Fortress, implementing this is surprisingly easy.

&lt;codeblock language=&quot;fortress&quot;&gt;
&lt;&lt;Hello.fss&gt;&gt;=
component HelloWorld
    export Executable

    run()=do
    	print &quot;Hello, world!\n&quot;
    end

end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9775</id>
      <timestamp>2007-04-16T11:20:11Z</timestamp>
      <contributor>
        <ip>80.34.137.78</ip>
      </contributor>
      <text xml:space="preserve">&lt;h1&gt;Hello World in Fortress&lt;/h1&gt;
In Fortress, implementing this is surprisingly easy.

&lt;codeblock language=&quot;fortress&quot;&gt;
&lt;&lt;Hello.fss&gt;&gt;=
component HelloWorld
    export Executable

    run()=do
    	print &quot;Hello, world!\n&quot;
    end

end
&lt;/codeblock&gt;

[[Category:Programming language:Fortress]]
[[Category:Hello World|Fortress]]</text>
    </revision>
    <revision>
      <id>9780</id>
      <timestamp>2007-04-16T14:32:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>moved &quot;hello world&quot; to separate article</comment>
      <text xml:space="preserve">This category contains code in the [http://en.wikipedia.org/wiki/Fortress_programming_language Fortress programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>10575</id>
      <timestamp>2007-06-21T21:35:30Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains code in the [http://en.wikipedia.org/wiki/Fortress_programming_language Fortress programming language].

[[Category:Programming languages|Fortress]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Go</title>
    <id>3953</id>
    <revision>
      <id>16783</id>
      <timestamp>2010-07-31T06:57:24Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Go_%28programming_language%29 Go programming language]. {{languageuserhelp|Go|Go}}

[[Category:Programming languages|Go]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Groovy</title>
    <id>2189</id>
    <revision>
      <id>5272</id>
      <timestamp>2006-05-28T14:25:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Groovy_programming_language Groovy] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5273</id>
      <timestamp>2006-05-28T14:26:14Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Groovy_programming_language Groovy] programming language. {{languageuserhelp|Groovy|Groovy}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5535</id>
      <timestamp>2006-06-01T04:48:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Groovy_programming_language Groovy] programming language. {{languageuserhelp|Groovy|Groovy}}

[[Category:Programming languages|Groovy]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Haskell</title>
    <id>1370</id>
    <revision>
      <id>1593</id>
      <timestamp>2006-03-03T02:20:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>category description</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].</text>
    </revision>
    <revision>
      <id>1595</id>
      <timestamp>2006-03-03T02:21:54Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming language:Haskell]]</text>
    </revision>
    <revision>
      <id>1596</id>
      <timestamp>2006-03-03T02:22:21Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>fix cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5536</id>
      <timestamp>2006-06-01T04:48:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>12202</id>
      <timestamp>2008-01-23T07:03:58Z</timestamp>
      <contributor>
        <ip>217.20.138.129</ip>
      </contributor>
      <comment>eltricro</comment>
      <text xml:space="preserve">racerroboc
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>12268</id>
      <timestamp>2008-01-23T07:20:57Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/217.20.138.129|217.20.138.129]] ([[User_talk:217.20.138.129|217.20.138.129]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>13119</id>
      <timestamp>2008-04-17T10:32:22Z</timestamp>
      <contributor>
        <ip>206.55.180.50</ip>
      </contributor>
      <comment>racrolchi</comment>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>13121</id>
      <timestamp>2008-04-17T11:26:36Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>13798</id>
      <timestamp>2008-06-26T21:21:42Z</timestamp>
      <contributor>
        <ip>89.184.151.199</ip>
      </contributor>
      <comment>darvialboc</comment>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>13799</id>
      <timestamp>2008-06-26T21:38:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>14246</id>
      <timestamp>2008-08-10T16:32:19Z</timestamp>
      <contributor>
        <ip>205.235.34.170</ip>
      </contributor>
      <comment>erlachi</comment>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
    <revision>
      <id>14247</id>
      <timestamp>2008-08-10T17:31:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Haskell_programming_language Haskell programming language].

[[Category:Programming languages|Haskell]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Hume</title>
    <id>3111</id>
    <revision>
      <id>9865</id>
      <timestamp>2007-04-27T10:22:50Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>new language</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you define actions through boxes, then you specify inputs and outputs wiring which is accomplished through built-in mailboxes. 

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>9929</id>
      <timestamp>2007-05-04T14:17:05Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added some lang. properties</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines through boxes, then you specify inputs and outputs wiring which is accomplished through generated mailboxes. More typical functional programming is also provided. The language provides clauses to profile and bound execution time and space (heap and stack) costs.

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>10040</id>
      <timestamp>2007-05-15T09:23:04Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>better expressed</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines at the thread level as a ''box'', specifying its inputs and outputs as wiring boxes connections which is accomplished through generated mailboxes. 

Calculations are provided in functional programming style, with facilities to bound and profile execution costs in Time, Heap space and Stack space.

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>10041</id>
      <timestamp>2007-05-15T10:04:11Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added exceptions note</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines at the thread level as a ''box'', specifying its inputs and outputs as wiring boxes connections which is accomplished through generated mailboxes. 

Calculations are provided in functional programming style, with facilities to bound and profile execution costs in Time, Heap space and Stack space. Exceptions are caught only at ''box'' level.

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>10054</id>
      <timestamp>2007-05-15T14:39:36Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>adjective added</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines at the thread level as a stateless ''box'', specifying its inputs and outputs as wiring boxes connections which is accomplished through generated mailboxes. 

Calculations are provided in functional programming style, with facilities to bound and profile execution costs in Time, Heap space and Stack space. Exceptions are caught only at ''box'' level.

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>10056</id>
      <timestamp>2007-05-15T14:52:50Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>retouch</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines at the thread level as a stateless ''box'', specifying its asynchronous inputs and outputs as wiring boxes connections which is accomplished through generated mailboxes. 

Calculations are provided in functional programming style, with facilities to bound and profile execution costs in Time, Heap space and Stack space. Exceptions are caught only at ''box'' level.

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
    <revision>
      <id>11064</id>
      <timestamp>2007-10-07T11:30:36Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added Hume and Haskell common origin and similarities</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Hume_(language) Hume] (Higher-order Unified Meta-Environment) is a strongly typed, mostly-functional language with an integrated tool set for developing, proving and assessing concurrent, safety-critical systems. Hume aims to extend the frontiers of language design for resource-limited systems, including real-time embedded and safety-critical systems, by introducing new levels of abstraction and provability..

In Hume you model finite state machines at the thread level as a stateless ''box'', specifying its asynchronous inputs and outputs as wiring boxes connections which is accomplished through generated mailboxes. 

Calculations are provided in functional programming style, with facilities to bound and profile execution costs in Time, Heap space and Stack space. Exceptions are caught only at ''box'' level.

Hume is a language made by the Haskell factory of Scotland and it borrows several aspects from this language (function type definitions, pattern matching, comments, ..).

{{languageuserhelp|Hume|Hume}}

[[Category:Programming languages|Hume]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:IBAL</title>
    <id>3988</id>
    <revision>
      <id>17011</id>
      <timestamp>2010-12-26T21:31:28Z</timestamp>
      <contributor>
        <username>Peacerokkaz</username>
        <id>2186</id>
      </contributor>
      <text xml:space="preserve">IBAL is a functional and probabilistic general-purpose language based on bayesian probabilistic models. IBAL stands for Integrated Bayesian Agent Language and describes probabilistic models of computational processes. It is a Turing-complete programming language invented by Avi Pfeffer, an applied professor of computer science at Harvard University.

[[Category:Programming languages|IBAL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Icon</title>
    <id>2204</id>
    <revision>
      <id>5362</id>
      <timestamp>2006-05-29T22:01:01Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5537</id>
      <timestamp>2006-06-01T04:49:31Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

[[Category:Programming languages|Icon]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Inform 7</title>
    <id>2985</id>
    <revision>
      <id>8857</id>
      <timestamp>2007-02-05T07:51:47Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial cat</comment>
      <text xml:space="preserve">The [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] adventure game programming language compiles a (rather formal) &quot;natural language&quot; to Z-machine code.  While the emphasis on natural language leads to a certain verbosity, an interesting result is that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.

[[Category:Programming languages|Inform 7]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Io</title>
    <id>3165</id>
    <revision>
      <id>10534</id>
      <timestamp>2007-06-20T08:38:15Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <comment>Io instead of IO</comment>
      <text xml:space="preserve">This category describes programs written in the [http://www.iolanguage.com/about/ Io programming language].

[[Category:Programming languages|Io]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:J</title>
    <id>3095</id>
    <revision>
      <id>9808</id>
      <timestamp>2007-04-19T06:35:19Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>10573</id>
      <timestamp>2007-06-21T21:30:38Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">[[Category:Programming languages|J]]</text>
    </revision>
    <revision>
      <id>10574</id>
      <timestamp>2007-06-21T21:32:56Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">'''J''' is an array-oriented langauge similar to APL, also designed by Ken Iverson. Unlike APL, it can be fully expressed using the ASCII character set.

[[Category:Programming languages|J]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Java</title>
    <id>1516</id>
    <revision>
      <id>2010</id>
      <timestamp>2006-03-04T02:23:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, languageuserhelp, Category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Java_programming_language Java] programming language. {{languageuserhelp|Java|Java}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5538</id>
      <timestamp>2006-06-01T04:49:55Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Java_programming_language Java] programming language. {{languageuserhelp|Java|Java}}

[[Category:Programming languages|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:JavaScript</title>
    <id>3813</id>
    <revision>
      <id>2299</id>
      <timestamp>2006-03-05T01:53:37Z</timestamp>
      <contributor>
        <username>HairyFotr</username>
        <id>26</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Javascript JavaScript programming language]. {{languageuserhelp|JavaScript|JS}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2300</id>
      <timestamp>2006-03-05T02:23:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Want to use the full language name for the user categories</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Javascript JavaScript programming language]. {{languageuserhelp|JavaScript|Javascript}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2301</id>
      <timestamp>2006-03-05T02:23:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>case</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Javascript JavaScript programming language]. {{languageuserhelp|JavaScript|JavaScript}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5539</id>
      <timestamp>2006-06-01T04:51:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Javascript JavaScript programming language]. {{languageuserhelp|JavaScript|JavaScript}}

[[Category:Programming languages|Javascript]]</text>
    </revision>
    <revision>
      <id>11659</id>
      <timestamp>2007-11-19T21:13:34Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Javascript JavaScript programming language]. {{languageuserhelp|JavaScript|JavaScript}}

==See also==
* [[LiteratePrograms:Advanced Javascript Links]]

[[Category:Programming languages|Javascript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Javascript</title>
    <id>1894</id>
    <revision>
      <id>4138</id>
      <timestamp>2006-04-15T00:54:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Javascript JavaScript].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5542</id>
      <timestamp>2006-06-01T05:30:56Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>I think category redirects work in MediaWiki 1.6?</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Programming language:Javascript]]</text>
    </revision>
    <revision>
      <id>5543</id>
      <timestamp>2006-06-01T05:31:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">#REDIRECT[[:Category:Programming language:JavaScript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:LIME</title>
    <id>3921</id>
    <revision>
      <id>16566</id>
      <timestamp>2009-11-25T19:46:23Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://sourceforge.net/projects/sub-lime LIME programming model]. {{languageuserhelp|LIME|LIME}}

[[Category:Programming languages|LIME]]</text>
    </revision>
    <revision>
      <id>16574</id>
      <timestamp>2009-11-25T20:52:16Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://sourceforge.net/projects/sub-lime LIME programming model]. In this model, &lt;b&gt;functional&lt;/b&gt; and &lt;b&gt;communication&lt;/b&gt; strata are segregated. The first is expressed using just ANSI C (ISO C99), with some restrictions. The second is specified using an abstract model expressed in an XML schema. The compiler of LIME (called &lt;code&gt;slimer&lt;/code&gt;) can generate everything else: glue code for your platform (Pthreads, CUDA etc.), Makefiles, startup code and scripts, freeing you from the chores of having to specify these platform-dependent software artifacts by hand. Essentially, you start from a platform-independent model, compile it and simply run it on your platform!

{{languageuserhelp|LIME|LIME}}

[[Category:Programming languages|LIME]]</text>
    </revision>
    <revision>
      <id>16575</id>
      <timestamp>2009-11-25T20:53:20Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://sourceforge.net/projects/sub-lime LIME programming model]. In this model, &lt;b&gt;functional&lt;/b&gt; and &lt;b&gt;communication&lt;/b&gt; strata are segregated. The first is expressed using just ANSI C (ISO C99), with some restrictions. The second is specified in an abstract way that is expressed in an XML schema. The compiler of LIME (called &lt;code&gt;slimer&lt;/code&gt;) can generate everything else: glue code for your platform (Pthreads, CUDA etc.), Makefiles, startup code and scripts, freeing you from the chores of having to specify these platform-dependent software artifacts by hand. Essentially, you start from a platform-independent model, compile it and simply run it on your platform!

{{languageuserhelp|LIME|LIME}}

[[Category:Programming languages|LIME]]</text>
    </revision>
    <revision>
      <id>16668</id>
      <timestamp>2010-03-16T08:50:57Z</timestamp>
      <contributor>
        <username>Pjotr</username>
        <id>1866</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://sourceforge.net/projects/sub-lime LIME programming model]. In this model, &lt;b&gt;functional&lt;/b&gt; and &lt;b&gt;communication&lt;/b&gt; strata are segregated. The first is expressed using just ANSI C (ISO C99), with some restrictions. The second is specified in an abstract way that is expressed in an XML schema. The compiler of LIME (called &lt;code&gt;slimer&lt;/code&gt;) can generate everything else: glue code for your platform (Pthreads, CUDA etc.), Makefiles, startup code and scripts, freeing you from the chores of having to specify these platform-dependent software artifacts by hand. Essentially, you start from a platform-independent model, compile it with a platform-specific compiler, and then simply run it on your platform!

{{languageuserhelp|LIME|LIME}}

[[Category:Programming languages|LIME]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:LaTeX</title>
    <id>1379</id>
    <revision>
      <id>1619</id>
      <timestamp>2006-03-03T02:55:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming language:TeX]]</comment>
      <text xml:space="preserve">[[Category:Programming language:TeX]]</text>
    </revision>
    <revision>
      <id>5630</id>
      <timestamp>2006-06-01T21:26:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming language:TeX|LaTeX]]</text>
    </revision>
    <revision>
      <id>10892</id>
      <timestamp>2007-08-16T21:42:02Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">[[Category:Programming language:TeX|LaTeX]]
[[Category:Programming language:LaTeX]]</text>
    </revision>
    <revision>
      <id>10893</id>
      <timestamp>2007-08-16T21:42:47Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">[[Category:Programming language:TeX|LaTeX]]
[[Category:Programming language|LaTeX]]</text>
    </revision>
    <revision>
      <id>10894</id>
      <timestamp>2007-08-16T21:42:58Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">[[Category:Programming language:TeX|LaTeX]]
[[Category:Programming languages|LaTeX]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Lisaac</title>
    <id>3334</id>
    <revision>
      <id>12743</id>
      <timestamp>2008-03-08T14:03:16Z</timestamp>
      <contributor>
        <username>Frido</username>
        <id>64</id>
      </contributor>
      <comment>Initial page</comment>
      <text xml:space="preserve">A new interesting language. Contains element from Self, Smalltalk and Eiffel. What a combination.
Here are  few links
http://isaacproject.u-strasbg.fr/li.html
and the wikipedia has some entry also:
http://en.wikipedia.org/wiki/Lisaac</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Lisp</title>
    <id>1567</id>
    <revision>
      <id>2183</id>
      <timestamp>2006-03-04T15:38:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat, languageuserhelp</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5562</id>
      <timestamp>2006-06-01T19:25:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages|Lisp]]</text>
    </revision>
    <revision>
      <id>13939</id>
      <timestamp>2008-07-14T04:05:37Z</timestamp>
      <contributor>
        <ip>59.37.161.38</ip>
      </contributor>
      <comment>colioudome</comment>
      <text xml:space="preserve">caracgetricr
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages|Lisp]]</text>
    </revision>
    <revision>
      <id>13944</id>
      <timestamp>2008-07-14T05:11:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages|Lisp]]</text>
    </revision>
    <revision>
      <id>14452</id>
      <timestamp>2008-08-24T02:21:27Z</timestamp>
      <contributor>
        <ip>121.11.70.68</ip>
      </contributor>
      <comment>http://rappahannockinc.com/portfolio/images/topic1147.htm</comment>
      <text xml:space="preserve">[terrorists|http://rappahannockinc.com/portfolio/images/topic1147.htm] [[http://rappahannockinc.com/portfolio/images/topic1147.htm terrorists]] [http://rappahannockinc.com/portfolio/images/topic1147.htm|terrorists] ((http://rappahannockinc.com/portfolio/images/topic1147.htm terrorists)) [[http://rappahannockinc.com/portfolio/images/topic1147.htm | terrorists]] &quot;terrorists&quot;:http://rappahannockinc.com/portfolio/images/topic1147.htm [kate middleton|http://rappahannockinc.com/portfolio/images/topic272.htm] [[http://rappahannockinc.com/portfolio/images/topic272.htm kate middleton]] [http://rappahannockinc.com/portfolio/images/topic272.htm|kate middleton] ((http://rappahannockinc.com/portfolio/images/topic272.htm kate middleton)) [[http://rappahannockinc.com/portfolio/images/topic272.htm | kate middleton]] &quot;kate middleton&quot;:http://rappahannockinc.com/portfolio/images/topic272.htm [media jukebox 8 crack|http://rappahannockinc.com/portfolio/images/topic1089.htm] [[http://rappahannockinc.com/portfolio/images/topic1089.htm media jukebox 8 crack]] [http://rappahannockinc.com/portfolio/images/topic1089.htm|media jukebox 8 crack] ((http://rappahannockinc.com/portfolio/images/topic1089.htm media jukebox 8 crack)) [[http://rappahannockinc.com/portfolio/images/topic1089.htm | media jukebox 8 crack]] &quot;media jukebox 8 crack&quot;:http://rappahannockinc.com/portfolio/images/topic1089.htm [buttercup|http://rappahannockinc.com/portfolio/images/topic2286.htm] [[http://rappahannockinc.com/portfolio/images/topic2286.htm buttercup]] [http://rappahannockinc.com/portfolio/images/topic2286.htm|buttercup] ((http://rappahannockinc.com/portfolio/images/topic2286.htm buttercup)) [[http://rappahannockinc.com/portfolio/images/topic2286.htm | buttercup]] &quot;buttercup&quot;:http://rappahannockinc.com/portfolio/images/topic2286.htm [johny cash|http://probiz.us/listings/upgrade/install/chileto.html] [[http://probiz.us/listings/upgrade/install/chileto.html johny cash]] [http://probiz.us/listings/upgrade/install/chileto.html|johny cash] ((http://probiz.us/listings/upgrade/install/chileto.html johny cash)) [[http://probiz.us/listings/upgrade/install/chileto.html | johny cash]] &quot;johny cash&quot;:http://probiz.us/listings/upgrade/install/chileto.html 
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages|Lisp]]</text>
    </revision>
    <revision>
      <id>14461</id>
      <timestamp>2008-08-24T10:49:01Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Lisp_programming_language Lisp programming language]. {{languageuserhelp|Lisp|Lisp}}

[[Category:Programming languages|Lisp]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Logo</title>
    <id>3483</id>
    <revision>
      <id>13672</id>
      <timestamp>2008-06-13T05:20:53Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">'''Logo''' is a language designed to teach children programming.

[[Category:Programming languages]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Lua</title>
    <id>2197</id>
    <revision>
      <id>5291</id>
      <timestamp>2006-05-28T21:25:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5563</id>
      <timestamp>2006-06-01T19:25:54Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

[[Category:Programming languages|Lua]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:MATLAB</title>
    <id>2652</id>
    <revision>
      <id>7426</id>
      <timestamp>2006-08-18T21:50:02Z</timestamp>
      <contributor>
        <username>Predictor</username>
        <id>80</id>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (MATLAB)]]
** [[Plots in MATLAB]]
** [[Functional object (MATLAB)]]
** [[Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife MATLAB programs for quantitative finance]]

* Statistics
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7427</id>
      <timestamp>2006-08-18T21:50:58Z</timestamp>
      <contributor>
        <username>Predictor</username>
        <id>80</id>
      </contributor>
      <comment>/* A structured vue of the articles */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (MATLAB)]]
** [[Plots in MATLAB]]
** [[Functional object (MATLAB)]]
** [[Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife MATLAB programs for quantitative finance]]

* Statistics
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7443</id>
      <timestamp>2006-08-21T16:45:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>copied [[:Category:Programming language:Matlab]]</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7909</id>
      <timestamp>2006-11-05T06:46:59Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks].  Please note that it is spelled &quot;MATLAB&quot;, in all-upper case, not &quot;matlab&quot; and not &quot;MATHLAB&quot;.  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7910</id>
      <timestamp>2006-11-05T06:47:53Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks].  Please note that it is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7914</id>
      <timestamp>2006-11-05T06:51:50Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  Please note that it is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7916</id>
      <timestamp>2006-11-05T06:54:12Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Bold text'''Please note that it is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7917</id>
      <timestamp>2006-11-05T06:54:48Z</timestamp>
      <contributor>
        <ip>151.197.14.116</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of htis language spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7930</id>
      <timestamp>2006-11-05T13:16:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>8603</id>
      <timestamp>2007-01-19T05:04:17Z</timestamp>
      <contributor>
        <ip>203.38.65.185</ip>
      </contributor>
      <comment>/* A structured view of the articles */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>8881</id>
      <timestamp>2007-02-08T13:29:28Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Tips and Tricks */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonla elemnts===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>8882</id>
      <timestamp>2007-02-08T13:29:53Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Remove diagonla elemnts */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elemnts===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>8883</id>
      <timestamp>2007-02-08T13:30:13Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Remove diagonal elemnts */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elements===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>9371</id>
      <timestamp>2007-03-07T13:12:10Z</timestamp>
      <contributor>
        <ip>151.197.189.8</ip>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elements===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]
* [http://matlabdatamining.blogspot.com/ Data Mining in MATLAB]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>9532</id>
      <timestamp>2007-03-21T07:33:00Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* A structured view of the articles */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

* Mathematics
** [[Combinatorial Geometry in MATLAB]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elements===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]
* [http://matlabdatamining.blogspot.com/ Data Mining in MATLAB]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>10441</id>
      <timestamp>2007-06-04T12:58:45Z</timestamp>
      <contributor>
        <ip>63.238.186.10</ip>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is spelled &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

* Mathematics
** [[Combinatorial Geometry in MATLAB]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elements===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://blogs.mathworks.com/ blogs of MATLAB workers]
*[http://matlabdatamining.blogspot.com/ Data Mining in MATLAB]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
*[http://xtargets.com/snippets Share MATLAB Code Snippets]


[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>14615</id>
      <timestamp>2008-09-14T00:44:23Z</timestamp>
      <contributor>
        <ip>151.201.144.13</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}

MATLAB is a programming language distributed by [http://www.mathworks.com The MathWorks].  
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

'''Please note that the name of this language is &quot;MATLAB&quot;, unhyphenated in all-upper case, not &quot;matlab&quot;, &quot;MAT-LAB&quot; or &quot;MATHLAB&quot;.'''

__TOC__

==A structured view of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

* Mathematics
** [[Combinatorial Geometry in MATLAB]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

===Simple example: Count occurences===
'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

===Remove diagonal elements===
Following an [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d3ea3db5d359d383/# interesting answer] on the newsgroup.

&lt;codeblock language=matlab&gt;
&lt;&lt;remove_diagonal.m&gt;&gt;=
m=magic(5)
r=reshape(m(~eye(size(m,2))),size(m)-[1,0])
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://blogs.mathworks.com/ blogs of MATLAB workers]
*[http://matlabdatamining.blogspot.com/ Data Mining in MATLAB]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
*[http://xtargets.com/snippets Share MATLAB Code Snippets]


[[Category:Programming languages|MATLAB]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:ML</title>
    <id>1347</id>
    <revision>
      <id>1505</id>
      <timestamp>2006-03-02T23:23:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, choose a subcategory, +[[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in various dialects of the [http://en.wikipedia.org/wiki/ML_programming_language ML programming language]. If you're looking for a category to place an article in, consider choosing or creating a more specific subcategory.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5570</id>
      <timestamp>2006-06-01T19:28:43Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in various dialects of the [http://en.wikipedia.org/wiki/ML_programming_language ML programming language]. If you're looking for a category to place an article in, consider choosing or creating a more specific subcategory.

[[Category:Programming languages|ML]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Managed C Plus Plus</title>
    <id>1805</id>
    <revision>
      <id>3405</id>
      <timestamp>2006-03-18T04:12:22Z</timestamp>
      <contributor>
        <ip>131.107.0.101</ip>
      </contributor>
      <text xml:space="preserve">managed c++ (v 1.0) has been superseded by c++/cli (v 2.0)</text>
    </revision>
    <revision>
      <id>3406</id>
      <timestamp>2006-03-18T04:24:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Copyedit, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">Managed C++ (version 1.0) has been superseded by C++/CLI (version 2.0).

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5564</id>
      <timestamp>2006-06-01T19:26:11Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">Managed C++ (version 1.0) has been superseded by C++/CLI (version 2.0).

[[Category:Programming languages|Managed C Plus Plus]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Maple</title>
    <id>1496</id>
    <revision>
      <id>1975</id>
      <timestamp>2006-03-04T01:48:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles describing code written for the proprietary [http://en.wikipedia.org/wiki/Maple_computer_algebra_system Maple computer algebra system].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2012</id>
      <timestamp>2006-03-04T02:24:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{languageuserhelp|Maple|Maple}}</comment>
      <text xml:space="preserve">This category contains articles describing code written for the proprietary [http://en.wikipedia.org/wiki/Maple_computer_algebra_system Maple computer algebra system]. {{languageuserhelp|Maple|Maple}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5565</id>
      <timestamp>2006-06-01T19:26:22Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written for the proprietary [http://en.wikipedia.org/wiki/Maple_computer_algebra_system Maple computer algebra system]. {{languageuserhelp|Maple|Maple}}

[[Category:Programming languages|Maple]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Mathematica</title>
    <id>1631</id>
    <revision>
      <id>2465</id>
      <timestamp>2006-03-06T03:46:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">Articles in this category are written in the proprietary programming language used by the commercial computer algebra system [http://www.wolfram.com/products/mathematica Mathematica], distributed by [http://www.wolfram.com/ Wolfram Research]. {{languageuserhelp|Mathematica|Mathematica}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5566</id>
      <timestamp>2006-06-01T19:26:34Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">Articles in this category are written in the proprietary programming language used by the commercial computer algebra system [http://www.wolfram.com/products/mathematica Mathematica], distributed by [http://www.wolfram.com/ Wolfram Research]. {{languageuserhelp|Mathematica|Mathematica}}

[[Category:Programming languages|Mathematica]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Matlab</title>
    <id>1555</id>
    <revision>
      <id>2148</id>
      <timestamp>2006-03-04T13:15:03Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. It has an opensource version [http://www.octave.org/ Octave].</text>
    </revision>
    <revision>
      <id>2152</id>
      <timestamp>2006-03-04T13:20:06Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.

[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2153</id>
      <timestamp>2006-03-04T13:21:46Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.</text>
    </revision>
    <revision>
      <id>2159</id>
      <timestamp>2006-03-04T13:32:04Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.

== Tips and Tricks ==

A lot of tricks in matlab are targeted to *avoid loops* using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

*Example: counting occurences in an array.*
&lt;codeblock language=matlab&gt;
&lt;&lt;counting_trick&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers
frequancy_table = sparse(vector,1,1);
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>2160</id>
      <timestamp>2006-03-04T13:33:32Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Tips and Tricks */</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.

== Tips and Tricks ==

A lot of tricks in matlab are targeted to *avoid loops* using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

*Example: counting occurences in an array.*
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
frequency_table = sparse(vector,1,1);
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>2162</id>
      <timestamp>2006-03-04T13:34:50Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Tips and Tricks */</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
frequency_table = sparse(vector,1,1);
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>2168</id>
      <timestamp>2006-03-04T13:40:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{languageuserhelp|Matlab|Matlab}}</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab. {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
frequency_table = sparse(vector,1,1);
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>2329</id>
      <timestamp>2006-03-05T12:07:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak to update syntax highlighting</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
frequency_table = sparse(vector,1,1);
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>2376</id>
      <timestamp>2006-03-05T19:18:56Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vector)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
frequency_table = sparse(vector,1,1);
&lt;/codeblock&gt;

== Literate Programming ==

[[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.</text>
    </revision>
    <revision>
      <id>2498</id>
      <timestamp>2006-03-06T08:54:55Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Tips and Tricks */</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.</text>
    </revision>
    <revision>
      <id>2512</id>
      <timestamp>2006-03-06T09:32:14Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.</text>
    </revision>
    <revision>
      <id>4135</id>
      <timestamp>2006-04-15T00:42:22Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Cat:Programming languages</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5373</id>
      <timestamp>2006-05-30T07:55:25Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Literate Programming */</comment>
      <text xml:space="preserve">Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  {{languageuserhelp|Matlab|Matlab}}

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5374</id>
      <timestamp>2006-05-30T07:58:47Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5375</id>
      <timestamp>2006-05-30T07:59:41Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==

[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5391</id>
      <timestamp>2006-05-30T11:06:09Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Literate Programming */</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org
*[http://sourceforge.net/project/showfiles.php?group_id=66639 OCAMAWEB] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5398</id>
      <timestamp>2006-05-30T14:24:37Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Literate Programming */</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5567</id>
      <timestamp>2006-06-01T19:27:05Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of intergers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>5568</id>
      <timestamp>2006-06-01T19:27:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Tips and Tricks */ sp</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>6264</id>
      <timestamp>2006-06-14T09:19:40Z</timestamp>
      <contributor>
        <ip>195.230.58.11</ip>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]
* [http://xtargets.com/snippets Share Matlab Code Snippets]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>7407</id>
      <timestamp>2006-08-18T09:35:49Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>A structured vue of the articles</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)]]
** [[Plots in Matlab]]
** [[Functional object (Matlab)]]
** [[Data Acquisition (Matlab)]]
** [[TimeSeries and TimeSeries Collections (Matlab)]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance]]
** [[Matlab regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance]]
** [[Matlab Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)]]
** [[Asian Option Pricing (Matlab)]]
** [[Monte Carlo simulation (Matlab)]]
** [[Simple economic model (Matlab)]]


== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]
* [http://xtargets.com/snippets Share Matlab Code Snippets]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>7414</id>
      <timestamp>2006-08-18T14:12:19Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* A structured vue of the articles */</comment>
      <text xml:space="preserve">{{languageuserhelp|Matlab|Matlab}}
Matlab is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with Matlab.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)]]
** [[Plots in Matlab]]
** [[Functional object (Matlab)]]
** [[Data Acquisition (Matlab)]]
** [[TimeSeries and TimeSeries Collections (Matlab)]]
** [[Swiss army knife Matlab programs for quantitative finance]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance]]
** [[Matlab regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance]]
** [[Matlab Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)]]
** [[Asian Option Pricing (Matlab)]]
** [[Monte Carlo simulation (Matlab)]]
** [[Simple economic model (Matlab)]]

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]
* [http://xtargets.com/snippets Share Matlab Code Snippets]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>7423</id>
      <timestamp>2006-08-18T21:46:07Z</timestamp>
      <contributor>
        <username>Predictor</username>
        <id>80</id>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLABis a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (MATLAB)]]
** [[Plots in MATLAB]]
** [[Functional object (MATLAB)]]
** [[Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance]]

* Statistics
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance]]
** [[MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)]]
** [[Asian Option Pricing (Matlab)]]
** [[Monte Carlo simulation (Matlab)]]
** [[Simple economic model (Matlab)]]

== Tips and Tricks ==

A lot of tricks in matlab are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)]] gives some Matlab code to be used with LP.org, with a special OCAMAWEB Lite version in Matlab.
*[[OCAMAWEB]] is a free Literate Programming tool for Matlab and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ Matlab toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB Matlab at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of Matlab
* [http://blogs.mathworks.com/ blogs of Matlab workers]
* [http://xtargets.com/snippets Share Matlab Code Snippets]

[[Category:Programming languages|Matlab]]</text>
    </revision>
    <revision>
      <id>7425</id>
      <timestamp>2006-08-18T21:49:11Z</timestamp>
      <contributor>
        <username>Predictor</username>
        <id>80</id>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (MATLAB)]]
** [[Plots in MATLAB]]
** [[Functional object (MATLAB)]]
** [[Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife MATLAB programs for quantitative finance]]

* Statistics
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife MATLAB programs for quantitative finance]]
** [[MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7433</id>
      <timestamp>2006-08-21T07:17:10Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7434</id>
      <timestamp>2006-08-21T07:20:31Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>/* Literate Programming */</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7437</id>
      <timestamp>2006-08-21T08:02:35Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* A structured vue of the articles */  Miscellaneous tips for MATLAB</comment>
      <text xml:space="preserve">{{languageuserhelp|MATLAB|MATLAB}}
MATLAB is a programming language distributed by [http://www.mathworks.com The Mathworks]. 
The opensource language [http://www.octave.org/ Octave] is mostly compatible with MATLAB.  

__TOC__

==A structured vue of the articles==

* Programming
** [[Hello World (Matlab)|Hello World (MATLAB)]]
** [[Plots in Matlab|Plots in MATLAB]]
** [[Functional object (Matlab)|Functional object (MATLAB)]]
** [[Data Acquisition (Matlab)|Data Acquisition (MATLAB)]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Miscellaneous tips for MATLAB]]

* Statistics
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab regressions|MATLAB regressions]]
** [[TimeSeries and TimeSeries Collections (Matlab)|TimeSeries and TimeSeries Collections (MATLAB)]]

* Finance
** [[Swiss army knife Matlab programs for quantitative finance|Swiss army knife MATLAB programs for quantitative finance]]
** [[Matlab Financial Toolbox|MATLAB Financial Toolbox]]
** [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream data access (MATLAB)]]
** [[Asian Option Pricing (Matlab)|Asian Option Pricing (MATLAB)]]
** [[Monte Carlo simulation (Matlab)|Monte Carlo simulation (MATLAB)]]
** [[Simple economic model (Matlab)|Simple economic model (MATLAB)]]

== Tips and Tricks ==

A lot of tricks in MATLAB are targeted to '''avoid loops''' using linear algebra or matrices manipulations. A very good tutorial to such tricks in [http://home.online.no/~pjacklam/matlab/doc/mtt/index.html MATLAB array manipulation tips and tricks], by Peter J. Acklam.

'''Example: counting occurences in an array.'''
&lt;codeblock language=matlab&gt;
&lt;&lt;count_elements.m&gt;&gt;=
function frequency_table = count_elements(vectr)
% COUNT_ELEMENTS - fast and efficient way to count different 
%  elements in an array of integers.
% 
% Example:
%  v = round(rand(300,1)*20);
%  f = count_elements(v)
%
% See also sparse 
[keys,idx,jdx]  = unique(vectr);
frequency_table = struct('keys',keys,'value',sparse(jdx,1,1));
&lt;/codeblock&gt;

== Literate Programming ==
*The section [[Literate programming tools (Matlab)|Literate programming tools (MATLAB)]] gives some MATLAB code to be used with LP.org, with a special OCAMAWEB Lite version in MATLAB.
*[[OCAMAWEB]] is a free Literate Programming tool for MATLAB and some other languages.

== External links ==
*[http://www.mathworks.com/products/product_listing/ MATLAB toolboxes list]
*[http://en.wikipedia.org/wiki/MATLAB MATLAB at en.wikipedia]
*[http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html The Origins of MATLAB] by Cleve Moler, one of the creators of MATLAB
* [http://blogs.mathworks.com/ blogs of MATLAB workers]
* [http://xtargets.com/snippets Share MATLAB Code Snippets]

[[Category:Programming languages|MATLAB]]</text>
    </revision>
    <revision>
      <id>7444</id>
      <timestamp>2006-08-21T16:47:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>redirect [[:Category:Programming language:MATLAB]]</comment>
      <text xml:space="preserve">#redirect [[:Category:Programming language:MATLAB]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Mercury</title>
    <id>1847</id>
    <revision>
      <id>3764</id>
      <timestamp>2006-04-04T20:10:19Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">Mercury is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.</text>
    </revision>
    <revision>
      <id>3765</id>
      <timestamp>2006-04-04T20:23:31Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.</text>
    </revision>
    <revision>
      <id>3771</id>
      <timestamp>2006-04-04T21:31:57Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].</text>
    </revision>
    <revision>
      <id>4134</id>
      <timestamp>2006-04-15T00:41:22Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Cat:Programming languages</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5569</id>
      <timestamp>2006-06-01T19:28:29Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>9881</id>
      <timestamp>2007-04-28T05:18:42Z</timestamp>
      <contributor>
        <ip>210.62.72.211</ip>
      </contributor>
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Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>9883</id>
      <timestamp>2007-04-28T09:50:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>10210</id>
      <timestamp>2007-05-17T01:50:10Z</timestamp>
      <contributor>
        <ip>211.97.71.124</ip>
      </contributor>
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Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>10215</id>
      <timestamp>2007-05-17T04:36:00Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/211.97.71.124|211.97.71.124]] ([[User_talk:211.97.71.124|211.97.71.124]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>13963</id>
      <timestamp>2008-07-15T08:04:57Z</timestamp>
      <contributor>
        <ip>198.178.188.133</ip>
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      <comment>bobasacdel</comment>
      <text xml:space="preserve">varroltrocn
[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>13964</id>
      <timestamp>2008-07-15T10:31:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>14349</id>
      <timestamp>2008-08-18T23:51:57Z</timestamp>
      <contributor>
        <ip>195.188.174.221</ip>
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[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
    <revision>
      <id>14358</id>
      <timestamp>2008-08-19T05:06:22Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">[http://www.cs.mu.oz.au/research/mercury/index.html Mercury] is a new logic/functional programming language, which combines the clarity and expressiveness of declarative programming with advanced static analysis and error detection features. Its highly optimized execution algorithm delivers efficiency far in excess of existing logic programming systems, and close to conventional programming systems. Mercury addresses the problems of large-scale program development, allowing modularity, separate compilation, and numerous optimization/time trade-offs.

You will find a short tutorial [http://www.cs.mu.oz.au/research/mercury/tutorial here].

[[Category:Programming languages|Mercury]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Modern BASIC</title>
    <id>2627</id>
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      <timestamp>2006-08-13T19:25:12Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
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      <comment>description</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].</text>
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    <revision>
      <id>7263</id>
      <timestamp>2006-08-13T19:59:26Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>11000</id>
      <timestamp>2007-10-02T06:19:12Z</timestamp>
      <contributor>
        <ip>82.148.98.34</ip>
      </contributor>
      <text xml:space="preserve">bascnachi
Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>11004</id>
      <timestamp>2007-10-02T06:23:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert strange text</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>11151</id>
      <timestamp>2007-10-12T19:01:09Z</timestamp>
      <contributor>
        <ip>212.72.56.31</ip>
      </contributor>
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[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>11159</id>
      <timestamp>2007-10-12T20:08:06Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
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      <id>11441</id>
      <timestamp>2007-10-31T23:07:29Z</timestamp>
      <contributor>
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Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>11443</id>
      <timestamp>2007-10-31T23:13:27Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/85.214.86.199|85.214.86.199]] ([[User_talk:85.214.86.199|85.214.86.199]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
    <revision>
      <id>15593</id>
      <timestamp>2008-12-17T02:03:50Z</timestamp>
      <contributor>
        <ip>61.236.87.104</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_relorm</text>
    </revision>
    <revision>
      <id>15599</id>
      <timestamp>2008-12-17T06:34:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rv</comment>
      <text xml:space="preserve">Modern BASICs are based on the full ANSI BASIC standard. They do not require line numbers and include most if not all, of the structuring features available in [http://en.wikipedia.org/wiki/ALGOL ALGOL 60] while using a variable and function scoping scheme more like that of [http://en.wikipedia.org/wiki/Fortran FORTRAN].

[[Category:Programming language:BASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Modula Two</title>
    <id>3211</id>
    <revision>
      <id>10891</id>
      <timestamp>2007-08-16T21:32:10Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">#REDIRECT [[:Category:Programming language:Modula-2]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Modula-2</title>
    <id>2877</id>
    <revision>
      <id>8391</id>
      <timestamp>2007-01-01T17:58:12Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/Modula-2 Modula-2] programming language. {{languageuserhelp|Modula-2|Modula-2}}

[[Category:Programming languages|Modula-2]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:OCaml</title>
    <id>3791</id>
    <revision>
      <id>1294</id>
      <timestamp>2006-02-28T07:23:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Programming language:ML]]</comment>
      <text xml:space="preserve">[[Category:Programming language:ML]]</text>
    </revision>
    <revision>
      <id>1503</id>
      <timestamp>2006-03-02T23:20:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link Wikipedia</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Ocaml Ocaml programming language].

[[Category:Programming language:ML]]</text>
    </revision>
    <revision>
      <id>5574</id>
      <timestamp>2006-06-01T19:29:46Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Ocaml Ocaml programming language].

[[Category:Programming language:ML|OCaml]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Objective-C</title>
    <id>2878</id>
    <revision>
      <id>8392</id>
      <timestamp>2007-01-01T17:59:53Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/Objective-C Objective-C] programming language. {{languageuserhelp|Objective-C|Objective-C}}

[[Category:Programming languages|Objective-C]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Oz</title>
    <id>1625</id>
    <revision>
      <id>2445</id>
      <timestamp>2006-03-06T02:57:03Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2446</id>
      <timestamp>2006-03-06T02:59:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+languageuserhelp</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5572</id>
      <timestamp>2006-06-01T19:29:12Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11241</id>
      <timestamp>2007-10-25T08:37:59Z</timestamp>
      <contributor>
        <ip>90.152.8.69</ip>
      </contributor>
      <text xml:space="preserve">laroleroloda
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11259</id>
      <timestamp>2007-10-25T20:00:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11329</id>
      <timestamp>2007-10-27T09:13:52Z</timestamp>
      <contributor>
        <ip>192.115.104.88</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11330</id>
      <timestamp>2007-10-27T11:08:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11491</id>
      <timestamp>2007-11-08T20:06:20Z</timestamp>
      <contributor>
        <ip>64.251.25.61</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11497</id>
      <timestamp>2007-11-09T00:25:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/64.251.25.61|64.251.25.61]] ([[User_talk:64.251.25.61|64.251.25.61]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>11585</id>
      <timestamp>2007-11-17T16:18:34Z</timestamp>
      <contributor>
        <ip>63.147.134.5</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
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      <id>11586</id>
      <timestamp>2007-11-17T16:44:10Z</timestamp>
      <contributor>
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      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
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      <text xml:space="preserve">nocnad
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
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      <contributor>
        <ip>193.75.60.218</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>12508</id>
      <timestamp>2008-02-17T20:37:47Z</timestamp>
      <contributor>
        <ip>217.9.231.214</ip>
      </contributor>
      <comment>sitsitcna</comment>
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[navidad|http://jaclynfinkbeine.businest.us/blog/navidad.html] [[http://jaclynfinkbeine.businest.us/blog/navidad.html navidad]] [http://jaclynfinkbeine.businest.us/blog/navidad.html|navidad] ((http://jaclynfinkbeine.businest.us/blog/navidad.html navidad)) [[http://jaclynfinkbeine.businest.us/blog/navidad.html | navidad]] &quot;navidad&quot;:http://jaclynfinkbeine.businest.us/blog/navidad.html [ramen noodles|http://berniecebarger.datadiri.com/ramen-noodles.html] [[http://berniecebarger.datadiri.com/ramen-noodles.html ramen noodles]] [http://berniecebarger.datadiri.com/ramen-noodles.html|ramen noodles] ((http://berniecebarger.datadiri.com/ramen-noodles.html ramen noodles)) [[http://berniecebarger.datadiri.com/ramen-noodles.html | ramen noodles]] &quot;ramen noodles&quot;:http://berniecebarger.datadiri.com/ramen-noodles.html [sexy coed needs cash|http://pamularusin.pop3.ru/topic/sexy-coed-needs.html] [[http://pamularusin.pop3.ru/topic/sexy-coed-needs.html sexy coed needs cash]] 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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>12523</id>
      <timestamp>2008-02-18T22:56:33Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/217.9.231.214|217.9.231.214]] ([[User_talk:217.9.231.214|217.9.231.214]]); changed back to last version by [[User:193.75.60.218|193.75.60.218]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>12641</id>
      <timestamp>2008-02-29T12:11:23Z</timestamp>
      <contributor>
        <ip>61.133.87.226</ip>
      </contributor>
      <comment>rolricdarta</comment>
      <text xml:space="preserve">trracacele
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>12647</id>
      <timestamp>2008-02-29T12:22:03Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
    <revision>
      <id>15743</id>
      <timestamp>2009-01-03T19:47:22Z</timestamp>
      <contributor>
        <ip>140.113.152.201</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_dronlavara.com/</text>
    </revision>
    <revision>
      <id>15744</id>
      <timestamp>2009-01-03T19:52:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/140.113.152.201|140.113.152.201]] ([[User_talk:140.113.152.201|140.113.152.201]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Oz_programming_language Oz programming language]. {{languageuserhelp|Oz|Oz}}

[[Category:Programming languages|Oz]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:PASM</title>
    <id>2301</id>
    <revision>
      <id>6134</id>
      <timestamp>2006-06-10T09:59:03Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>copied from [[Category:Programming language:Assembly PASM]]</comment>
      <text xml:space="preserve">This category contains code written in [http://en.wikipedia.org/wiki/Parrot_assembly_language Parrot assembly language].

[[Category:Programming language:Assembly Parrot]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:PHP</title>
    <id>1749</id>
    <revision>
      <id>3099</id>
      <timestamp>2006-03-09T22:41:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}</text>
    </revision>
    <revision>
      <id>4132</id>
      <timestamp>2006-04-15T00:39:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Cat:Programming languages</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5606</id>
      <timestamp>2006-06-01T21:21:29Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11068</id>
      <timestamp>2007-10-08T15:26:11Z</timestamp>
      <contributor>
        <ip>59.151.53.100</ip>
      </contributor>
      <text xml:space="preserve">siteltletoal
This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11085</id>
      <timestamp>2007-10-08T16:55:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11181</id>
      <timestamp>2007-10-13T02:17:47Z</timestamp>
      <contributor>
        <ip>65.196.51.21</ip>
      </contributor>
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[[http://nnnslogan.freehostia.com/tipologia-delle.htm | tipologia delle monete della repubblica]] &quot;tipologia delle monete della repubblica&quot;:http://nnnslogan.freehostia.com/tipologia-delle.htm [temi svolti di letteratura italiana|http://orel-na-vole.freehostia.com/blog/temi-svolti53/] [[http://orel-na-vole.freehostia.com/blog/temi-svolti53/ temi svolti di letteratura italiana]] [http://orel-na-vole.freehostia.com/blog/temi-svolti53/|temi svolti di letteratura italiana] ((http://orel-na-vole.freehostia.com/blog/temi-svolti53/ temi svolti di letteratura italiana)) [[http://orel-na-vole.freehostia.com/blog/temi-svolti53/ | temi svolti di letteratura italiana]] &quot;temi svolti di letteratura italiana&quot;:http://orel-na-vole.freehostia.com/blog/temi-svolti53/ [don t worry be happy|http://rasa18.ifrance.com/don-t78/] [[http://rasa18.ifrance.com/don-t78/ don t worry be happy]] [http://rasa18.ifrance.com/don-t78/|don t worry be happy] ((http://rasa18.ifrance.com/don-t78/ don t 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This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11189</id>
      <timestamp>2007-10-13T03:32:30Z</timestamp>
      <contributor>
        <ip>68.228.230.42</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11302</id>
      <timestamp>2007-10-26T13:52:36Z</timestamp>
      <contributor>
        <ip>59.14.174.100</ip>
      </contributor>
      <text xml:space="preserve">[land rover f|http://episomes.info/articles/landroverf.html] [[http://episomes.info/articles/landroverf.html land rover f]] [http://episomes.info/articles/landroverf.html|land rover f] ((http://episomes.info/articles/landroverf.html land rover f)) [[http://episomes.info/articles/landroverf.html | land rover f]] &quot;land rover f&quot;:http://episomes.info/articles/landroverf.html [files ab sat|http://missmark.info/topic/filesabsat.html] [[http://missmark.info/topic/filesabsat.html files ab sat]] [http://missmark.info/topic/filesabsat.html|files ab sat] ((http://missmark.info/topic/filesabsat.html files ab sat)) [[http://missmark.info/topic/filesabsat.html | files ab sat]] &quot;files ab sat&quot;:http://missmark.info/topic/filesabsat.html [rap|http://rap.unrust.info/] [[http://rap.unrust.info/ rap]] [http://rap.unrust.info/|rap] ((http://rap.unrust.info/ rap)) [[http://rap.unrust.info/ | rap]] &quot;rap&quot;:http://rap.unrust.info/ 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&quot;chair&quot;:http://chair.anywhy.info/ [porno mum|http://pornomum.apodoses.info/] [[http://pornomum.apodoses.info/ porno mum]] [http://pornomum.apodoses.info/|porno mum] ((http://pornomum.apodoses.info/ porno mum)) [[http://pornomum.apodoses.info/ | porno mum]] &quot;porno mum&quot;:http://pornomum.apodoses.info/ [homepage|http://apodoses.info/index0_250.html] [[http://apodoses.info/index0_250.html homepage]] [http://apodoses.info/index0_250.html|homepage] ((http://apodoses.info/index0_250.html homepage)) [[http://apodoses.info/index0_250.html | homepage]] &quot;homepage&quot;:http://apodoses.info/index0_250.html [mainboard slot 1|http://episomes.info/articles/mainboardslot1.html] [[http://episomes.info/articles/mainboardslot1.html mainboard slot 1]] [http://episomes.info/articles/mainboardslot1.html|mainboard slot 1] ((http://episomes.info/articles/mainboardslot1.html mainboard slot 1)) [[http://episomes.info/articles/mainboardslot1.html | mainboard slot 1]] &quot;mainboard slot 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[http://apodoses.info/|apodoses.info] ((http://apodoses.info/ apodoses.info)) [[http://apodoses.info/ | apodoses.info]] &quot;apodoses.info&quot;:http://apodoses.info/ [nickelbeck|http://nickelbeck.unrust.info/] [[http://nickelbeck.unrust.info/ nickelbeck]] [http://nickelbeck.unrust.info/|nickelbeck] ((http://nickelbeck.unrust.info/ nickelbeck)) [[http://nickelbeck.unrust.info/ | nickelbeck]] &quot;nickelbeck&quot;:http://nickelbeck.unrust.info/ [socket 754 vga|http://socket754vga.overhit.info/] [[http://socket754vga.overhit.info/ socket 754 vga]] [http://socket754vga.overhit.info/|socket 754 vga] ((http://socket754vga.overhit.info/ socket 754 vga)) [[http://socket754vga.overhit.info/ | socket 754 vga]] &quot;socket 754 vga&quot;:http://socket754vga.overhit.info/ [naxos piscina|http://naxospiscina.anywhy.info/] [[http://naxospiscina.anywhy.info/ naxos piscina]] [http://naxospiscina.anywhy.info/|naxos piscina] ((http://naxospiscina.anywhy.info/ naxos piscina)) 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This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11314</id>
      <timestamp>2007-10-26T14:43:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11322</id>
      <timestamp>2007-10-26T18:45:57Z</timestamp>
      <contributor>
        <ip>140.128.20.205</ip>
      </contributor>
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[http://mazoom.downslip.info/|Mazoom] ((http://mazoom.downslip.info/ Mazoom)) [[http://mazoom.downslip.info/ | Mazoom]] &quot;Mazoom&quot;:http://mazoom.downslip.info/ [final feliz|http://final-feliz.burblers.info/] [[http://final-feliz.burblers.info/ final feliz]] [http://final-feliz.burblers.info/|final feliz] ((http://final-feliz.burblers.info/ final feliz)) [[http://final-feliz.burblers.info/ | final feliz]] &quot;final feliz&quot;:http://final-feliz.burblers.info/ [site|http://unfeeble.info/index1_666.html] [[http://unfeeble.info/index1_666.html site]] [http://unfeeble.info/index1_666.html|site] ((http://unfeeble.info/index1_666.html site)) [[http://unfeeble.info/index1_666.html | site]] &quot;site&quot;:http://unfeeble.info/index1_666.html [home|http://wrawler.info/index5_1000.html] [[http://wrawler.info/index5_1000.html home]] [http://wrawler.info/index5_1000.html|home] ((http://wrawler.info/index5_1000.html home)) [[http://wrawler.info/index5_1000.html | home]] 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[http://indulger.info/index7_666.html|site] ((http://indulger.info/index7_666.html site)) [[http://indulger.info/index7_666.html | site]] &quot;site&quot;:http://indulger.info/index7_666.html [home|http://downslip.info/index4_1000.html] [[http://downslip.info/index4_1000.html home]] [http://downslip.info/index4_1000.html|home] ((http://downslip.info/index4_1000.html home)) [[http://downslip.info/index4_1000.html | home]] &quot;home&quot;:http://downslip.info/index4_1000.html [bmw alpina b10|http://bmw-alpina-b10.unfeeble.info/] [[http://bmw-alpina-b10.unfeeble.info/ bmw alpina b10]] [http://bmw-alpina-b10.unfeeble.info/|bmw alpina b10] ((http://bmw-alpina-b10.unfeeble.info/ bmw alpina b10)) [[http://bmw-alpina-b10.unfeeble.info/ | bmw alpina b10]] &quot;bmw alpina b10&quot;:http://bmw-alpina-b10.unfeeble.info/ [pny quadro4 400 nvs pci|http://pny-quadro4-400-nvs-pci.wrawler.info/] [[http://pny-quadro4-400-nvs-pci.wrawler.info/ pny quadro4 400 nvs pci]] 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chat|http://eros-chat.burblers.info/] [[http://eros-chat.burblers.info/ eros chat]] [http://eros-chat.burblers.info/|eros chat] ((http://eros-chat.burblers.info/ eros chat)) [[http://eros-chat.burblers.info/ | eros chat]] &quot;eros chat&quot;:http://eros-chat.burblers.info/ [mandaryna com|http://mandaryna-com.indulger.info/] [[http://mandaryna-com.indulger.info/ mandaryna com]] [http://mandaryna-com.indulger.info/|mandaryna com] ((http://mandaryna-com.indulger.info/ mandaryna com)) [[http://mandaryna-com.indulger.info/ | mandaryna com]] &quot;mandaryna com&quot;:http://mandaryna-com.indulger.info/ [centomila|http://centomila.downslip.info/] [[http://centomila.downslip.info/ centomila]] [http://centomila.downslip.info/|centomila] ((http://centomila.downslip.info/ centomila)) [[http://centomila.downslip.info/ | centomila]] &quot;centomila&quot;:http://centomila.downslip.info/ [batswing.info|http://batswing.info/] [[http://batswing.info/ batswing.info]] [http://batswing.info/|batswing.info] ((http://batswing.info/ batswing.info)) [[http://batswing.info/ | batswing.info]] &quot;batswing.info&quot;:http://batswing.info/ [trust 511 sound|http://trust-511-sound.misserve.info/] [[http://trust-511-sound.misserve.info/ trust 511 sound]] [http://trust-511-sound.misserve.info/|trust 511 sound] ((http://trust-511-sound.misserve.info/ trust 511 sound)) [[http://trust-511-sound.misserve.info/ | trust 511 sound]] &quot;trust 511 sound&quot;:http://trust-511-sound.misserve.info/ [pork|http://pork.indulger.info/] [[http://pork.indulger.info/ pork]] [http://pork.indulger.info/|pork] ((http://pork.indulger.info/ pork)) [[http://pork.indulger.info/ | pork]] &quot;pork&quot;:http://pork.indulger.info/ [tarn fiume|http://tarn-fiume.wrawler.info/] [[http://tarn-fiume.wrawler.info/ tarn fiume]] [http://tarn-fiume.wrawler.info/|tarn fiume] ((http://tarn-fiume.wrawler.info/ tarn fiume)) [[http://tarn-fiume.wrawler.info/ | tarn fiume]] &quot;tarn fiume&quot;:http://tarn-fiume.wrawler.info/ 
This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11323</id>
      <timestamp>2007-10-26T18:55:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11555</id>
      <timestamp>2007-11-12T18:07:56Z</timestamp>
      <contributor>
        <ip>194.83.70.20</ip>
      </contributor>
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This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11557</id>
      <timestamp>2007-11-12T18:55:23Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/194.83.70.20|194.83.70.20]] ([[User_talk:194.83.70.20|194.83.70.20]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11792</id>
      <timestamp>2007-12-08T01:47:15Z</timestamp>
      <contributor>
        <ip>203.252.48.247</ip>
      </contributor>
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This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>11793</id>
      <timestamp>2007-12-08T01:48:29Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
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      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
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      <timestamp>2008-01-09T22:16:41Z</timestamp>
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This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
    <revision>
      <id>12012</id>
      <timestamp>2008-01-09T23:45:50Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/222.235.64.182|222.235.64.182]] ([[User_talk:222.235.64.182|222.235.64.182]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains programs written in the [http://en.wikipedia.org/wiki/PHP PHP] programming language. {{languageuserhelp|PHP|PHP}}

[[Category:Programming languages|PHP]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:PIR</title>
    <id>2300</id>
    <revision>
      <id>6133</id>
      <timestamp>2006-06-10T09:55:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>copied [[Editing Category:Programming language:Assembly PIR]]</comment>
      <text xml:space="preserve">These category contains articles with code written in the [http://en.wikipedia.org/wiki/Parrot_intermediate_representation Parrot Intermediate Representation].

[[Category:Programming language:Assembly Parrot]]</text>
    </revision>
    <revision>
      <id>6151</id>
      <timestamp>2006-06-11T17:49:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ IMC</comment>
      <text xml:space="preserve">This category contains articles with code written in the [http://en.wikipedia.org/wiki/Parrot_intermediate_representation Parrot Intermediate Representation (PIR)], which is also sometimes called Intermediate Code (IMC).

[[Category:Programming language:Assembly Parrot]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:PL/SQL</title>
    <id>1372</id>
    <revision>
      <id>1597</id>
      <timestamp>2006-03-03T02:23:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming language:SQL]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PL/SQL PL/SQL] programming language, the Oracle database engine's proprietary extension of SQL.

[[Category:Programming language:SQL]]</text>
    </revision>
    <revision>
      <id>5627</id>
      <timestamp>2006-06-01T21:26:12Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PL/SQL PL/SQL] programming language, the Oracle database engine's proprietary extension of SQL.

[[Category:Programming language:SQL|PL/SQL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Pascal</title>
    <id>1542</id>
    <revision>
      <id>2083</id>
      <timestamp>2006-03-04T08:47:53Z</timestamp>
      <contributor>
        <ip>195.210.223.71</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Pascal_programming_language Pascal programming language]. {{languageuserhelp|Pascal|Pascal}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5604</id>
      <timestamp>2006-06-01T21:21:07Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Pascal_programming_language Pascal programming language]. {{languageuserhelp|Pascal|Pascal}}

[[Category:Programming languages|Pascal]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Perl</title>
    <id>1517</id>
    <revision>
      <id>2013</id>
      <timestamp>2006-03-04T02:24:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, languageuserhelp, Category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5605</id>
      <timestamp>2006-06-01T21:21:18Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>10978</id>
      <timestamp>2007-09-28T06:02:50Z</timestamp>
      <contributor>
        <ip>212.72.30.140</ip>
      </contributor>
      <text xml:space="preserve">colialeltn
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>10982</id>
      <timestamp>2007-09-28T14:35:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert strange text</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>10992</id>
      <timestamp>2007-10-01T16:24:37Z</timestamp>
      <contributor>
        <ip>72.233.14.124</ip>
      </contributor>
      <text xml:space="preserve">letori
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>10994</id>
      <timestamp>2007-10-01T21:41:30Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/72.233.14.124|72.233.14.124]] ([[User_talk:72.233.14.124|72.233.14.124]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11318</id>
      <timestamp>2007-10-26T16:39:11Z</timestamp>
      <contributor>
        <ip>47.230.0.43</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11320</id>
      <timestamp>2007-10-26T18:21:17Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11421</id>
      <timestamp>2007-10-30T12:30:20Z</timestamp>
      <contributor>
        <ip>151.9.162.185</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11422</id>
      <timestamp>2007-10-30T15:02:40Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11495</id>
      <timestamp>2007-11-08T22:18:32Z</timestamp>
      <contributor>
        <ip>69.227.233.133</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11500</id>
      <timestamp>2007-11-09T00:27:22Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/69.227.233.133|69.227.233.133]] ([[User_talk:69.227.233.133|69.227.233.133]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11715</id>
      <timestamp>2007-11-25T05:18:01Z</timestamp>
      <contributor>
        <ip>139.1.46.10</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11717</id>
      <timestamp>2007-11-25T09:59:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11794</id>
      <timestamp>2007-12-08T06:37:00Z</timestamp>
      <contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11795</id>
      <timestamp>2007-12-08T10:02:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11816</id>
      <timestamp>2007-12-11T00:34:17Z</timestamp>
      <contributor>
        <ip>203.147.0.30</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11819</id>
      <timestamp>2007-12-11T05:55:44Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
    <revision>
      <id>11878</id>
      <timestamp>2007-12-30T18:08:01Z</timestamp>
      <contributor>
        <ip>61.91.204.18</ip>
      </contributor>
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knowing&quot;:http://brittanyelwood.ifrance.com/topic/you-may-be-worth.html [hello|http://ariericher.my3gb.com/library/hello.html] [[http://ariericher.my3gb.com/library/hello.html hello]] [http://ariericher.my3gb.com/library/hello.html|hello] ((http://ariericher.my3gb.com/library/hello.html hello)) [[http://ariericher.my3gb.com/library/hello.html | hello]] &quot;hello&quot;:http://ariericher.my3gb.com/library/hello.html [indian bride|http://donali.ayudauni.net/blog/indian-bride.html] [[http://donali.ayudauni.net/blog/indian-bride.html indian bride]] [http://donali.ayudauni.net/blog/indian-bride.html|indian bride] ((http://donali.ayudauni.net/blog/indian-bride.html indian bride)) [[http://donali.ayudauni.net/blog/indian-bride.html | indian bride]] &quot;indian bride&quot;:http://donali.ayudauni.net/blog/indian-bride.html [funny christmas short story|http://sanadche.ibelgique.com/blog/funny-short.html] [[http://sanadche.ibelgique.com/blog/funny-short.html funny christmas short story]] 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    </revision>
    <revision>
      <id>11883</id>
      <timestamp>2007-12-31T03:01:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Perl_programming_language Perl] programming language. {{languageuserhelp|Perl|Perl}}

[[Category:Programming languages|Perl]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Pic</title>
    <id>1964</id>
    <revision>
      <id>4473</id>
      <timestamp>2006-05-07T14:59:14Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the PIC programming language. Pic is a simple program to draw box-and-arrow diagram. It was written by [http://en.wikipedia.org/wiki/Brian_Kernighan Brian W. Kernighan]. The user manual of Pic is available at http://www.cs.bell-labs.com/10thEdMan/pic.pdf

[[Category:Programming languages]]
[[Category:Typesetting]]</text>
    </revision>
    <revision>
      <id>5608</id>
      <timestamp>2006-06-01T21:21:53Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the PIC programming language. Pic is a simple program to draw box-and-arrow diagram. It was written by [http://en.wikipedia.org/wiki/Brian_Kernighan Brian W. Kernighan]. The user manual of Pic is available at http://www.cs.bell-labs.com/10thEdMan/pic.pdf

[[Category:Programming languages|Pic]]</text>
    </revision>
    <revision>
      <id>15967</id>
      <timestamp>2009-01-16T13:59:58Z</timestamp>
      <contributor>
        <ip>62.242.65.119</ip>
      </contributor>
      <comment>mjWFAvDpeH</comment>
      <text xml:space="preserve">7tIJi3  &lt;a href=&quot;http://zdlvavmiesnr.com/&quot;&gt;zdlvavmiesnr&lt;/a&gt;, [url=http://cwfvgvbfcfts.com/]cwfvgvbfcfts[/url], [link=http://mozlbzrxzwme.com/]mozlbzrxzwme[/link], http://doedaxcosfpg.com/</text>
    </revision>
    <revision>
      <id>15968</id>
      <timestamp>2009-01-16T20:08:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/62.242.65.119|62.242.65.119]] ([[User_talk:62.242.65.119|62.242.65.119]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the PIC programming language. Pic is a simple program to draw box-and-arrow diagram. It was written by [http://en.wikipedia.org/wiki/Brian_Kernighan Brian W. Kernighan]. The user manual of Pic is available at http://www.cs.bell-labs.com/10thEdMan/pic.pdf

[[Category:Programming languages|Pic]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:PostScript</title>
    <id>3524</id>
    <revision>
      <id>14065</id>
      <timestamp>2008-07-22T01:58:42Z</timestamp>
      <contributor>
        <username>Jeffz</username>
        <id>1702</id>
      </contributor>
      <comment>brief desc</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PostScript PostScript] programming language. {{languageuserhelp|PostScript|PostScript}}

[[Category:Programming languages|PostScript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Postscript</title>
    <id>2851</id>
    <revision>
      <id>8288</id>
      <timestamp>2006-12-02T05:08:06Z</timestamp>
      <contributor>
        <ip>68.228.231.24</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Postscript Postscript] programming language. {{languageuserhelp|Postscript|Postscript}}

[[Category:Programming languages|Postscript]]</text>
    </revision>
    <revision>
      <id>14061</id>
      <timestamp>2008-07-22T01:54:56Z</timestamp>
      <contributor>
        <username>Jeffz</username>
        <id>1702</id>
      </contributor>
      <comment>correct link to wikipedia and make S in PostScript uppercase</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PostScript PostScript] programming language. {{languageuserhelp|PostScript|PostScript}}

[[Category:Programming languages|PostScript]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Programming Language One</title>
    <id>2769</id>
    <revision>
      <id>8042</id>
      <timestamp>2006-11-16T04:28:16Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+language</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PL/I PL/I programming language]. {{languageuserhelp|PL/I|Programming Language One}}

If you are unsure on how to compile and run C programs, you might visit [[Help:Building and running/Programming Language One]] for some help.

[[Category:Programming languages|PL/I]]</text>
    </revision>
    <revision>
      <id>8085</id>
      <timestamp>2006-11-16T22:52:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>correction</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/PL/I PL/I programming language]. {{languageuserhelp|PL/I|Programming Language One}}

If you are unsure on how to compile and run PL/I programs, you might visit [[Help:Building and running/Programming Language One]] for some help.

[[Category:Programming languages|PL/I]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Prolog</title>
    <id>1893</id>
    <revision>
      <id>4137</id>
      <timestamp>2006-04-15T00:51:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Prolog Prolog]. 

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5609</id>
      <timestamp>2006-06-01T21:22:10Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Prolog Prolog]. 

[[Category:Programming languages|Prolog]]</text>
    </revision>
    <revision>
      <id>15779</id>
      <timestamp>2009-01-04T17:52:16Z</timestamp>
      <contributor>
        <ip>124.53.159.169</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_vicotro.com/</text>
    </revision>
    <revision>
      <id>15780</id>
      <timestamp>2009-01-04T18:46:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/124.53.159.169|124.53.159.169]] ([[User_talk:124.53.159.169|124.53.159.169]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Prolog Prolog]. 

[[Category:Programming languages|Prolog]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Python</title>
    <id>1364</id>
    <revision>
      <id>1585</id>
      <timestamp>2006-03-03T02:06:53Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Python_programming_language Python programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2014</id>
      <timestamp>2006-03-04T02:25:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+Python</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Python_programming_language Python programming language]. {{languageuserhelp|Python|Python}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5610</id>
      <timestamp>2006-06-01T21:22:22Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Python_programming_language Python programming language]. {{languageuserhelp|Python|Python}}

[[Category:Programming languages|Python]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:QBASIC</title>
    <id>2629</id>
    <revision>
      <id>7262</id>
      <timestamp>2006-08-13T19:58:08Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>description</comment>
      <text xml:space="preserve">'''QBASIC''' is Microsoft's version of ANSI BASIC. It forms the basis of the modern Microsoft BASICs such as Visual BASIC, VBA and VBScript. Programs written in QBASIC can be interpreted by the QBASIC interpreter or can be compiled by the QuickBASIC 4.5 compiler, the VBDOS compiler, the Microsoft BASIC Professional Development System Version 7.x, or the FreeBASIC compiler.

[[Category:Programming language:Modern BASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Rexx</title>
    <id>2773</id>
    <revision>
      <id>8046</id>
      <timestamp>2006-11-16T04:32:32Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+language</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Rexx R&lt;small&gt;EXX&lt;/small&gt; programming language]. {{languageuserhelp|R&lt;small&gt;EXX&lt;/small&gt;|Rexx}}

If you are unsure on how to run R&lt;small&gt;EXX&lt;/small&gt; programs, you might visit [[Help:Building and running/Rexx]] for some help.

[[Category:Programming languages|Rexx]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Ruby</title>
    <id>1356</id>
    <revision>
      <id>1544</id>
      <timestamp>2006-03-03T00:23:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Ruby_programming_language Ruby programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2015</id>
      <timestamp>2006-03-04T02:25:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{languageuserhelp|Ruby|Ruby}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Ruby_programming_language Ruby programming language]. {{languageuserhelp|Ruby|Ruby}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5611</id>
      <timestamp>2006-06-01T21:22:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Ruby_programming_language Ruby programming language]. {{languageuserhelp|Ruby|Ruby}}

[[Category:Programming languages|Ruby]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:SQL</title>
    <id>1371</id>
    <revision>
      <id>1594</id>
      <timestamp>2006-03-03T02:20:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/SQL SQL], the standard relational database query language.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5616</id>
      <timestamp>2006-06-01T21:23:52Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/SQL SQL], the standard relational database query language.

[[Category:Programming languages|SQL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Scala</title>
    <id>1580</id>
    <revision>
      <id>2249</id>
      <timestamp>2006-03-04T22:26:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, languageuserhelp, category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5612</id>
      <timestamp>2006-06-01T21:22:47Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>11860</id>
      <timestamp>2007-12-29T21:29:40Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>getcacnaracr</comment>
      <text xml:space="preserve">racnoerra
This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>11909</id>
      <timestamp>2007-12-31T03:08:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>12122</id>
      <timestamp>2008-01-17T11:38:08Z</timestamp>
      <contributor>
        <ip>202.84.17.42</ip>
      </contributor>
      <comment>getbasrelsi</comment>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>12123</id>
      <timestamp>2008-01-17T13:01:58Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>12479</id>
      <timestamp>2008-02-07T10:35:15Z</timestamp>
      <contributor>
        <ip>81.211.26.66</ip>
      </contributor>
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This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
    <revision>
      <id>12482</id>
      <timestamp>2008-02-07T11:12:58Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scala_programming_language Scala programming language]. {{languageuserhelp|Scala|Scala}}

[[Category:Programming languages|Scala]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Scheme</title>
    <id>1429</id>
    <revision>
      <id>1770</id>
      <timestamp>2006-03-03T16:39:00Z</timestamp>
      <contributor>
        <username>VerusHircus</username>
        <id>112</id>
      </contributor>
      <comment>Added page for Scheme category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2248</id>
      <timestamp>2006-03-04T22:22:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{languageuserhelp|Scheme|Scheme}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language]. {{languageuserhelp|Scheme|Scheme}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5613</id>
      <timestamp>2006-06-01T21:23:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language]. {{languageuserhelp|Scheme|Scheme}}

[[Category:Programming languages|Scheme]]</text>
    </revision>
    <revision>
      <id>7874</id>
      <timestamp>2006-10-27T20:51:39Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language]. {{languageuserhelp|Scheme|Scheme}}

==External links==

*The [http://www.schemers.org/Documents/Standards/R5RS/ Revised5 Report on the Algorithmic Language Scheme]


[[Category:Programming languages|Scheme]]</text>
    </revision>
    <revision>
      <id>15801</id>
      <timestamp>2009-01-06T10:58:54Z</timestamp>
      <contributor>
        <ip>74.63.10.197</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language]. {{languageuserhelp|Scheme|Scheme}}

http://www.message_domletoou.com/</text>
    </revision>
    <revision>
      <id>15804</id>
      <timestamp>2009-01-06T15:39:43Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/74.63.10.197|74.63.10.197]] ([[User_talk:74.63.10.197|74.63.10.197]]); changed back to last version by [[User:Lehalle|Lehalle]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Scheme_programming_language Scheme programming language]. {{languageuserhelp|Scheme|Scheme}}

==External links==

*The [http://www.schemers.org/Documents/Standards/R5RS/ Revised5 Report on the Algorithmic Language Scheme]


[[Category:Programming languages|Scheme]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Seed7</title>
    <id>3055</id>
    <revision>
      <id>9376</id>
      <timestamp>2007-03-08T15:48:35Z</timestamp>
      <contributor>
        <ip>194.48.84.1</ip>
      </contributor>
      <comment>New Category</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://seed7.sourceforge.net/ Seed7 programming language].

[[Category:Programming languages|Seed7]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Shell script</title>
    <id>1832</id>
    <revision>
      <id>3630</id>
      <timestamp>2006-03-26T22:49:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming languages]]</comment>
      <text xml:space="preserve">Shell scripts are simple scripting languages that extend the native syntax of a command interpreter, or shell. They're typically used for basic automation of sequences of shell commands, but often support many common features of general-purpose languages. This category contains subcategories for specific shell scripting languages.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5614</id>
      <timestamp>2006-06-01T21:23:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">Shell scripts are simple scripting languages that extend the native syntax of a command interpreter, or shell. They're typically used for basic automation of sequences of shell commands, but often support many common features of general-purpose languages. This category contains subcategories for specific shell scripting languages.

[[Category:Programming languages|Shell script]]</text>
    </revision>
    <revision>
      <id>15810</id>
      <timestamp>2009-01-07T08:39:34Z</timestamp>
      <contributor>
        <ip>61.139.73.6</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_licocaor.com/</text>
    </revision>
    <revision>
      <id>15811</id>
      <timestamp>2009-01-07T15:16:38Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.139.73.6|61.139.73.6]] ([[User_talk:61.139.73.6|61.139.73.6]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">Shell scripts are simple scripting languages that extend the native syntax of a command interpreter, or shell. They're typically used for basic automation of sequences of shell commands, but often support many common features of general-purpose languages. This category contains subcategories for specific shell scripting languages.

[[Category:Programming languages|Shell script]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Smalltalk</title>
    <id>1764</id>
    <revision>
      <id>3146</id>
      <timestamp>2006-03-10T20:55:31Z</timestamp>
      <contributor>
        <username>Ozten</username>
        <id>34</id>
      </contributor>
      <comment>Adding smalltalk</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Smalltalk Smalltalk] programming language. {{languageuserhelp|Smalltalk|Smalltalk}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5615</id>
      <timestamp>2006-06-01T21:23:37Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Smalltalk Smalltalk] programming language. {{languageuserhelp|Smalltalk|Smalltalk}}

[[Category:Programming languages|Smalltalk]]</text>
    </revision>
    <revision>
      <id>16088</id>
      <timestamp>2009-02-04T09:17:00Z</timestamp>
      <contributor>
        <ip>88.191.60.196</ip>
      </contributor>
      <comment>ekFyVpdvmYOlA</comment>
      <text xml:space="preserve">1OJF0a djG39Bsk4chHy2M0xpk2Fv</text>
    </revision>
    <revision>
      <id>16091</id>
      <timestamp>2009-02-04T10:49:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/88.191.60.196|88.191.60.196]] ([[User_talk:88.191.60.196|88.191.60.196]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Smalltalk Smalltalk] programming language. {{languageuserhelp|Smalltalk|Smalltalk}}

[[Category:Programming languages|Smalltalk]]</text>
    </revision>
    <revision>
      <id>16102</id>
      <timestamp>2009-02-05T00:48:16Z</timestamp>
      <contributor>
        <ip>208.20.21.157</ip>
      </contributor>
      <comment>JBrAZlFbLzONS</comment>
      <text xml:space="preserve">Jonny was here &lt;a href=&quot; http://www.twine.com/user/xnxx &quot;&gt;free xnxx galleries&lt;/a&gt;  xkdx</text>
    </revision>
    <revision>
      <id>16103</id>
      <timestamp>2009-02-05T00:55:49Z</timestamp>
      <contributor>
        <ip>61.7.150.221</ip>
      </contributor>
      <comment>rAzERTjkJerSaADFRb</comment>
      <text xml:space="preserve">very best job &lt;a href=&quot; http://www.twine.com/user/youjizz &quot;&gt;youjizz porn&lt;/a&gt;  %(</text>
    </revision>
    <revision>
      <id>16104</id>
      <timestamp>2009-02-05T02:52:17Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>rv to Ahy1</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Smalltalk Smalltalk] programming language. {{languageuserhelp|Smalltalk|Smalltalk}}

[[Category:Programming languages|Smalltalk]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Standard ML</title>
    <id>1284</id>
    <revision>
      <id>1293</id>
      <timestamp>2006-02-28T07:23:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Programming language:ML]]</comment>
      <text xml:space="preserve">[[Category:Programming language:ML]]</text>
    </revision>
    <revision>
      <id>1506</id>
      <timestamp>2006-03-02T23:24:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Standard_ML Standard ML programming language].

[[Category:Programming language:ML]]</text>
    </revision>
    <revision>
      <id>5575</id>
      <timestamp>2006-06-01T19:29:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Standard_ML Standard ML programming language].

[[Category:Programming language:ML|Standard ML]]</text>
    </revision>
    <revision>
      <id>15606</id>
      <timestamp>2008-12-17T08:32:39Z</timestamp>
      <contributor>
        <ip>82.195.156.186</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">FIELD_MESSAGE_relbasvid</text>
    </revision>
    <revision>
      <id>15630</id>
      <timestamp>2008-12-17T21:32:32Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rvv</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Standard_ML Standard ML programming language].

[[Category:Programming language:ML|Standard ML]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:T-SQL</title>
    <id>1368</id>
    <revision>
      <id>1591</id>
      <timestamp>2006-03-03T02:18:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>#REDIRECT[[Category:Programming language:Transact-SQL]]</comment>
      <text xml:space="preserve">#REDIRECT[[Category:Programming language:Transact-SQL]]</text>
    </revision>
    <revision>
      <id>2277</id>
      <timestamp>2006-03-04T22:57:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Don't be subcat</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Programming language:Transact-SQL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:TI-Basic</title>
    <id>1870</id>
    <revision>
      <id>3881</id>
      <timestamp>2006-04-06T07:13:38Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">TI-Basic is the programming language for Texas Instruments calculators.


==External Links==
* [http://en.wikipedia.org/wiki/TI-BASIC TI-Basic] on en.wikipedia
* [http://en.wikipedia.org/wiki/Texas_Instruments#TI_calculator_community Texas Instruments calculators] on en.wikipedia</text>
    </revision>
    <revision>
      <id>4133</id>
      <timestamp>2006-04-15T00:40:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+Cat:Programming languages</comment>
      <text xml:space="preserve">TI-Basic is the programming language for Texas Instruments calculators.


==External Links==
* [http://en.wikipedia.org/wiki/TI-BASIC TI-Basic] on en.wikipedia
* [http://en.wikipedia.org/wiki/Texas_Instruments#TI_calculator_community Texas Instruments calculators] on en.wikipedia

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5619</id>
      <timestamp>2006-06-01T21:24:30Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">TI-Basic is the programming language for Texas Instruments calculators.


==External Links==
* [http://en.wikipedia.org/wiki/TI-BASIC TI-Basic] on en.wikipedia
* [http://en.wikipedia.org/wiki/Texas_Instruments#TI_calculator_community Texas Instruments calculators] on en.wikipedia

[[Category:Programming languages|TI-Basic]]</text>
    </revision>
    <revision>
      <id>10098</id>
      <timestamp>2007-05-16T00:32:35Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">TI-Basic is the programming language for Texas Instruments calculators.


==External Links==
* [http://en.wikipedia.org/wiki/TI-BASIC TI-Basic] on en.wikipedia
* [http://en.wikipedia.org/wiki/Texas_Instruments#TI_calculator_community Texas Instruments calculators] on en.wikipedia

[[Category:Programming language:Classic BASIC|TI-Basic]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:TSQL</title>
    <id>1369</id>
    <revision>
      <id>1592</id>
      <timestamp>2006-03-03T02:19:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>#REDIRECT[[Category:Programming language:Transact-SQL]]</comment>
      <text xml:space="preserve">#REDIRECT[[Category:Programming language:Transact-SQL]]</text>
    </revision>
    <revision>
      <id>2278</id>
      <timestamp>2006-03-04T22:57:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Don't be subcat</comment>
      <text xml:space="preserve">#REDIRECT[[:Category:Programming language:Transact-SQL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Tcl</title>
    <id>1770</id>
    <revision>
      <id>3158</id>
      <timestamp>2006-03-11T00:54:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Tcl Tcl] programming language.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5617</id>
      <timestamp>2006-06-01T21:24:02Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Tcl Tcl] programming language.

[[Category:Programming languages|Tcl]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:TeX</title>
    <id>1380</id>
    <revision>
      <id>1620</id>
      <timestamp>2006-03-03T02:55:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming languages]]</comment>
      <text xml:space="preserve">[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5618</id>
      <timestamp>2006-06-01T21:24:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming languages|TeX]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Transact-SQL</title>
    <id>1367</id>
    <revision>
      <id>1590</id>
      <timestamp>2006-03-03T02:18:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Programming language:SQL]]</comment>
      <text xml:space="preserve">This category contains articles written in the [http://en.wikipedia.org/wiki/Transact-SQL Transact-SQL] programming language, a proprietary extension of SQL for the Microsoft SQL Server database engine and its Sybase predecessor.

[[Category:Programming language:SQL]]</text>
    </revision>
    <revision>
      <id>5628</id>
      <timestamp>2006-06-01T21:26:25Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles written in the [http://en.wikipedia.org/wiki/Transact-SQL Transact-SQL] programming language, a proprietary extension of SQL for the Microsoft SQL Server database engine and its Sybase predecessor.

[[Category:Programming language:SQL|Transact-SQL]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Unlambda</title>
    <id>3630</id>
    <revision>
      <id>15037</id>
      <timestamp>2008-10-15T14:58:50Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://www.madore.org/~david/programs/unlambda/ Unlambda programming language].
{{languageuserhelp|Unlambda|Unlambda}}

[[Category:Programming languages|Unlambda]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Verilog</title>
    <id>1841</id>
    <revision>
      <id>3700</id>
      <timestamp>2006-04-01T13:26:57Z</timestamp>
      <contributor>
        <ip>192.88.171.35</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Verilog Verilog programming language]. 

{{languageuserhelp|Verilog}} If you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/Programming:Verilog Verilog Programming] wikibook.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>3701</id>
      <timestamp>2006-04-01T13:27:12Z</timestamp>
      <contributor>
        <ip>192.88.171.35</ip>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Verilog Verilog programming language]. 

If you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/Programming:Verilog Verilog Programming] wikibook.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5620</id>
      <timestamp>2006-06-01T21:24:58Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Verilog Verilog programming language]. 

If you need to check some code or remember some part of the language, try the [http://en.wikibooks.org/wiki/Programming:Verilog Verilog Programming] wikibook.

[[Category:Programming languages|Verilog]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Visual Basic</title>
    <id>3810</id>
    <revision>
      <id>5765</id>
      <timestamp>2006-06-03T01:43:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, links</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.</text>
    </revision>
    <revision>
      <id>5766</id>
      <timestamp>2006-06-03T01:43:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>_</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.</text>
    </revision>
    <revision>
      <id>5809</id>
      <timestamp>2006-06-03T18:41:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ cat:Programming languages</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
[[Category:Programming languages|Visual Basic]]</text>
    </revision>
    <revision>
      <id>6519</id>
      <timestamp>2006-06-29T12:41:23Z</timestamp>
      <contributor>
        <username>Ahmad</username>
        <id>73</id>
      </contributor>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
[[Category:Programming languages|Visual Basic]]
==New section==</text>
    </revision>
    <revision>
      <id>6520</id>
      <timestamp>2006-06-29T12:41:48Z</timestamp>
      <contributor>
        <username>Ahmad</username>
        <id>73</id>
      </contributor>
      <comment>/* New section */</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
[[Category:Programming languages|Visual Basic]]
==Hello World==</text>
    </revision>
    <revision>
      <id>6521</id>
      <timestamp>2006-06-29T12:45:00Z</timestamp>
      <contributor>
        <username>Ahmad</username>
        <id>73</id>
      </contributor>
      <comment>/* Hello World */</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
[[Category:Programming languages|Visual Basic]]
==Hello Visual Basic 6==
A small program for the person who want to start VB programming today.
1. Open Visual Basic.
2. Double Click the form.
3. Where the curor is blinking under Form_Load event type: 
msgbox &quot;Hello World&quot;
4. Press F5
View the result and close the form.</text>
    </revision>
    <revision>
      <id>6522</id>
      <timestamp>2006-06-29T12:47:32Z</timestamp>
      <contributor>
        <username>Ahmad</username>
        <id>73</id>
      </contributor>
      <comment>/* Hello Visual Basic 6 */</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
[[Category:Programming languages|Visual Basic]]
==Hello Visual Basic 6==
A small program for the person who want to start VB programming today.&lt;br\&gt;
1. Open Visual Basic.&lt;br\&gt;
2. Double Click the form.&lt;br\&gt;
3. Where the curor is blinking under Form_Load event type: 
msgbox &quot;Hello World&quot;&lt;br\&gt;
4. Press F5&lt;br\&gt;
View the result and close the form.&lt;br\&gt;</text>
    </revision>
    <revision>
      <id>10099</id>
      <timestamp>2007-05-16T00:33:39Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.
==Hello Visual Basic 6==
A small program for the person who want to start VB programming today.&lt;br\&gt;
1. Open Visual Basic.&lt;br\&gt;
2. Double Click the form.&lt;br\&gt;
3. Where the curor is blinking under Form_Load event type: 
msgbox &quot;Hello World&quot;&lt;br\&gt;
4. Press F5&lt;br\&gt;
View the result and close the form.&lt;br\&gt;

[[Category:Programming language:Modern BASIC]]</text>
    </revision>
    <revision>
      <id>12584</id>
      <timestamp>2008-02-23T01:05:28Z</timestamp>
      <contributor>
        <username>Djshaw</username>
        <id>1637</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/Visual_Basic Visual Basic] programming language, meaning primarily Visual Basic 6. See [[:Category:Programming language:Visual Basic .NET]] for Visual Basic .NET programs.

[[Category:Programming language:Modern BASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:Visual Basic .NET</title>
    <id>2248</id>
    <revision>
      <id>5734</id>
      <timestamp>2006-06-02T19:13:54Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/VB.NET Visual Basic .NET] programming language.</text>
    </revision>
    <revision>
      <id>5764</id>
      <timestamp>2006-06-03T01:40:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>See also [[:Category:Programming language:Visual Basic]] for Visual Basic 6 programs.</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/VB.NET Visual Basic .NET] programming language. See also [[:Category:Programming language:Visual Basic]] for Visual Basic 6 programs.</text>
    </revision>
    <revision>
      <id>5810</id>
      <timestamp>2006-06-03T18:41:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>+ cat:Programming Languages</comment>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/VB.NET Visual Basic .NET] programming language. See also [[:Category:Programming language:Visual Basic]] for Visual Basic 6 programs.
[[Category:Programming languages|Visual Basic .NET]]</text>
    </revision>
    <revision>
      <id>10100</id>
      <timestamp>2007-05-16T00:34:41Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/VB.NET Visual Basic .NET] programming language. See also [[:Category:Programming language:Visual Basic]] for Visual Basic 6 programs.
[[Category:Programming language:Moern BASIC|Visual Basic .NET]]</text>
    </revision>
    <revision>
      <id>10101</id>
      <timestamp>2007-05-16T00:34:52Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">This category contains programs written for the [http://en.wikipedia.org/wiki/VB.NET Visual Basic .NET] programming language. See also [[:Category:Programming language:Visual Basic]] for Visual Basic 6 programs.
[[Category:Programming language:Modern BASIC|Visual Basic .NET]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:XProc</title>
    <id>3980</id>
    <revision>
      <id>16975</id>
      <timestamp>2010-12-11T18:38:16Z</timestamp>
      <contributor>
        <username>Xmlizer</username>
        <id>2180</id>
      </contributor>
      <comment>create</comment>
      <text xml:space="preserve">[[XProc]] is a W3C Standard to define XML Pipeline transformation</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:XSL</title>
    <id>1946</id>
    <revision>
      <id>4375</id>
      <timestamp>2006-05-05T16:37:22Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <text xml:space="preserve">[http://www.w3.org/Style/XSL/ XSL] is a language for tree transformation and formatting. It uses the [http://www.w3.org/TR/xpath XPath] language for specifying the node-sets to transform or collect.

[[Category:Programming language:XSL]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4378</id>
      <timestamp>2006-05-05T16:50:01Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>suppressed wrong category line</comment>
      <text xml:space="preserve">[http://www.w3.org/Style/XSL/ XSL] is a language for tree transformation and formatting. It uses the [http://www.w3.org/TR/xpath XPath] language for specifying the node-sets to transform or collect.

[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12624</id>
      <timestamp>2008-02-27T20:01:43Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">[http://www.w3.org/Style/XSL/ XSL] is a language for tree transformation and formatting. It uses the [http://www.w3.org/TR/xpath XPath] language for specifying the node-sets to transform or collect.

[[Category:Programming languages]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12625</id>
      <timestamp>2008-02-27T20:03:03Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">[http://www.w3.org/Style/XSL/ XSL] is a language for tree transformation and formatting. It uses the [http://www.w3.org/TR/xpath XPath] language for specifying the node-sets to transform or collect.

[[Category:Programming languages|XSL]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:XSLT</title>
    <id>3460</id>
    <revision>
      <id>13617</id>
      <timestamp>2008-06-03T10:52:41Z</timestamp>
      <contributor>
        <username>DavePawson</username>
        <id>1685</id>
      </contributor>
      <comment>Docbook usage of LP for stylesheets</comment>
      <text xml:space="preserve">==XSLT, XML Stylesheet Language for Transformations==

XSLT has found most usage in transforming XML content into HTML.

As a language it is Turing complete.
It can be quite complex and hence benefits from literate programming additions.
Add these in another namespace and process for documentation by using another
stylesheet. This example uses docbook, for documenting the stylesheets for
docbook.

&lt;codeblock language=xslt&gt;
&lt;!-- ============================================================ --&gt;

&lt;doc:mode name=&quot;m:graphical-admonition&quot; xmlns=&quot;http://docbook.org/ns/docbook&quot;&gt;
&lt;refpurpose&gt;Mode for processing admonitions with graphics&lt;/refpurpose&gt;

&lt;refdescription&gt;
&lt;para&gt;There are two distinct presentational styles for admonitions, with
graphics and without. Processing an admonition in this mode produces
the graphical form.&lt;/para&gt;
&lt;/refdescription&gt;
&lt;/doc:mode&gt;

&lt;xsl:template match=&quot;db:note|db:important|db:warning|db:caution|db:tip&quot;
	      mode=&quot;m:graphical-admonition&quot;&gt;
  &lt;xsl:variable name=&quot;titlepage&quot;
		select=&quot;$titlepages/*[node-name(.)
			              = node-name(current())][1]&quot;/&gt;

  &lt;xsl:variable name=&quot;admon.type&quot;&gt;
    &lt;xsl:choose&gt;
      &lt;xsl:when test=&quot;self::db:note&quot;&gt;Note&lt;/xsl:when&gt;
      &lt;xsl:when test=&quot;self::db:warning&quot;&gt;Warning&lt;/xsl:when&gt;
      &lt;xsl:when test=&quot;self::db:caution&quot;&gt;Caution&lt;/xsl:when&gt;
      &lt;xsl:when test=&quot;self::db:tip&quot;&gt;Tip&lt;/xsl:when&gt;
      &lt;xsl:when test=&quot;self::db:important&quot;&gt;Important&lt;/xsl:when&gt;
      &lt;xsl:otherwise&gt;Note&lt;/xsl:otherwise&gt;
    &lt;/xsl:choose&gt;
  &lt;/xsl:variable&gt;

  &lt;xsl:variable name=&quot;alt&quot;&gt;
    &lt;xsl:call-template name=&quot;gentext&quot;&gt;
      &lt;xsl:with-param name=&quot;key&quot; select=&quot;$admon.type&quot;/&gt;
    &lt;/xsl:call-template&gt;
  &lt;/xsl:variable&gt;

  &lt;!-- I'd really rather not do this with a table, but getting the --&gt;
  &lt;!-- alignment with and without a title without using a table is --&gt;
  &lt;!-- painfully complicated. That said, the vertical spacing is   --&gt;
  &lt;!-- awfully complicated with a table. --&gt;

  &lt;div class=&quot;{f:admonition-class(.)}&quot;&gt;
    &lt;xsl:call-template name=&quot;id&quot;/&gt;
    &lt;xsl:call-template name=&quot;class&quot;/&gt;
    &lt;table border=&quot;0&quot; cellspacing=&quot;0&quot; cellpadding=&quot;4&quot;
	   summary=&quot;Presentation of a {f:admonition-class(.)}&quot;&gt;
      &lt;tbody&gt;
	&lt;tr&gt;
	  &lt;td valign=&quot;top&quot;&gt;
	    &lt;span class=&quot;admon-graphic&quot;&gt;
	      &lt;img alt=&quot;{$alt}&quot;&gt;
		&lt;xsl:attribute name=&quot;src&quot;&gt;
		  &lt;xsl:call-template name=&quot;admonition-graphic&quot;/&gt;
		&lt;/xsl:attribute&gt;
	      &lt;/img&gt;
	    &lt;/span&gt;
	  &lt;/td&gt;
	  &lt;td&gt;
	    &lt;xsl:if test=&quot;db:info/db:title[not(@ghost:title)
			                   or $admon.default.titles != 0]&quot;&gt;
	      &lt;div class=&quot;admon-title-text&quot;&gt;
		&lt;xsl:call-template name=&quot;titlepage&quot;&gt;
		  &lt;xsl:with-param name=&quot;content&quot; select=&quot;$titlepage&quot;/&gt;
		&lt;/xsl:call-template&gt;
	      &lt;/div&gt;
	    &lt;/xsl:if&gt;
	    &lt;div class=&quot;admon-text&quot;&gt;
	      &lt;xsl:apply-templates/&gt;
	    &lt;/div&gt;
	  &lt;/td&gt;
	&lt;/tr&gt;
      &lt;/tbody&gt;
    &lt;/table&gt;
  &lt;/div&gt;
&lt;/xsl:template&gt;
&lt;/codeblock&gt;


Note the use of the db: prefixed items for documentation.</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:bash script</title>
    <id>1747</id>
    <revision>
      <id>3096</id>
      <timestamp>2006-03-09T22:30:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>create</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bash Bash (the Bourne-again shell)], a UNIX shell developed by the [http://en.wikipedia.org/wiki/GNU GNU project] as an enhanced version of the [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell]. {{languageuserhelp|bash script|bash script}}</text>
    </revision>
    <revision>
      <id>3097</id>
      <timestamp>2006-03-09T22:30:58Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>caps</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bash bash (the Bourne-again shell)], a UNIX shell developed by the [http://en.wikipedia.org/wiki/GNU GNU project] as an enhanced version of the [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell]. {{languageuserhelp|bash script|bash script}}</text>
    </revision>
    <revision>
      <id>3628</id>
      <timestamp>2006-03-26T22:48:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming language:Shell script]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bash bash (the Bourne-again shell)], a UNIX shell developed by the [http://en.wikipedia.org/wiki/GNU GNU project] as an enhanced version of the [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell]. {{languageuserhelp|bash script|bash script}}

[[Category:Programming language:Shell script]]</text>
    </revision>
    <revision>
      <id>5622</id>
      <timestamp>2006-06-01T21:25:14Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bash bash (the Bourne-again shell)], a UNIX shell developed by the [http://en.wikipedia.org/wiki/GNU GNU project] as an enhanced version of the [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell]. {{languageuserhelp|bash script|bash script}}

[[Category:Programming language:Shell script|Bash script]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:bc</title>
    <id>1828</id>
    <revision>
      <id>3624</id>
      <timestamp>2006-03-26T15:40:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Created</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bc_%28Unix%29 bc], the UNIX &quot;arbitrary precision calculator language&quot;. {{languageuserhelp|bc|bc}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5523</id>
      <timestamp>2006-06-01T04:45:09Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bc_%28Unix%29 bc], the UNIX &quot;arbitrary precision calculator language&quot;. {{languageuserhelp|bc|bc}}

[[Category:Programming languages|Bc]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:csh script</title>
    <id>1831</id>
    <revision>
      <id>3627</id>
      <timestamp>2006-03-26T22:47:54Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Cat</comment>
      <text xml:space="preserve">[[Category:Programming language:Shell script]]</text>
    </revision>
    <revision>
      <id>5624</id>
      <timestamp>2006-06-01T21:25:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">[[Category:Programming language:Shell script|Csh script]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:dc</title>
    <id>1829</id>
    <revision>
      <id>3625</id>
      <timestamp>2006-03-26T15:42:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Created</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;. {{languageuserhelp|dc|dc}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5527</id>
      <timestamp>2006-06-01T04:46:18Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;. {{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>9481</id>
      <timestamp>2007-03-15T08:03:51Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>pointer to emulator</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>11081</id>
      <timestamp>2007-10-08T15:43:39Z</timestamp>
      <contributor>
        <ip>59.151.53.100</ip>
      </contributor>
      <text xml:space="preserve">getdar
This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>11098</id>
      <timestamp>2007-10-08T16:57:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>11192</id>
      <timestamp>2007-10-13T04:14:23Z</timestamp>
      <contributor>
        <ip>129.123.104.8</ip>
      </contributor>
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This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>11207</id>
      <timestamp>2007-10-13T07:56:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>14199</id>
      <timestamp>2008-08-05T17:48:03Z</timestamp>
      <contributor>
        <ip>121.11.69.194</ip>
      </contributor>
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This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
    <revision>
      <id>14202</id>
      <timestamp>2008-08-05T19:26:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/121.11.69.194|121.11.69.194]] ([[User_talk:121.11.69.194|121.11.69.194]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Dc_%28Unix%29 dc], the UNIX &quot;reverse-polish desk calculator&quot;.  (should one's system lack a native ''dc'' implementation, the partial emulator [[Desk calculator (Python)]] may be of interest).

{{languageuserhelp|dc|dc}}

[[Category:Programming languages|Dc]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:occam</title>
    <id>1392</id>
    <revision>
      <id>1655</id>
      <timestamp>2006-03-03T05:14:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>new cat with correct capitalization</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Occam_programming_language occam programming language].

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2017</id>
      <timestamp>2006-03-04T02:25:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{languageuserhelp|occam|occam}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Occam_programming_language occam programming language]. {{languageuserhelp|occam|occam}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>5571</id>
      <timestamp>2006-06-01T19:28:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in the [http://en.wikipedia.org/wiki/Occam_programming_language occam programming language]. {{languageuserhelp|occam|occam}}

[[Category:Programming languages|Occam]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:sed</title>
    <id>2779</id>
    <revision>
      <id>8073</id>
      <timestamp>2006-11-16T21:51:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing code for [http://en.wikipedia.org/wiki/Sed sed] - the UNIX '''S'''tream '''ED'''itor.</text>
    </revision>
    <revision>
      <id>8075</id>
      <timestamp>2006-11-16T21:57:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Category:Programming languages]]</comment>
      <text xml:space="preserve">This category contains articles describing code for [http://en.wikipedia.org/wiki/Sed sed] - the UNIX '''S'''tream '''ED'''itor.

[[Category:Programming languages|sed]]</text>
    </revision>
    <revision>
      <id>8076</id>
      <timestamp>2006-11-16T21:58:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>upper-case this time</comment>
      <text xml:space="preserve">This category contains articles describing code for [http://en.wikipedia.org/wiki/Sed sed] - the UNIX '''S'''tream '''ED'''itor.

[[Category:Programming languages|Sed]]</text>
    </revision>
    <revision>
      <id>10112</id>
      <timestamp>2007-05-16T06:41:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>copied some text from [[Category:Programming language:Sed]]</comment>
      <text xml:space="preserve">This category contains articles describing code for [http://en.wikipedia.org/wiki/Sed sed] - the UNIX '''S'''tream '''ED'''itor. [http://en.wikipedia.org/wiki/Sed Sed], Although not a general purpose programming language, it is [http://sed.sourceforge.net/grabbag/scripts/turing.txt turing complete].

[[Category:Programming languages|Sed]]</text>
    </revision>
    <revision>
      <id>10121</id>
      <timestamp>2007-05-16T08:32:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>rm extra link</comment>
      <text xml:space="preserve">This category contains articles describing code for [http://en.wikipedia.org/wiki/Sed sed] - the UNIX '''S'''tream '''ED'''itor. Although not a general purpose programming language, it is [http://sed.sourceforge.net/grabbag/scripts/turing.txt turing complete].

[[Category:Programming languages|Sed]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:sh</title>
    <id>3452</id>
    <revision>
      <id>13575</id>
      <timestamp>2008-05-29T03:24:20Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">This category contains articles describing code written in the &quot;sh&quot; programming language. {{languageuserhelp|sh|sh}} if you need to check some code or remember some part of the language.

[[Category:Programming languages|sh]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming language:sh script</title>
    <id>1612</id>
    <revision>
      <id>2377</id>
      <timestamp>2006-03-05T19:29:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell], the standard UNIX shell.

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>2391</id>
      <timestamp>2006-03-05T20:52:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{languageuserhelp|sh script|sh script}}</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell], the standard UNIX shell. {{languageuserhelp|sh script|sh script}}

[[Category:Programming languages]]</text>
    </revision>
    <revision>
      <id>3629</id>
      <timestamp>2006-03-26T22:48:06Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Programming language:Shell script]]</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell], the standard UNIX shell. {{languageuserhelp|sh script|sh script}}

[[Category:Programming language:Shell script]]</text>
    </revision>
    <revision>
      <id>5626</id>
      <timestamp>2006-06-01T21:25:59Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>cat sort key</comment>
      <text xml:space="preserve">This category contains articles describing code written in [http://en.wikipedia.org/wiki/Bourne_shell Bourne shell], the standard UNIX shell. {{languageuserhelp|sh script|sh script}}

[[Category:Programming language:Shell script|Sh script]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Programming languages</title>
    <id>1349</id>
    <revision>
      <id>1509</id>
      <timestamp>2006-03-02T23:27:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains various programming languages that code can be written in, intended to be used to mark articles written in those languages. Everything listed here should also be listed in the template [[Template:List of programming languages]].</text>
    </revision>
    <revision>
      <id>1510</id>
      <timestamp>2006-03-02T23:27:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix link</comment>
      <text xml:space="preserve">This category contains various programming languages that code can be written in, intended to be used to mark articles written in those languages. Everything listed here should also be listed in the template [[Template:List of programming language categories]].</text>
    </revision>
  </page>
  <page>
    <title>Category:Prototype pattern</title>
    <id>1674</id>
    <revision>
      <id>2680</id>
      <timestamp>2006-03-06T21:15:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Proxy pattern</title>
    <id>1682</id>
    <revision>
      <id>2688</id>
      <timestamp>2006-03-06T21:18:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Pseudorandom number generators</title>
    <id>1920</id>
    <revision>
      <id>4265</id>
      <timestamp>2006-04-24T09:30:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, a category and some links</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Pseudorandom_number_generator pseudorandom number generator] is a deterministic algorithm that generates a sequence of numbers with properties similar to a truly &quot;random&quot; sequence, where each value is chosen independently from a given statistical distribution, usually the uniform distribution. They are widely used in [[:Category:Simulators and emulators|simulations]], [[:Category:Randomized algorithms|randomized algorithms]], [[:Category:cryptography|cryptography]], and [[:Category:Artificial intelligence|artificial intelligence]].

[[Category:Numerical computing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:QR decomposition</title>
    <id>1989</id>
    <revision>
      <id>4641</id>
      <timestamp>2006-05-13T02:48:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition] is a matrix decomposition that writes a matrix as the product of an orthogonal matrix and an upper (or lower) triangular matrix.

&lt;noinclude&gt;
[[Category:Matrix algebra]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Quantitative finance</title>
    <id>1638</id>
    <revision>
      <id>2489</id>
      <timestamp>2006-03-06T06:59:42Z</timestamp>
      <contributor>
        <ip>81.185.32.104</ip>
      </contributor>
      <text xml:space="preserve">Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [[http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA]]
* Risk control
* Quantitative trading

Used languages are usually:
* C++
* Visual Basic
* and more sophistcated tools (like S-plus or Matlab)</text>
    </revision>
    <revision>
      <id>2490</id>
      <timestamp>2006-03-06T07:00:59Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [[http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA]])
* Risk control
* Quantitative trading

Used languages are usually:
* C++
* Visual Basic
* and more sophistiacated tools (like S-plus or Matlab)</text>
    </revision>
    <revision>
      <id>2491</id>
      <timestamp>2006-03-06T07:05:08Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

Used languages are usually:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophistiacated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])</text>
    </revision>
    <revision>
      <id>2497</id>
      <timestamp>2006-03-06T08:21:18Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

Used languages are usually:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophistiacated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2513</id>
      <timestamp>2006-03-06T09:33:34Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox MCQF}}
|}
&lt;/div&gt;

Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

Used languages are usually:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophistiacated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2515</id>
      <timestamp>2006-03-06T09:43:57Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox MCQF|maintain}}
|}
&lt;/div&gt;

Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

Used languages are usually:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophistiacated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2516</id>
      <timestamp>2006-03-06T09:44:15Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox MCQF|page}}
|}
&lt;/div&gt;

Softwares are used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

Used languages are usually:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophistiacated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2727</id>
      <timestamp>2006-03-06T23:30:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>sp and gr</comment>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox MCQF|page}}
|}
&lt;/div&gt;

Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2816</id>
      <timestamp>2006-03-07T17:31:18Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2918</id>
      <timestamp>2006-03-08T08:57:58Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Community article|MCQF|Matlab Community for Quantitative Finance}}
|}
&lt;/div&gt;

Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading
* Market economic modelling

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>2968</id>
      <timestamp>2006-03-08T20:21:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move tag to talk page</comment>
      <text xml:space="preserve">Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading
* Market economic modelling

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Programming_language:C_Plus_Plus]]
[[Category:Programming_language:Visual_Basic]]
[[Category:Programming_language:SPlus]]
[[Category:Programming_language:Matlab]]</text>
    </revision>
    <revision>
      <id>3156</id>
      <timestamp>2006-03-11T00:10:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>recat</comment>
      <text xml:space="preserve">Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading
* Market economic modelling

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Top level subject areas]]</text>
    </revision>
    <revision>
      <id>3157</id>
      <timestamp>2006-03-11T00:10:25Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>missing -</comment>
      <text xml:space="preserve">Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading
* Market economic modelling

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])


[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>4256</id>
      <timestamp>2006-04-23T07:05:31Z</timestamp>
      <contributor>
        <ip>62.62.170.59</ip>
      </contributor>
      <text xml:space="preserve">Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
* Risk control
* Quantitative trading
* Market economic modelling

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>5100</id>
      <timestamp>2006-05-23T06:51:30Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Software is used in three main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>5178</id>
      <timestamp>2006-05-26T08:03:26Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
# Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
# Risk control
** Value at Risk
** Copula models
# Quantitative trading
** Market impact models
# Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Montecarlo simulations]]
* [[Finite Difference methods]]

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>5179</id>
      <timestamp>2006-05-26T08:05:30Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <minor/>
      <comment>most common algorithms</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
# Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
# Risk control
** Value at Risk
** Copula models
# Quantitative trading
** Market impact models
# Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>5237</id>
      <timestamp>2006-05-28T09:32:12Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>list correction</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>6338</id>
      <timestamp>2006-06-20T13:30:23Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crutial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>6339</id>
      <timestamp>2006-06-20T13:32:21Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crutial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>6340</id>
      <timestamp>2006-06-20T13:34:02Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Financial Data providers */</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crutial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as Matlab have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>6341</id>
      <timestamp>2006-06-20T13:34:35Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Financial Data providers */</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crutial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as [[:Category:Programming language:Matlab|Matlab]] have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>7810</id>
      <timestamp>2006-10-13T15:05:50Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Financial Data providers */</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crucial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as [[:Category:Programming language:Matlab|Matlab]] have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>10741</id>
      <timestamp>2007-07-24T05:46:58Z</timestamp>
      <contributor>
        <ip>60.12.9.106</ip>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crucial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as [[:Category:Programming language:Matlab|Matlab]] have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]
* The [http://www.mathfinance.cn/ Quantitative Finance Code Index]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>13995</id>
      <timestamp>2008-07-17T19:48:36Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** [[High Frequency Finance]]
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crucial point in quantitative finance is to access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as [[:Category:Programming language:Matlab|Matlab]] have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]
* The [http://www.mathfinance.cn/ Quantitative Finance Code Index]

[[Category:Top-level subject areas]]</text>
    </revision>
    <revision>
      <id>15711</id>
      <timestamp>2008-12-29T13:07:43Z</timestamp>
      <contributor>
        <ip>192.165.213.18</ip>
      </contributor>
      <text xml:space="preserve">Software is used in four main areas in Quantitative Finance:
* Derivatives Pricing and Hedging (see for instance [http://www-rocq.inria.fr/mathfi/Premia/index.html PREMIA])
** [[Derivatives Pricing]]
** Hedging
* Risk control
** Value at Risk
** Copula models
* Quantitative trading
** [[High Frequency Finance]]
** Market impact models
* Market economic modelling
** Game theory

The most commonly used languages are:
* [[:Category:Programming_language:C_Plus_Plus|C++]]
* [[:Category:Programming_language:Visual_Basic|Visual Basic]]
* and more sophisticated tools (like [[:Category:Programming_language:SPlus|S-plus]] or [[:Category:Programming_language:Matlab|Matlab]])

The most used algorithms are:
* [[Monte Carlo simulations]]
* [[Finite Difference methods]]

==Financial Data providers==

A crucial point in quantitative finance is to have access to accurate data.

The main data provider are:

* Bloomberg
* Reuters
* Thomson Financial
** See for instance the [[Matlab Thomson Financial DataStream data access]] article.

Some high level programming language as [[:Category:Programming language:Matlab|Matlab]] have [[Data Acquisition (Matlab)|Data access toolboxes]].

==External links==
* [http://www.fenews.com/fen18/rapid.html Rapid Development and Deployment of a Financial Application (Matlab)]
* The [http://extranet.datastream.com/ Thomson Datastream Research Extranet]
* The [http://www.mathfinance.cn/ Quantitative Finance Code Index]

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Quicksort</title>
    <id>1399</id>
    <revision>
      <id>1677</id>
      <timestamp>2006-03-03T10:32:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Quicksort quicksort] sorting algorithm.

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Quicksort-based expected linear selection</title>
    <id>1815</id>
    <revision>
      <id>3508</id>
      <timestamp>2006-03-22T12:46:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Order statistic algorithms]]</comment>
      <text xml:space="preserve">One of the most straightforward and practical algorithms for determining the ''n''th smallest or large elements of a list is based on [[:Category:quicksort|quicksort]]. The algorithm requires expected linear time (that is, requires linear time with high probability) and is largely identical to quicksort except that instead of recurring on both sublists, it only recurs on the one containing the desired element.

[[Category:Order statistic algorithms]]</text>
    </revision>
    <revision>
      <id>3509</id>
      <timestamp>2006-03-22T12:48:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>nth_element</comment>
      <text xml:space="preserve">One of the most straightforward and practical algorithms for determining the ''n''th smallest or large elements of a list is based on [[:Category:quicksort|quicksort]]. The algorithm requires expected linear time (that is, requires linear time with high probability) and is largely identical to quicksort except that instead of recurring on both sublists, it only recurs on the one containing the desired element.

C++'s standard &lt;code&gt;nth_element&lt;/code&gt; algorithm is almost always based on this algorithm.

[[Category:Order statistic algorithms]]</text>
    </revision>
    <revision>
      <id>3647</id>
      <timestamp>2006-03-28T20:40:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Typos</comment>
      <text xml:space="preserve">One of the most straightforward and practical algorithms for determining the ''n''th smallest or largest element of a list is based on [[:Category:quicksort|quicksort]]. The algorithm requires expected linear time (that is, requires linear time with high probability) and is largely identical to quicksort except that instead of recurring on both sublists, it only recurs on the one containing the desired element.

C++'s standard &lt;code&gt;nth_element&lt;/code&gt; algorithm is almost always based on this algorithm.

[[Category:Order statistic algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Quine</title>
    <id>1704</id>
    <revision>
      <id>2777</id>
      <timestamp>2006-03-07T12:43:43Z</timestamp>
      <contributor>
        <username>Nikie</username>
        <id>22</id>
      </contributor>
      <text xml:space="preserve">This category contains [http://en.wikipedia.org/wiki/Quine Quines]</text>
    </revision>
    <revision>
      <id>2784</id>
      <timestamp>2006-03-07T13:55:03Z</timestamp>
      <contributor>
        <username>Nikie</username>
        <id>22</id>
      </contributor>
      <text xml:space="preserve">This category contains [http://en.wikipedia.org/wiki/Quine Quines]

[[Category:Computer science theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Quine-McCluskey algorithm</title>
    <id>2243</id>
    <revision>
      <id>5685</id>
      <timestamp>2006-06-02T03:49:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, [[Category:Boolean logic]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Quine-McCluskey_algorithm Quine-McCluskey algorithm] is a two-level logic minimization method. It takes a boolean formula and attempts to reduce it to an equivalent, more succinct boolean formula. For example, suppose A, B, C and boolean variables, and the logical negation of X is written as &lt;math&gt;\bar{X}&lt;/math&gt;. Then we could reduce this boolean formula ''f'':

:&lt;math&gt;f(A,B,C) = \bar{A}\bar{B}\bar{C} + \bar{A}B + AB\bar{C} + AC&lt;/math&gt;

To this equivalent formula:

:&lt;math&gt;f(A,B,C) = B + AC + \bar{A}\bar{C}&lt;/math&gt;

[[Category:Boolean logic]]</text>
    </revision>
    <revision>
      <id>5686</id>
      <timestamp>2006-06-02T03:50:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link Karnaugh maps</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Quine-McCluskey_algorithm Quine-McCluskey algorithm] is a two-level logic minimization method. It takes a boolean formula and attempts to reduce it to an equivalent, more succinct boolean formula. For example, suppose A, B, C and boolean variables, and the logical negation of X is written as &lt;math&gt;\bar{X}&lt;/math&gt;. Then we could reduce this boolean formula ''f'':

:&lt;math&gt;f(A,B,C) = \bar{A}\bar{B}\bar{C} + \bar{A}B + AB\bar{C} + AC&lt;/math&gt;

To this equivalent formula:

:&lt;math&gt;f(A,B,C) = B + AC + \bar{A}\bar{C}&lt;/math&gt;

This boolean formula minimization problem is also solved by [http://en.wikipedia.org/wiki/Karnaugh_map Karnaugh maps], but in a less systematic and scalable way.

[[Category:Boolean logic]]</text>
    </revision>
    <revision>
      <id>5690</id>
      <timestamp>2006-06-02T06:22:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>&lt;noinclude&gt; around cats</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Quine-McCluskey_algorithm Quine-McCluskey algorithm] is a two-level logic minimization method. It takes a boolean formula and attempts to reduce it to an equivalent, more succinct boolean formula. For example, suppose A, B, C and boolean variables, and the logical negation of X is written as &lt;math&gt;\bar{X}&lt;/math&gt;. Then we could reduce this boolean formula ''f'':

:&lt;math&gt;f(A,B,C) = \bar{A}\bar{B}\bar{C} + \bar{A}B + AB\bar{C} + AC&lt;/math&gt;

To this equivalent formula:

:&lt;math&gt;f(A,B,C) = B + AC + \bar{A}\bar{C}&lt;/math&gt;

This boolean formula minimization problem is also solved by [http://en.wikipedia.org/wiki/Karnaugh_map Karnaugh maps], but in a less systematic and scalable way.

&lt;noinclude&gt;
[[Category:Boolean logic]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>10971</id>
      <timestamp>2007-09-24T10:56:37Z</timestamp>
      <contributor>
        <ip>68.237.84.249</ip>
      </contributor>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Quine-McCluskey_algorithm Quine-McCluskey algorithm] is a two-level logic minimization method. It takes a boolean formula and attempts to reduce it to an equivalent, more succinct boolean formula. For example, suppose A, B and C are boolean variables, and the logical negation of X is written as &lt;math&gt;\bar{X}&lt;/math&gt;. Then we could reduce this boolean formula ''f'':

:&lt;math&gt;f(A,B,C) = \bar{A}\bar{B}\bar{C} + \bar{A}B + AB\bar{C} + AC&lt;/math&gt;

To this equivalent formula:

:&lt;math&gt;f(A,B,C) = B + AC + \bar{A}\bar{C}&lt;/math&gt;

This boolean formula minimization problem is also solved by [http://en.wikipedia.org/wiki/Karnaugh_map Karnaugh maps], but in a less systematic and scalable way.

&lt;noinclude&gt;
[[Category:Boolean logic]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:R250</title>
    <id>1921</id>
    <revision>
      <id>4269</id>
      <timestamp>2006-04-24T09:42:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Pseudorandom number generators]]</comment>
      <text xml:space="preserve">R250 is a pseudorandom number generator based on generalized feedback shift registers (GFSRs) invented by Kirkpatrick and Stoll in 1981. Specifically, it is the member GFSR(250,103) of the class of GFSRs. It has fairly good statistical properties (although these are improved in [[:Category:R521|R521]]) and a period of 2&lt;sup&gt;250&lt;/sup&gt;. See [http://www.qbrundage.com/michaelb/pubs/essays/random_number_generation Michael Brundage's discussion of R250] and [http://portal.acm.org/citation.cfm?id=321765.321777&amp;coll=GUIDE&amp;dl=ACM&amp;idx=J401&amp;part=periodical&amp;WantType=periodical&amp;title=Journal%20of%20the%20ACM%20(JACM) the original paper on GFSRs] (ACM login required).
[[Category:Pseudorandom number generators]]</text>
    </revision>
    <revision>
      <id>4270</id>
      <timestamp>2006-04-24T09:43:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Clarify</comment>
      <text xml:space="preserve">R250 is a pseudorandom number generator based on generalized feedback shift registers (GFSRs) invented by Kirkpatrick and Stoll in 1981. Specifically, it is the member GFSR(250,103) of the class of GFSRs. It has fairly good statistical properties (although these are improved by combining it with [[:Category:R521|R521]]) and a period of 2&lt;sup&gt;250&lt;/sup&gt;. See [http://www.qbrundage.com/michaelb/pubs/essays/random_number_generation Michael Brundage's discussion of R250] and [http://portal.acm.org/citation.cfm?id=321765.321777&amp;coll=GUIDE&amp;dl=ACM&amp;idx=J401&amp;part=periodical&amp;WantType=periodical&amp;title=Journal%20of%20the%20ACM%20(JACM) the original paper on GFSRs] (ACM login required).

[[Category:Pseudorandom number generators]]</text>
    </revision>
    <revision>
      <id>4271</id>
      <timestamp>2006-04-24T09:50:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Change link</comment>
      <text xml:space="preserve">R250 is a pseudorandom number generator based on generalized feedback shift registers (GFSRs) invented by Kirkpatrick and Stoll in 1981. Specifically, it is the member GFSR(250,103) of the class of GFSRs. It has fairly good statistical properties (although these are improved by combining it with R521 to form [[:Category:R250/521|R250/521]]) and a period of 2&lt;sup&gt;250&lt;/sup&gt;. See [http://www.qbrundage.com/michaelb/pubs/essays/random_number_generation Michael Brundage's discussion of R250] and [http://portal.acm.org/citation.cfm?id=321765.321777&amp;coll=GUIDE&amp;dl=ACM&amp;idx=J401&amp;part=periodical&amp;WantType=periodical&amp;title=Journal%20of%20the%20ACM%20(JACM) the original paper on GFSRs] (ACM login required).

[[Category:Pseudorandom number generators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:R250/521</title>
    <id>1922</id>
    <revision>
      <id>4272</id>
      <timestamp>2006-04-24T09:51:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Pseudorandom number generators]]</comment>
      <text xml:space="preserve">R250/521 is a pseudorandom number generator invented by Heuer et al in 1997 based on the generalized feedback shift registers (GFSRs) invented by Kirkpatrick and Stoll in 1981. It combines the members GFSR(250,103) and GFSR(521,168) of the class of GFSRs in a way that attains better statistical properties than both. See [http://www.qbrundage.com/michaelb/pubs/essays/random_number_generation Michael Brundage's discussion of R250/521] and [http://astro.uchicago.edu/~andrey/classes/rseminar/docs/rng_tests_janke1.pdf some more discussion].

[[Category:Pseudorandom number generators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:RGB to HSV color space conversion</title>
    <id>1975</id>
    <revision>
      <id>4559</id>
      <timestamp>2006-05-12T01:04:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, links, category</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/RGB_color_model RGB color space], used directly by most computer devices, expresses colors as an additive combination of three additive primary colors of light: red, green, and blue. A commonly used color space that corresponds more naturally to human perception is the [http://en.wikipedia.org/wiki/HSV_color_space HSV color space], whose three components are hue, saturation, and value. The formulas used to convert RGB to HSV depend on which of the RGB components is largest and which is smallest, and are described at ''[http://en.wikipedia.org/wiki/HSV_color_space#Transformation_from_RGB_to_HSV Transformation from RGB to HSV]''.

&lt;noinclude&gt;
[[Category:Color space conversion]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Rabin-Karp string search algorithm</title>
    <id>2267</id>
    <revision>
      <id>5920</id>
      <timestamp>2006-06-05T10:47:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>From [[Rabin-Karp string search algorithm]]</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Rabin-Karp_string_search_algorithm Rabin-Karp string search algorithm] is an algorithm based on hashing for finding a substring inside a large string quickly. Although it has bad worst case time, it is quick on average and in practice, and it is particularly suited to searching for many different strings at once.

[[Category:String search algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Radix sort</title>
    <id>1459</id>
    <revision>
      <id>1862</id>
      <timestamp>2006-03-03T20:15:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Radix_sort radix sort], a specialized sorting algorithm for strings and integers.

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Randomized algorithms</title>
    <id>1314</id>
    <revision>
      <id>1369</id>
      <timestamp>2006-02-28T20:10:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">This category contains articles describing randomized algorithms, algorithms that use a source of random bits to solve a problem efficiently on average. Note that many of these will rely on pseudorandom generators, since there is limited hardware and software support for true randomness.

[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>1370</id>
      <timestamp>2006-02-28T20:10:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Link Wikipedia</comment>
      <text xml:space="preserve">This category contains articles describing [http://en.wikipedia.org/wiki/Randomized_algorithm randomized algorithms], algorithms that use a source of random bits to solve a problem efficiently on average. Note that many of these will rely on pseudorandom generators, since there is limited hardware and software support for true randomness.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Raster algorithms</title>
    <id>3137</id>
    <revision>
      <id>10239</id>
      <timestamp>2007-05-18T07:46:46Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">[[Category:Graphics]]</text>
    </revision>
    <revision>
      <id>10240</id>
      <timestamp>2007-05-18T07:49:43Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>description</comment>
      <text xml:space="preserve">This category contains articles on algorithms for drawing [http://en.wikipedia.org/wiki/Raster_graphics raster graphics].
 
[[Category:Graphics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Red-black tree</title>
    <id>1423</id>
    <revision>
      <id>1747</id>
      <timestamp>2006-03-03T12:44:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Binary search tree]]</comment>
      <text xml:space="preserve">[[Category:Binary search tree]]</text>
    </revision>
    <revision>
      <id>2060</id>
      <timestamp>2006-03-04T04:07:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move to [[Category:Balanced tree]]</comment>
      <text xml:space="preserve">[[Category:Balanced tree]]</text>
    </revision>
    <revision>
      <id>7944</id>
      <timestamp>2006-11-07T01:03:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Text, noinclude</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Red-black_tree red-black tree] is a type of self-balancing binary search tree typically used to implement associative arrays. It has O(log ''n'') worst-case time for each operation and is quite efficient in practice. Unfortunately, it's also quite complex to implement, requiring a number of subtle cases for both insertion and deletion.
&lt;noinclude&gt;
[[Category:Balanced tree]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Reduction from SAT to 3CNFSAT</title>
    <id>1818</id>
    <revision>
      <id>3512</id>
      <timestamp>2006-03-22T13:03:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Reductions]]</comment>
      <text xml:space="preserve">One of the first problems to be shown NP-complete was the [boolean satisfiability problem] ('''SAT'''). A surprising fact is that we do not need the full generality of boolean formulas to achieve this hardness result; it suffices to consider formulas that are both in [http://en.wikipedia.org/wiki/Conjunctive_normal_form conjunctive normal form] ('''CNF'''). In conjunctive normal form these properties hold:
* All negations (NOTs) are applied directly to input variables. A variable or its negation is referred to as a ''literal''.
* The formula is a conjunction (AND) of clauses, where each clause is a disjunction (OR) of literals.

A simple example might be:

:&lt;math&gt;(x_1 \vee x_3 \vee \neg{x_4}) \wedge (\neg{x_1} \vee x_3 \vee x_5 \vee x_{10}) \wedge (x_2 \vee \neg{x_{10}})&lt;/math&gt;

Moreover, we can limit ourselves to formulas where every clause contains only three literals, like the first clause above. This is called 3CNF form, and the satisfiability problem for it is called '''3CNFSAT'''. We will give an efficient polynomial-time algorithm that converts any boolean formula to a 3CNF formula that is satisfiable if and only if the original formula is (the definition of a many-one reduction).

&lt;noinclude&gt;
[[Category:Reductions]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>3513</id>
      <timestamp>2006-03-22T13:03:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>italics</comment>
      <text xml:space="preserve">One of the first problems to be shown NP-complete was the [boolean satisfiability problem] ('''SAT'''). A surprising fact is that we do not need the full generality of boolean formulas to achieve this hardness result; it suffices to consider formulas that are both in [http://en.wikipedia.org/wiki/Conjunctive_normal_form conjunctive normal form] ('''CNF'''). In conjunctive normal form these properties hold:
* All negations (NOTs) are applied directly to input variables. A variable or its negation is referred to as a ''literal''.
* The formula is a conjunction (AND) of ''clauses'', where each clause is a disjunction (OR) of literals.

A simple example might be:

:&lt;math&gt;(x_1 \vee x_3 \vee \neg{x_4}) \wedge (\neg{x_1} \vee x_3 \vee x_5 \vee x_{10}) \wedge (x_2 \vee \neg{x_{10}})&lt;/math&gt;

Moreover, we can limit ourselves to formulas where every clause contains only three literals, like the first clause above. This is called 3CNF form, and the satisfiability problem for it is called '''3CNFSAT'''. We will give an efficient polynomial-time algorithm that converts any boolean formula to a 3CNF formula that is satisfiable if and only if the original formula is (the definition of a many-one reduction).

&lt;noinclude&gt;
[[Category:Reductions]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>3514</id>
      <timestamp>2006-03-22T13:05:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link Wikipedia on Many-one_reduction</comment>
      <text xml:space="preserve">One of the first problems to be shown NP-complete was the [boolean satisfiability problem] ('''SAT'''). A surprising fact is that we do not need the full generality of boolean formulas to achieve this hardness result; it suffices to consider formulas that are both in [http://en.wikipedia.org/wiki/Conjunctive_normal_form conjunctive normal form] ('''CNF'''). In conjunctive normal form these properties hold:
* All negations (NOTs) are applied directly to input variables. A variable or its negation is referred to as a ''literal''.
* The formula is a conjunction (AND) of ''clauses'', where each clause is a disjunction (OR) of literals.

A simple example might be:

:&lt;math&gt;(x_1 \vee x_3 \vee \neg{x_4}) \wedge (\neg{x_1} \vee x_3 \vee x_5 \vee x_{10}) \wedge (x_2 \vee \neg{x_{10}})&lt;/math&gt;

Moreover, we can limit ourselves to formulas where every clause contains only three literals, like the first clause above. This is called 3CNF form, and the satisfiability problem for it is called '''3CNFSAT'''. We will give an efficient polynomial-time algorithm that converts any boolean formula to a 3CNF formula that is satisfiable if and only if the original formula is (the definition of a [http://en.wikipedia.org/wiki/Many-one_reduction many-one reduction]).

&lt;noinclude&gt;
[[Category:Reductions]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Reductions</title>
    <id>1772</id>
    <revision>
      <id>3165</id>
      <timestamp>2006-03-11T05:50:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Computer science theory]]</comment>
      <text xml:space="preserve">This category's articles exhibit [http://en.wikipedia.org/wiki/Reduction_%28complexity%29 formal reductions] from one problem to another. These are both important in theory, particularly in the definition of completeness, and a valuable way of applying existing algorithms to new problems with little coding effort.

[[Category:Computer science theory]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Rot13</title>
    <id>3027</id>
    <revision>
      <id>9173</id>
      <timestamp>2007-02-17T20:29:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added new category</comment>
      <text xml:space="preserve">This category's articles describe programs that perform the [http://en.wikipedia.org/wiki/Rot13 Rot13] cypher. There is a [http://www.miranda.org/~jkominek/rot13/ site] that list many hundreds of implementations of this example (but please don't copy content from them).

[[Category:Introductory examples]]</text>
    </revision>
    <revision>
      <id>9175</id>
      <timestamp>2007-02-17T20:32:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added introduction with links to Wikipedia aricle and the Rot13 site</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Rot13 Rot13] is a simple substitution cypher that is used as a simple, but easy to break, obfuscation technique. For example it is used in some email or online forums to hide punchlines to jokes or answers to quizzes. It is similar in operation to the [http://en.wikipedia.org/wiki/Base64 base-64] algorithm used to hide user names and passwords from the casual observer in the HTTP [http://en.wikipedia.org/wiki/Basic_authentication_scheme basic authentication scheme]. Like all substitution cyphers, it is easy to break (even easier if you know or can guess that it's been used). But it is a nice example that can serve as a introductory example for most programming languages. It also has the interesting property of symmetry: the encrypted text can be passed though the same process to return the plain text. 

This category's articles describe programs that perform the Rot13 cypher. There is a [http://www.miranda.org/~jkominek/rot13/ site] that list many hundreds of implementations of this example (but please don't copy content from them).

[[Category:Introductory examples]]
[[Category:Ciphers]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Scientific computing</title>
    <id>3575</id>
    <revision>
      <id>14740</id>
      <timestamp>2008-09-26T20:57:33Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=perl&gt;

&lt;&lt;rand_prime.pl&gt;&gt;=
#!/usr/bin/perl

use strict;

use Math::BigInt::GMP;

# Precondition: a, n &gt;= 0; n is odd
use strict;
use warnings;
#use diagnostics;

use Crypt::OpenSSL::Random;
use Data::Dumper;
use Math::BigInt;
use Math::BigFloat;

sub brand {
   my $number = shift;
   my $n = Math::BigInt-&gt;new($number);
   my $l = Math::BigFloat-&gt;new($n + 1)-&gt;blog(2)-&gt;bceil;
   my $r = 0;

   while ($r == 0 or $r &gt;= $n) {
        my $x = Crypt::OpenSSL::Random::random_pseudo_bytes(10);
        $r = Math::BigInt-&gt;new('0b' . unpack(&quot;B$l&quot;, $x));
        if ($r &lt; $n and $r) {
            last;
        } else {
#           printf &quot;rand miss\n&quot;;
        }
    }
    return $r;
}


sub jacobi
{
  my ($a, $n) = @_;

die unless defined $a;

  if ($a == 0) {                # identity 1
    return ($n == 1) ? 1 : 0;
  }
  if ($a == 2) {                # identity 2
    my $x = $n % 8;
    if ($x == 1 || $x == 7) {
      return 1;
    } elsif ($x == 3 || $x == 5) {
      return -1;
    }
  }
  if ( $a &gt;= $n ) {             # identity 3
    return jacobi($a % $n, $n);
  }
  if ($a % 2 == 0) {            # identity 4
    return jacobi(2, $n) * jacobi($a/2, $n);
  }
  die if $a % 2 == 0;
                                # identities 5 and 6
  return ($a % 4 == 3 &amp;&amp; $n % 4 == 3) ? -jacobi($n, $a) : jacobi($n, $a);
}
sub check
{
    my $number = shift;

    my $n = Math::BigInt-&gt;new($number);

    return 'Composite 0' if $n-&gt;copy-&gt;bmod(2) == 0;

    my $a = 0;
    while ($a == 0) {
        $a = brand($number);
    }
    return 'Composite 1' if (1 != $a-&gt;copy-&gt;bgcd($n));

    my $x = ($n - 1) / 2;

    my $q =  $a-&gt;copy-&gt;bmodpow($x, $n);

#    die 'bad math' unless $q == $q_p;

    my $j = jacobi($a, $n);

    $j %= $n;

    if ($j == $q) {
        return 'Prime.';
    } else {
        return 'Composite 2';
    }
}

my $number = shift || die &quot;Need a number.&quot;;
my $loops = shift || 10;

die if ($loops &lt; 0);

my $c = 0;

while ($c++ &lt; $loops) {
    my $ret = check($number);
    if ($ret =~ /Composite/) {
        print $ret, &quot;\n&quot;;
        exit;
    }
}

print &quot;This is only a 1/2^&quot;, $loops, &quot; chance that $number is not prime\n&quot;;

&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>14741</id>
      <timestamp>2008-09-26T20:58:10Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Security</title>
    <id>1317</id>
    <revision>
      <id>1375</id>
      <timestamp>2006-02-28T20:23:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category is for articles related to computer security and security best practices. Be warned that these articles may contain examples of insecure code for demonstration purposes.</text>
    </revision>
    <revision>
      <id>1519</id>
      <timestamp>2006-03-02T23:32:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category is for articles related to computer security and security best practices. Be warned that these articles may contain examples of insecure code for demonstration purposes.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Selection algorithm</title>
    <id>2218</id>
    <revision>
      <id>5490</id>
      <timestamp>2006-05-31T21:05:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, Wikipedia link, no category yet</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Selection_algorithm selection algorithm] computes the ''k''th largest or ''k''th smallest element in an unordered list of values. A particularly common case is finding the median. Another common selection problem is finding the ''k'' largest or ''k'' smallest elements in a list in order. The most efficient known selection algorithms in practice and theory are based on the partition operation used in [[:Category:Quicksort|quicksort]].</text>
    </revision>
    <revision>
      <id>6403</id>
      <timestamp>2006-06-21T23:04:41Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ Category:Algorithms</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Selection_algorithm selection algorithm] computes the ''k''th largest or ''k''th smallest element in an unordered list of values. A particularly common case is finding the median. Another common selection problem is finding the ''k'' largest or ''k'' smallest elements in a list in order. The most efficient known selection algorithms in practice and theory are based on the partition operation used in [[:Category:Quicksort|quicksort]].

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Selection sort</title>
    <id>1457</id>
    <revision>
      <id>1858</id>
      <timestamp>2006-03-03T20:12:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Sorting algorithms]]</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Selection_sort selection sort], a simple sorting algorithm that is the basis of more advanced algorithms such as [[Category:Heapsort|heapsort]].

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>2494</id>
      <timestamp>2006-03-06T07:35:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix link</comment>
      <text xml:space="preserve">This category's articles describe implementations of [http://en.wikipedia.org/wiki/Selection_sort selection sort], a simple sorting algorithm that is the basis of more advanced algorithms such as [[:Category:Heapsort|heapsort]].

[[Category:Sorting algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Servers</title>
    <id>1767</id>
    <revision>
      <id>3150</id>
      <timestamp>2006-03-10T23:08:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">This category contains implementations of network servers.

[[Category:Networking]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Shell sort</title>
    <id>2219</id>
    <revision>
      <id>5492</id>
      <timestamp>2006-05-31T21:22:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, cat</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Shell_sort Shell sort] is a relatively simple sorting algorithm based on [[:Category:Insertion_sort|insertion sort]]. It operates by taking every ''k''th element of the list and performing and insertion sort on this subset. It does this for several values of ''k'' in a row until ''k''=1, at which point it is performing insertion sort; but the previous iterations moved each element closer to its final position, speeding up this final pass dramatically.

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>5493</id>
      <timestamp>2006-05-31T21:22:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Shell_sort Shell sort] is a relatively simple sorting algorithm based on [[:Category:Insertion_sort|insertion sort]]. It operates by taking every ''k''th element of the list and performing an insertion sort on this subset. It does this for several values of ''k'' in a row until ''k''=1, at which point it is performing insertion sort; but the previous iterations moved each element closer to its final position, speeding up this final pass dramatically.

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>5494</id>
      <timestamp>2006-05-31T21:23:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Example, clarify</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Shell_sort Shell sort] is a relatively simple sorting algorithm based on [[:Category:Insertion_sort|insertion sort]]. It operates by taking every ''k''th element of the list and performing an insertion sort on this subset. It does this for several decreasing values of ''k'', such as 23, 10, 4, and 1, until ''k''=1, at which point it is performing insertion sort; but the previous iterations moved each element closer to its final position, speeding up this final pass dramatically.

[[Category:Sorting algorithms]]</text>
    </revision>
    <revision>
      <id>5495</id>
      <timestamp>2006-05-31T21:24:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>&lt;noinclude&gt; around cat</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Shell_sort Shell sort] is a relatively simple sorting algorithm based on [[:Category:Insertion_sort|insertion sort]]. It operates by taking every ''k''th element of the list and performing an insertion sort on this subset. It does this for several decreasing values of ''k'', such as 23, 10, 4, and 1, until ''k''=1, at which point it is performing insertion sort; but the previous iterations moved each element closer to its final position, speeding up this final pass dramatically.

&lt;noinclude&gt;
[[Category:Sorting algorithms]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Shortest path algorithms</title>
    <id>2246</id>
    <revision>
      <id>5696</id>
      <timestamp>2006-06-02T08:01:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">A shortest path algorithm finds the shortest possible sequence of edges connecting two vertices in a graph. Here, &quot;shortest&quot; may refer to the number of edges, but more generally refers to the sum of the weights of the edges, where each edge has a numeric value denoted as its weight. There are three main kinds:

* Point-to-point shortest path: finds the shortest path between a single source vertex and a single destination vertex.
* Single-source shortest path: finds the shortest paths between a single source vertex and all other vertices in the graph simultaneously.
* All-pairs shortest path: finds the shortest paths between every pair of vertices in the graph simultaneously.

[[Category:Graph algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Shunting yard algorithm</title>
    <id>3288</id>
    <revision>
      <id>12065</id>
      <timestamp>2008-01-12T15:34:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains articles describing [http://en.wikipedia.org/wiki/Shunting_yard_algorithm the shunting yard algorithm].

[[Category:Parsers]]
[[Category:Compilers and programming languages]]</text>
    </revision>
    <revision>
      <id>12070</id>
      <timestamp>2008-01-12T15:38:24Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>rm extra cat.</comment>
      <text xml:space="preserve">This category contains articles describing [http://en.wikipedia.org/wiki/Shunting_yard_algorithm the shunting yard algorithm].

[[Category:Parsers]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Sierpinski triangle</title>
    <id>3201</id>
    <revision>
      <id>10797</id>
      <timestamp>2007-07-30T22:57:46Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">A crude [http://en.wikipedia.org/wiki/Sierpinski_triangle Sierpinski triangle] can be seen by plotting the state of a one-dimensional [http://en.wikipedia.org/wiki/Cellular_automaton cellular automata] over time.

[[Category:Cellular automata]]</text>
    </revision>
    <revision>
      <id>10805</id>
      <timestamp>2007-07-30T23:03:40Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">A crude [http://en.wikipedia.org/wiki/Sierpinski_triangle Sierpinski triangle] can be seen by plotting the state of a one-dimensional [http://en.wikipedia.org/wiki/Cellular_automaton cellular automata] over time.

==theory==
A one-dimensional cellular automaton is a linear space of cells, each of which has a state. The automaton changes in discrete time steps called generations. In each generation the state of each cell is decided according to a set of rules that is based on the states of neighboring cells. In the case of one-dimensional cellular automaton each cell has its state decided by considering three cells, itself and its left and right neighboring cells. 

The Sierpinski cellular automaton has two states, Empty and Full. The only rule states that a cell will be set to Full if and only if of the three states considered exactly one or two are Full. 

When run output similar to the following will be produced.

&lt;codeblock&gt;
                                        @                                       
                                       @@@                                      
                                      @@ @@                                     
                                     @@@@@@@                                    
                                    @@     @@                                   
                                   @@@@   @@@@                                  
                                  @@  @@ @@  @@                                 
                                 @@@@@@@@@@@@@@@                                
                                @@             @@                               
                               @@@@           @@@@                              
                              @@  @@         @@  @@                             
                             @@@@@@@@       @@@@@@@@                            
                            @@      @@     @@      @@                           
                           @@@@    @@@@   @@@@    @@@@                          
                          @@  @@  @@  @@ @@  @@  @@  @@                         
                         @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@                        
                        @@                             @@                       
                       @@@@                           @@@@                      
                      @@  @@                         @@  @@                     
                     @@@@@@@@                       @@@@@@@@                    
                    @@      @@                     @@      @@                   
                   @@@@    @@@@                   @@@@    @@@@                  
                  @@  @@  @@  @@                 @@  @@  @@  @@                 
                 @@@@@@@@@@@@@@@@               @@@@@@@@@@@@@@@@                
                @@              @@             @@              @@               
               @@@@            @@@@           @@@@            @@@@              
              @@  @@          @@  @@         @@  @@          @@  @@             
             @@@@@@@@        @@@@@@@@       @@@@@@@@        @@@@@@@@            
            @@      @@      @@      @@     @@      @@      @@      @@           
           @@@@    @@@@    @@@@    @@@@   @@@@    @@@@    @@@@    @@@@          
          @@  @@  @@  @@  @@  @@  @@  @@ @@  @@  @@  @@  @@  @@  @@  @@         
         @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
&lt;/codeblock&gt;

Note that the state transformation rule is most easily expressed by observing that a cell is set to Empty when its context triple is all alike, and to Full when there are any differences.

[[Category:Cellular automata]]</text>
    </revision>
    <revision>
      <id>16440</id>
      <timestamp>2009-05-18T11:44:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* theory */ style</comment>
      <text xml:space="preserve">A crude [http://en.wikipedia.org/wiki/Sierpinski_triangle Sierpinski triangle] can be seen by plotting the state of a one-dimensional [http://en.wikipedia.org/wiki/Cellular_automaton cellular automata] over time.

==Theory==
A one-dimensional cellular automaton is a linear space of cells, each of which has a state. The automaton changes in discrete time steps called generations. In each generation the state of each cell is decided according to a set of rules that is based on the states of neighboring cells. In the case of one-dimensional cellular automaton each cell has its state decided by considering three cells, itself and its left and right neighboring cells. 

The Sierpinski cellular automaton has two states, Empty and Full. The only rule states that a cell will be set to Full if and only if of the three states considered exactly one or two are Full. 

When run output similar to the following will be produced.

&lt;codeblock&gt;
                                        @                                       
                                       @@@                                      
                                      @@ @@                                     
                                     @@@@@@@                                    
                                    @@     @@                                   
                                   @@@@   @@@@                                  
                                  @@  @@ @@  @@                                 
                                 @@@@@@@@@@@@@@@                                
                                @@             @@                               
                               @@@@           @@@@                              
                              @@  @@         @@  @@                             
                             @@@@@@@@       @@@@@@@@                            
                            @@      @@     @@      @@                           
                           @@@@    @@@@   @@@@    @@@@                          
                          @@  @@  @@  @@ @@  @@  @@  @@                         
                         @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@                        
                        @@                             @@                       
                       @@@@                           @@@@                      
                      @@  @@                         @@  @@                     
                     @@@@@@@@                       @@@@@@@@                    
                    @@      @@                     @@      @@                   
                   @@@@    @@@@                   @@@@    @@@@                  
                  @@  @@  @@  @@                 @@  @@  @@  @@                 
                 @@@@@@@@@@@@@@@@               @@@@@@@@@@@@@@@@                
                @@              @@             @@              @@               
               @@@@            @@@@           @@@@            @@@@              
              @@  @@          @@  @@         @@  @@          @@  @@             
             @@@@@@@@        @@@@@@@@       @@@@@@@@        @@@@@@@@            
            @@      @@      @@      @@     @@      @@      @@      @@           
           @@@@    @@@@    @@@@    @@@@   @@@@    @@@@    @@@@    @@@@          
          @@  @@  @@  @@  @@  @@  @@  @@ @@  @@  @@  @@  @@  @@  @@  @@         
         @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
&lt;/codeblock&gt;

Note that the state transformation rule is most easily expressed by observing that a cell is set to Empty when its context triple is all alike, and to Full when there are any differences.

[[Category:Cellular automata]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Sieve of Eratosthenes</title>
    <id>2761</id>
    <revision>
      <id>8007</id>
      <timestamp>2006-11-14T10:03:01Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Wikipedia article: [http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes]

[[Category:Number theory]]</text>
    </revision>
    <revision>
      <id>8412</id>
      <timestamp>2007-01-02T18:11:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Brief description</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes Sieve of Eratosthenes] is an algorithm for rapidly locating all the prime numbers in a certain range of integers. It operates by marking as composite all nontrivial multiples of each prime in sequence until only primes remain unmarked. It is most well-suited to implementation using arrays, which are compact and feature random access.

&lt;noinclude&gt;
[[Category:Number theory]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Signal processing</title>
    <id>1888</id>
    <revision>
      <id>4120</id>
      <timestamp>2006-04-13T15:36:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">This category contains algorithms for processing discrete signals such as audio, video, and image signals stored in a digital form.

[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Simulators and emulators</title>
    <id>1321</id>
    <revision>
      <id>1390</id>
      <timestamp>2006-02-28T21:51:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category contains code for simulating and emulating devices and operating systems on other devices and operating systems.</text>
    </revision>
    <revision>
      <id>1520</id>
      <timestamp>2006-03-02T23:32:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains code for simulating and emulating devices and operating systems on other devices and operating systems.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Singleton pattern</title>
    <id>1621</id>
    <revision>
      <id>2430</id>
      <timestamp>2006-03-06T01:38:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, category</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Singleton_pattern singleton pattern] is designed to restrict instantiation of a class to one (or a few) objects.

[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Singly linked list</title>
    <id>1415</id>
    <revision>
      <id>1737</id>
      <timestamp>2006-03-03T12:33:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <text xml:space="preserve">[[Category:Linked list]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Skip list</title>
    <id>1376</id>
    <revision>
      <id>1608</id>
      <timestamp>2006-03-03T02:35:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Data structures]]</comment>
      <text xml:space="preserve">A skip list is an efficient container data structure generalizing the simple linked list. These articles implement the data structure and its operations.

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Software engineering</title>
    <id>1613</id>
    <revision>
      <id>2383</id>
      <timestamp>2006-03-05T20:37:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Top-level subject areas]]</comment>
      <text xml:space="preserve">This category contains programs involving or related to [http://en.wikipedia.org/wiki/Software_engineering software engineering].

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Software translation</title>
    <id>3320</id>
    <revision>
      <id>12515</id>
      <timestamp>2008-02-18T18:47:26Z</timestamp>
      <contributor>
        <username>Haakon</username>
        <id>531</id>
      </contributor>
      <text xml:space="preserve">Translators of free (as in freedom) software needs quicker tools that allow for distributed translation teams, and a wiki like Literate Programs fit the bill. If a browser is the only tool needed, the barrier to participate in translation would be significantly lowered.</text>
    </revision>
    <revision>
      <id>12516</id>
      <timestamp>2008-02-18T18:47:49Z</timestamp>
      <contributor>
        <username>Haakon</username>
        <id>531</id>
      </contributor>
      <text xml:space="preserve">Translators of free (as in freedom) software need quicker tools that allow for distributed translation teams, and a wiki like Literate Programs fit the bill. If a browser is the only tool needed, the barrier to participate in translation would be significantly lowered.</text>
    </revision>
    <revision>
      <id>12517</id>
      <timestamp>2008-02-18T18:56:32Z</timestamp>
      <contributor>
        <username>Haakon</username>
        <id>531</id>
      </contributor>
      <text xml:space="preserve">Translators of free (as in freedom) software need quicker tools that allow for distributed translation teams, and a wiki like Literate Programs fit the bill. If a browser is the only tool needed, the barrier to participate in translation would be significantly lowered.

[[http://en.literateprograms.org/LiteratePrograms:Public_forum#Translation_of_POT.2FPO-files_using_wiki Haakon Meland Eriksen and Derek Ross on this topic]]</text>
    </revision>
    <revision>
      <id>12518</id>
      <timestamp>2008-02-18T18:56:49Z</timestamp>
      <contributor>
        <username>Haakon</username>
        <id>531</id>
      </contributor>
      <text xml:space="preserve">Translators of free (as in freedom) software need quicker tools that allow for distributed translation teams, and a wiki like Literate Programs fit the bill. If a browser is the only tool needed, the barrier to participate in translation would be significantly lowered.

[http://en.literateprograms.org/LiteratePrograms:Public_forum#Translation_of_POT.2FPO-files_using_wiki Haakon Meland Eriksen and Derek Ross on this topic]</text>
    </revision>
  </page>
  <page>
    <title>Category:Sorting algorithms</title>
    <id>1303</id>
    <revision>
      <id>1353</id>
      <timestamp>2006-02-28T19:34:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Sorting_algorithm sorting algorithms], programs designed to place a list of values in sorted order.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Soundex</title>
    <id>2856</id>
    <revision>
      <id>8299</id>
      <timestamp>2006-12-03T04:40:09Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>Create category</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Soundex Soundex] algorithm for codifying English surnames.</text>
    </revision>
    <revision>
      <id>8302</id>
      <timestamp>2006-12-03T09:55:05Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Soundex Soundex] algorithm for codifying English surnames.

[[Category:Databases]]</text>
    </revision>
    <revision>
      <id>10651</id>
      <timestamp>2007-07-07T01:49:35Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Soundex Soundex] algorithm for codifying English surnames.

[[Category:Databases]]
[[Category:Linguistics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Spatial color quantization</title>
    <id>1994</id>
    <revision>
      <id>4659</id>
      <timestamp>2006-05-13T18:19:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">[http://www-dbv.cs.uni-bonn.de/abstracts/puzicha.TR98-1.html Spatial color quantization] is a relatively new [[:Category:color quantization|color quantization]] algorithm that combines dithering and palette generation into a single step and uses a simple model of human perception. [http://www-dbv.cs.uni-bonn.de/quant/ Sample images] suggest that its visual quality is superior to that of other algorithms, especially at low numbers of colors, although it is more computationally expensive.

&lt;noinclude&gt;
[[Category:Color quantization]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Splay tree</title>
    <id>1973</id>
    <revision>
      <id>4555</id>
      <timestamp>2006-05-11T12:38:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, category</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Splay_tree Splay trees] are a typing of balanced binary search tree that dynamically rebalance the tree to move frequently accessed items nearer the root, providing faster access to them in the future. They are simple to implement and provide amortized O(log ''n'') bounds on insertion, deletion, and lookup operations.

&lt;noinclude&gt;
[[Category:Balanced tree]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>4556</id>
      <timestamp>2006-05-11T14:15:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Splay_tree Splay trees] are a type of balanced binary search tree that dynamically rebalance the tree to move frequently accessed items nearer the root, providing faster access to them in the future. They are simple to implement and provide amortized O(log ''n'') bounds on insertion, deletion, and lookup operations.

&lt;noinclude&gt;
[[Category:Balanced tree]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>4560</id>
      <timestamp>2006-05-12T02:44:53Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>link http://en.wikipedia.org/wiki/Big_O_notation</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Splay_tree Splay trees] are a type of balanced binary search tree that dynamically rebalance the tree to move frequently accessed items nearer the root, providing faster access to them in the future. They are simple to implement and provide amortized [http://en.wikipedia.org/wiki/Big_O_notation O](log ''n'') bounds on insertion, deletion, and lookup operations.

&lt;noinclude&gt;
[[Category:Balanced tree]]
&lt;/noinclude&gt;</text>
    </revision>
    <revision>
      <id>4561</id>
      <timestamp>2006-05-12T02:45:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>maybe this will look better</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Splay_tree Splay trees] are a type of balanced binary search tree that dynamically rebalance the tree to move frequently accessed items nearer the root, providing faster access to them in the future. They are simple to implement and provide amortized [http://en.wikipedia.org/wiki/Big_O_notation O(log ''n'')] bounds on insertion, deletion, and lookup operations.

&lt;noinclude&gt;
[[Category:Balanced tree]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Stack</title>
    <id>2837</id>
    <revision>
      <id>8215</id>
      <timestamp>2006-11-28T14:56:39Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Stack</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Stack_%28data_structure%29 stacks].

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:State pattern</title>
    <id>1690</id>
    <revision>
      <id>2696</id>
      <timestamp>2006-03-06T21:21:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Statistics</title>
    <id>2830</id>
    <revision>
      <id>8204</id>
      <timestamp>2006-11-28T03:09:44Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Statistics</comment>
      <text xml:space="preserve">This category contains programs related to [http://en.wikipedia.org/wiki/Statistics statistics]

[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Strategy pattern</title>
    <id>1691</id>
    <revision>
      <id>2697</id>
      <timestamp>2006-03-06T21:21:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:String search algorithms</title>
    <id>2176</id>
    <revision>
      <id>5224</id>
      <timestamp>2006-05-27T08:36:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Algorithms]]</comment>
      <text xml:space="preserve">String search algorithms attempt to locate a sequence of characters somewhere inside a given piece of text that meets certain criteria. For example, it might be used to find &quot;at&quot; inside the word &quot;hatter&quot;. There are a variety of efficient solutions to this problem based on hashing, automata, and other sophisticated techniques.

[[Category:Algorithms]]</text>
    </revision>
    <revision>
      <id>5225</id>
      <timestamp>2006-05-27T08:36:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Link</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/String_searching_algorithm String search algorithms] attempt to locate a sequence of characters somewhere inside a given piece of text that meets certain criteria. For example, it might be used to find &quot;at&quot; inside the word &quot;hatter&quot;. There are a variety of efficient solutions to this problem based on hashing, automata, and other sophisticated techniques.

[[Category:Algorithms]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Suffix tree</title>
    <id>2802</id>
    <revision>
      <id>8156</id>
      <timestamp>2006-11-23T23:28:39Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Suffix tree</comment>
      <text xml:space="preserve">This category contains implementations of [http://en.wikipedia.org/wiki/Suffix_tree suffix trees].

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Symbolic mathematics</title>
    <id>1383</id>
    <revision>
      <id>1624</id>
      <timestamp>2006-03-03T03:04:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Discrete and symbolic mathematics]]</comment>
      <text xml:space="preserve">[[Category:Discrete and symbolic mathematics]]</text>
    </revision>
  </page>
  <page>
    <title>Category:T-tree</title>
    <id>2206</id>
    <revision>
      <id>5366</id>
      <timestamp>2006-05-29T22:14:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link, [[Category:Data structures]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/T-tree T-tree] is a tree data structure based on [[:Category:AVL tree|AVL trees]] and [[:Category:B-tree|B-trees]] that is useful for indexing in-memory databases. Rotations are performed just as in an AVL tree, but each node holds multiple items, allowing the cost of rotations to be amortized over more operations.

&lt;noinclude&gt;
[[Category:Data structures]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Template method pattern</title>
    <id>1692</id>
    <revision>
      <id>2698</id>
      <timestamp>2006-03-06T21:22:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:The Knight's Tour</title>
    <id>3567</id>
    <revision>
      <id>14702</id>
      <timestamp>2008-09-23T13:41:47Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Shared text box |
The [http://en.wikipedia.org/wiki/Knight's_tour Knight's Tour] 

}}</text>
    </revision>
    <revision>
      <id>14703</id>
      <timestamp>2008-09-23T13:44:41Z</timestamp>
      <contributor>
        <username>Gam3</username>
        <id>530</id>
      </contributor>
      <text xml:space="preserve">{{Shared text box |
The Knight's Tour on [http://en.wikipedia.org/wiki/Knight's_tour Wikipedia] and on 
[http://mathworld.wolfram.com/KnightsTour.html Wolfram]

}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Tic Tac Toe</title>
    <id>3231</id>
    <revision>
      <id>11048</id>
      <timestamp>2007-10-05T01:22:32Z</timestamp>
      <contributor>
        <ip>201.58.16.158</ip>
      </contributor>
      <text xml:space="preserve">Simple implementations of the &quot;tic tac toe&quot; game using a brute-force minimax algorithm.</text>
    </revision>
    <revision>
      <id>11053</id>
      <timestamp>2007-10-05T13:28:59Z</timestamp>
      <contributor>
        <username>Ffao</username>
        <id>1259</id>
      </contributor>
      <comment>add cat</comment>
      <text xml:space="preserve">Simple implementations of the &quot;tic tac toe&quot; game using a brute-force minimax algorithm.

[[Category:Games and entertainment]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Top-level subject areas</title>
    <id>1350</id>
    <revision>
      <id>1521</id>
      <timestamp>2006-03-02T23:33:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category directly contains the top-level subject areas that are not a subcategory of any other subject area, and indirectly contains all subject areas. All subcategories listed here should also be listed in [[Template:List of subject areas]].</text>
    </revision>
  </page>
  <page>
    <title>Category:Topological sort</title>
    <id>3470</id>
    <revision>
      <id>13630</id>
      <timestamp>2008-06-05T22:17:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>empty</comment>
      <text xml:space="preserve">&lt;!-- empty --&gt;</text>
    </revision>
    <revision>
      <id>16208</id>
      <timestamp>2009-03-08T10:57:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Trial division</title>
    <id>2670</id>
    <revision>
      <id>7519</id>
      <timestamp>2006-08-29T22:02:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Integer factorization]], [[Category:Primality testing]]</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Trial_division Trial division], perhaps the simplest algorithm for factoring and primality testing, simply attempts to divide a number by all possible factors. Divisions that have no remainder (go in evenly) reveal factors. We only have to test up to the square root of ''n'', since if ''x'' is a factor, so is ''n''/''x''. If no factors between 2 and &lt;math&gt;\sqrt{n}&lt;/math&gt; (inclusive) are found, the number is prime.

&lt;nowiki&gt;
[[Category:Integer factorization]]
[[Category:Primality testing]]
&lt;/nowiki&gt;</text>
    </revision>
    <revision>
      <id>7520</id>
      <timestamp>2006-08-29T22:02:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Wrong tag</comment>
      <text xml:space="preserve">[http://en.wikipedia.org/wiki/Trial_division Trial division], perhaps the simplest algorithm for factoring and primality testing, simply attempts to divide a number by all possible factors. Divisions that have no remainder (go in evenly) reveal factors. We only have to test up to the square root of ''n'', since if ''x'' is a factor, so is ''n''/''x''. If no factors between 2 and &lt;math&gt;\sqrt{n}&lt;/math&gt; (inclusive) are found, the number is prime.

&lt;noinclude&gt;
[[Category:Integer factorization]]
[[Category:Primality testing]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Trie</title>
    <id>2158</id>
    <revision>
      <id>5092</id>
      <timestamp>2006-05-20T20:43:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, link Wikipedia, [[Category:Data structures]]</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Trie trie] is an efficient map data structure for maps with string keys. No strings are stored in the tree, and lookup is less expensive than in a binary search tree because only comparisons of single characters are performed. Tries can also implement maps with integer keys, which can be seen as strings of bits.

[[Category:Data structures]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Trigonometric functions</title>
    <id>2715</id>
    <revision>
      <id>7698</id>
      <timestamp>2006-10-02T03:14:29Z</timestamp>
      <contributor>
        <ip>202.168.50.40</ip>
      </contributor>
      <comment>Add CORDIC algorithm</comment>
      <text xml:space="preserve">* [[Trigonometric functions using CORDIC algorithm (Python)]]</text>
    </revision>
    <revision>
      <id>7714</id>
      <timestamp>2006-10-02T10:35:01Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>[[Category:Numerical special functions]], wikipedia link</comment>
      <text xml:space="preserve">See also [http://en.wikipedia.org trigonometric functions] on Wikipedia.

[[Category:Numerical special functions]]</text>
    </revision>
    <revision>
      <id>7715</id>
      <timestamp>2006-10-02T10:35:15Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">See also [http://en.wikipedia.org/wiki/Trigonometric_function trigonometric functions] on Wikipedia.

[[Category:Numerical special functions]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Turing machine simulators</title>
    <id>1324</id>
    <revision>
      <id>1400</id>
      <timestamp>2006-02-28T23:05:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, [[Category:Abstract machine simulators]]</comment>
      <text xml:space="preserve">This category contains article describing simulators for a basic single-tape [http://en.wikipedia.org/wiki/Turing_machine Turing machine]. The ability to write such a simulator in a language constitutes a proof that that language is [http://en.wikipedia.org/wiki/Turing_completeness Turing-complete].

[[Category:Abstract machine simulators]]</text>
    </revision>
    <revision>
      <id>5924</id>
      <timestamp>2006-06-05T10:50:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Update cat</comment>
      <text xml:space="preserve">This category contains article describing simulators for a basic single-tape [http://en.wikipedia.org/wiki/Turing_machine Turing machine]. The ability to write such a simulator in a language constitutes a proof that that language is [http://en.wikipedia.org/wiki/Turing_completeness Turing-complete].

[[Category:Abstract machine generators and simulators]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Typesetting</title>
    <id>1965</id>
    <revision>
      <id>4474</id>
      <timestamp>2006-05-07T15:00:26Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains articles relating to typesetting.

[[Category:Top-level subject areas]]</text>
    </revision>
  </page>
  <page>
    <title>Category:UUencode</title>
    <id>3176</id>
    <revision>
      <id>10653</id>
      <timestamp>2007-07-07T01:53:21Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">Implementations of the [http://en.wikipedia.org/wiki/Uuencode UUencode] encoding algorithm used for moving binary files through text-only channels, such as email or netnews.</text>
    </revision>
  </page>
  <page>
    <title>Category:Unrolled linked list</title>
    <id>1811</id>
    <revision>
      <id>3502</id>
      <timestamp>2006-03-22T12:16:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Create, [[Category:Linked list]]</comment>
      <text xml:space="preserve">An [http://en.wikipedia.org/wiki/Unrolled_linked_list unrolled linked list] is a linked list that stores several data elements, up to some small fixed limit, in each node. It has benefits in cache performance and space usage over standard linked lists, especially for small elements such as bits, characters, words, and pointers.

[[Category:Linked list]]</text>
    </revision>
    <revision>
      <id>3503</id>
      <timestamp>2006-03-22T12:19:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>noinclude</comment>
      <text xml:space="preserve">An [http://en.wikipedia.org/wiki/Unrolled_linked_list unrolled linked list] is a linked list that stores several data elements, up to some small fixed limit, in each node. It has benefits in cache performance and space usage over standard linked lists, especially for small elements such as bits, characters, words, and pointers.

&lt;noinclude&gt;
[[Category:Linked list]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:User interface design</title>
    <id>2637</id>
    <revision>
      <id>7298</id>
      <timestamp>2006-08-14T20:27:03Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">Programs which improve the available user interface facilities</text>
    </revision>
  </page>
  <page>
    <title>Category:Userboxes:Programming languages</title>
    <id>1408</id>
    <revision>
      <id>1702</id>
      <timestamp>2006-03-03T11:26:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest.</text>
    </revision>
    <revision>
      <id>1703</id>
      <timestamp>2006-03-03T11:26:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Userboxes]]</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest.

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>1726</id>
      <timestamp>2006-03-03T12:04:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Instructions on use</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}
|}
&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C|C|C}}
|-
|{{Userbox PL2|Lisp|Lisp|Lisp}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;pre&gt;

[[Category:Userboxes]]&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>1727</id>
      <timestamp>2006-03-03T12:05:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}
|}
&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C|C|C}}
|-
|{{Userbox PL2|Lisp|Lisp|Lisp}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>1728</id>
      <timestamp>2006-03-03T12:05:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Remove tag</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}
|}
&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C|C|C}}
|-
|{{Userbox PL2|Lisp|Lisp|Lisp}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>1943</id>
      <timestamp>2006-03-04T00:28:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix example</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}
|}&lt;/div&gt;
&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB|Visual Basic}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>1944</id>
      <timestamp>2006-03-04T00:29:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix divs</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB|Visual Basic}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>1955</id>
      <timestamp>2006-03-04T01:29:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Extraneous &lt;/div&gt;</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Minimal|has minimal experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB|Visual Basic}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>2037</id>
      <timestamp>2006-03-04T03:50:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Minimal-&gt;Some</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB|Visual Basic}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>2730</id>
      <timestamp>2006-03-06T23:52:37Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link :Category:Users by programming language</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each takes three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accomodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB|Visual Basic}}
|-
|{{Userbox PL2|PHP|PHP|PHP}}
|-
|{{Userbox PL1|Haskell|Haskell|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>9104</id>
      <timestamp>2007-02-16T03:06:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rework instructions to match recent changes to userboxes</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>11723</id>
      <timestamp>2007-11-25T13:17:37Z</timestamp>
      <contributor>
        <ip>194.69.1.23</ip>
      </contributor>
      <text xml:space="preserve">alzelbas
These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>11729</id>
      <timestamp>2007-11-25T14:01:11Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/194.69.1.23|194.69.1.23]] ([[User_talk:194.69.1.23|194.69.1.23]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>12804</id>
      <timestamp>2008-03-13T12:56:02Z</timestamp>
      <contributor>
        <ip>222.127.228.22</ip>
      </contributor>
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These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>12806</id>
      <timestamp>2008-03-13T14:47:46Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/222.127.228.22|222.127.228.22]] ([[User_talk:222.127.228.22|222.127.228.22]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>15993</id>
      <timestamp>2009-01-18T12:52:47Z</timestamp>
      <contributor>
        <ip>221.120.250.107</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_cadron.com/</text>
    </revision>
    <revision>
      <id>15998</id>
      <timestamp>2009-01-18T19:57:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.120.250.107|221.120.250.107]] ([[User_talk:221.120.250.107|221.120.250.107]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
    <revision>
      <id>16128</id>
      <timestamp>2009-02-06T09:47:47Z</timestamp>
      <contributor>
        <ip>62.99.163.242</ip>
      </contributor>
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    </revision>
    <revision>
      <id>16135</id>
      <timestamp>2009-02-06T10:58:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/62.99.163.242|62.99.163.242]] ([[User_talk:62.99.163.242|62.99.163.242]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">These are userboxes intended for specifying your level of proficiency with various languages, with PL1 being the lowest and PL3 the highest. Each box will automatically add you to a category listed under [[:Category:Users by programming language]]. People looking for help in certain languages can then find people who know the language. To stack the userboxes on the right-hand side of your user page, just use a table like this (generally we list the most proficient languages first):

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:C Plus Plus|C++]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:C Plus Plus:Experts|expert programmer in C++]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Visual Basic|VB]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Visual Basic:Knows|knows Visual Basic]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #EFEFEF;&quot;
| style=&quot;width: 45px; height: 45px; background: #E1E1E1; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:PHP|PHP]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:PHP:Knows|knows PHP]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #BC9779;&quot;
| style=&quot;width: 45px; height: 45px; background: #AF8D71; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Haskell|Haskell]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user [[:Category:Users:Haskell:Some|has some experience with Haskell]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;
&lt;pre&gt;
&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|{{Userbox PL3|C++|C++|C Plus Plus}}
|-
|{{Userbox PL2|Visual Basic|VB}}
|-
|{{Userbox PL2|PHP}}
|-
|{{Userbox PL1|Haskell}}
|}
&lt;/div&gt;
&lt;/pre&gt;


== Arguments ==
Each userbox takes up to three arguments:

# The name to be displayed in the right half of the box. Usually the full language name.
# The name to be displayed in large letters in the left half of the box. The full name if short, otherwise possibly an abbreviation. If it doesn't fit, the left half will expand to accommodate it.
# The category name in [[:Category:Programming languages]] corresponding to the language.

The second and third arguments only need to be included if they are different than the language name. For example, you might want to abbreviate the name &quot;Javascript&quot; in the template

&lt;div class=&quot;tright&quot;&gt;
{|cellspacing=&quot;0&quot; cellpadding=&quot;0&quot;
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|Javascript]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|-
|&lt;div style=&quot;float: left; border: solid #000000 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: #FFF242;&quot;
| style=&quot;width: 45px; height: 45px; background: #E7DB3B; text-align: center; font-size: 14pt;&quot;| '''[[:Category:Programming language:Javascript|JS]]'''
| style=&quot;font-size: 8pt; padding: 4pt; line-height: 1.25em;&quot; | &lt;div class=&quot;brightlinks&quot;&gt;This user is an [[:Category:Users:Javascript:Experts|expert programmer in Javascript]].&lt;/div&gt;
|}&lt;/div&gt;
|}&lt;/div&gt;

:&lt;nowiki&gt;{{Userbox PL3|Javascript}}&lt;/nowiki&gt; 

to &quot;JS&quot;, so that the left half of the box doesn't grow too large. To do that, you would supply the abbreviation as the second argument to the userbox template:

:&lt;nowiki&gt;{{Userbox PL3|Javascript|JS}}&lt;/nowiki&gt;
 

[[Category:Userboxes]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Users by programming language</title>
    <id>1488</id>
    <revision>
      <id>1965</id>
      <timestamp>2006-03-04T01:37:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">This category categorizes users by the programming languages they know and how well they know them.</text>
    </revision>
    <revision>
      <id>2975</id>
      <timestamp>2006-03-08T20:30:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Link [[:Category:Userboxes:Programming languages]]</comment>
      <text xml:space="preserve">This category categorizes users by the programming languages they know and how well they know them. For instructions on adding yourself, see [[:Category:Userboxes:Programming languages]].</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:ALGOL 68:Experts</title>
    <id>3604</id>
    <revision>
      <id>14926</id>
      <timestamp>2008-10-10T13:32:11Z</timestamp>
      <contributor>
        <username>NevilleDNZ</username>
        <id>1731</id>
      </contributor>
      <comment>first try</comment>
      <text xml:space="preserve">{{User PL3 category description|ALGOL 68|ALGOL 68}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:ALGOL:Experts</title>
    <id>3449</id>
    <revision>
      <id>13570</id>
      <timestamp>2008-05-29T03:16:10Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|ALGOL|ALGOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:ALGOL:Knows</title>
    <id>3450</id>
    <revision>
      <id>13571</id>
      <timestamp>2008-05-29T03:16:20Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|ALGOL|ALGOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:ALGOL:Some</title>
    <id>3448</id>
    <revision>
      <id>13569</id>
      <timestamp>2008-05-29T03:15:55Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|ALGOL|ALGOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:APL:Experts</title>
    <id>3437</id>
    <revision>
      <id>13557</id>
      <timestamp>2008-05-29T03:11:34Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|APL|APL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:APL:Knows</title>
    <id>3438</id>
    <revision>
      <id>13558</id>
      <timestamp>2008-05-29T03:11:43Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|APL|APL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:APL:Some</title>
    <id>3436</id>
    <revision>
      <id>13556</id>
      <timestamp>2008-05-29T03:11:24Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|APL|APL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:AWK:Experts</title>
    <id>2306</id>
    <revision>
      <id>6153</id>
      <timestamp>2006-06-11T18:00:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL3 category description|AWK|AWK}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:AWK:Knows</title>
    <id>2307</id>
    <revision>
      <id>6154</id>
      <timestamp>2006-06-11T18:00:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|AWK|AWK}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:AWK:Some</title>
    <id>2308</id>
    <revision>
      <id>6155</id>
      <timestamp>2006-06-11T18:01:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|AWK|AWK}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Ada:Experts</title>
    <id>1401</id>
    <revision>
      <id>1680</id>
      <timestamp>2006-03-03T10:52:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Users by programming language]]</comment>
      <text xml:space="preserve">[[Category:Users by programming language]]</text>
    </revision>
    <revision>
      <id>1963</id>
      <timestamp>2006-03-04T01:36:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move category to template, add description</comment>
      <text xml:space="preserve">{{User PL3 category description|Ada|Ada}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Ada:Knows</title>
    <id>1508</id>
    <revision>
      <id>1998</id>
      <timestamp>2006-03-04T02:17:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|Ada|Ada}}</comment>
      <text xml:space="preserve">{{User PL2 category description|Ada|Ada}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Ada:Some</title>
    <id>1528</id>
    <revision>
      <id>2044</id>
      <timestamp>2006-03-04T03:53:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|Ada|Ada}}</comment>
      <text xml:space="preserve">{{User PL1 category description|Ada|Ada}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Alice ML:Experts</title>
    <id>1860</id>
    <revision>
      <id>3848</id>
      <timestamp>2006-04-05T21:02:19Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{User PL3 category description|Alice ML|Alice ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Alice ML:Knows</title>
    <id>1861</id>
    <revision>
      <id>3849</id>
      <timestamp>2006-04-05T21:02:30Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{User PL2 category description|Alice ML|Alice ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Alice ML:Some</title>
    <id>1862</id>
    <revision>
      <id>3850</id>
      <timestamp>2006-04-05T21:02:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{User PL1 category description|Alice ML|Alice ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Amiga E:Experts</title>
    <id>3782</id>
    <revision>
      <id>15850</id>
      <timestamp>2009-01-08T17:46:29Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>antispam measure</comment>
      <text xml:space="preserve">-</text>
    </revision>
    <revision>
      <id>16218</id>
      <timestamp>2009-03-08T11:05:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Blank</comment>
      <text xml:space="preserve" />
    </revision>
  </page>
  <page>
    <title>Category:Users:AppleScript:Some</title>
    <id>2871</id>
    <revision>
      <id>8374</id>
      <timestamp>2007-01-01T14:32:07Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">This category contains users who have identified themselves as having some limited experience with the AppleScript programming language. Also see [[:Category:Users:AppleScript:Experts]] and [[:Category:Users:AppleScript:Knows]]. 

[[Category:Users by programming language]]</text>
    </revision>
    <revision>
      <id>8375</id>
      <timestamp>2007-01-01T14:32:33Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>updated category</comment>
      <text xml:space="preserve">This category contains users who have identified themselves as having some limited experience with the AppleScript programming language. Also see [[:Category:Users:AppleScript:Experts]] and [[:Category:Users:AppleScript:Knows]]. 

[[Category:Users by programming language|AppleScript]]</text>
    </revision>
    <revision>
      <id>8382</id>
      <timestamp>2007-01-01T14:43:11Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>using template</comment>
      <text xml:space="preserve">{{User PL1 category description|AppleScript|AppleScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Assembly Intel x86:Knows</title>
    <id>3260</id>
    <revision>
      <id>11801</id>
      <timestamp>2007-12-08T16:30:17Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|Assembly Intel x86|Intel x86 Assembly}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Assembly:Experts</title>
    <id>2774</id>
    <revision>
      <id>8047</id>
      <timestamp>2006-11-16T04:36:01Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+category</comment>
      <text xml:space="preserve">{{User PL3 category description|Assembly|Assembly}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Assembly:Knows</title>
    <id>2775</id>
    <revision>
      <id>8048</id>
      <timestamp>2006-11-16T04:36:20Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+category</comment>
      <text xml:space="preserve">{{User PL2 category description|Assembly|Assembly}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Assembly:Some</title>
    <id>2776</id>
    <revision>
      <id>8049</id>
      <timestamp>2006-11-16T04:36:34Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+category</comment>
      <text xml:space="preserve">{{User PL1 category description|Assembly|Assembly}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Awk:Experts</title>
    <id>3422</id>
    <revision>
      <id>13536</id>
      <timestamp>2008-05-29T03:00:22Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|Awk|Awk}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Awk:Knows</title>
    <id>3421</id>
    <revision>
      <id>13535</id>
      <timestamp>2008-05-29T03:00:05Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|Awk|Awk}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Awk:Some</title>
    <id>3423</id>
    <revision>
      <id>13537</id>
      <timestamp>2008-05-29T03:00:32Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|Awk|Awk}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:BASIC:Experts</title>
    <id>2608</id>
    <revision>
      <id>7134</id>
      <timestamp>2006-08-07T16:21:56Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>init</comment>
      <text xml:space="preserve">{{User PL3 category description|BASIC|BASIC}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:BASIC:Knows</title>
    <id>2607</id>
    <revision>
      <id>7133</id>
      <timestamp>2006-08-07T16:21:31Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>init</comment>
      <text xml:space="preserve">{{User PL2 category description|BASIC|BASIC}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:BASIC:Some</title>
    <id>2609</id>
    <revision>
      <id>7135</id>
      <timestamp>2006-08-07T16:22:08Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>init</comment>
      <text xml:space="preserve">{{User PL1 category description|BASIC|BASIC}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Batch files:Experts</title>
    <id>2899</id>
    <revision>
      <id>8518</id>
      <timestamp>2007-01-09T00:40:46Z</timestamp>
      <contributor>
        <username>Purodha</username>
        <id>129</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Batch files|Batch files}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Batch files:Knows</title>
    <id>2900</id>
    <revision>
      <id>8519</id>
      <timestamp>2007-01-09T00:41:02Z</timestamp>
      <contributor>
        <username>Purodha</username>
        <id>129</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Batch files|Batch files}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Batch files:Some</title>
    <id>2901</id>
    <revision>
      <id>8520</id>
      <timestamp>2007-01-09T00:41:20Z</timestamp>
      <contributor>
        <username>Purodha</username>
        <id>129</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Batch files|Batch files}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Plus Plus:Experts</title>
    <id>1487</id>
    <revision>
      <id>1962</id>
      <timestamp>2006-03-04T01:35:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description</comment>
      <text xml:space="preserve">{{User PL3 category description|C Plus Plus|C++}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Plus Plus:Knows</title>
    <id>1510</id>
    <revision>
      <id>2000</id>
      <timestamp>2006-03-04T02:18:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|C Plus Plus|C++}}</comment>
      <text xml:space="preserve">{{User PL2 category description|C Plus Plus|C++}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Plus Plus:Some</title>
    <id>1529</id>
    <revision>
      <id>2045</id>
      <timestamp>2006-03-04T03:53:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|C Plus Plus|C++}}</comment>
      <text xml:space="preserve">{{User PL1 category description|C Plus Plus|C++}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Sharp:Experts</title>
    <id>1489</id>
    <revision>
      <id>1966</id>
      <timestamp>2006-03-04T01:39:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description template</comment>
      <text xml:space="preserve">{{User PL3 category description|C Sharp|C#}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Sharp:Knows</title>
    <id>1512</id>
    <revision>
      <id>2002</id>
      <timestamp>2006-03-04T02:18:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|C Sharp|C#}}</comment>
      <text xml:space="preserve">{{User PL2 category description|C Sharp|C#}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C Sharp:Some</title>
    <id>1530</id>
    <revision>
      <id>2046</id>
      <timestamp>2006-03-04T03:53:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|C Sharp|C#}}</comment>
      <text xml:space="preserve">{{User PL1 category description|C Sharp|C#}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C:Experts</title>
    <id>1484</id>
    <revision>
      <id>1956</id>
      <timestamp>2006-03-04T01:31:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description with template</comment>
      <text xml:space="preserve">{{User PL3 category description|C|C}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C:Knows</title>
    <id>3804</id>
    <revision>
      <id>1996</id>
      <timestamp>2006-03-04T02:16:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|C|C}}</comment>
      <text xml:space="preserve">{{User PL2 category description|C|C}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:C:Some</title>
    <id>1527</id>
    <revision>
      <id>2043</id>
      <timestamp>2006-03-04T03:53:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|C|C}}</comment>
      <text xml:space="preserve">{{User PL1 category description|C|C}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:COBOL:Experts</title>
    <id>3428</id>
    <revision>
      <id>13544</id>
      <timestamp>2008-05-29T03:05:08Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|COBOL|COBOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:COBOL:Knows</title>
    <id>3429</id>
    <revision>
      <id>13545</id>
      <timestamp>2008-05-29T03:05:17Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|COBOL|COBOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:COBOL:Some</title>
    <id>3427</id>
    <revision>
      <id>13543</id>
      <timestamp>2008-05-29T03:04:53Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|COBOL|COBOL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSP:Experts</title>
    <id>2705</id>
    <revision>
      <id>7652</id>
      <timestamp>2006-09-16T06:27:05Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>template</comment>
      <text xml:space="preserve">{{User PL3 category description|CSP|CSP}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSP:Knows</title>
    <id>2706</id>
    <revision>
      <id>7653</id>
      <timestamp>2006-09-16T06:27:27Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{User PL2 category description|CSP|CSP}}</comment>
      <text xml:space="preserve">{{User PL2 category description|CSP|CSP}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSP:Some</title>
    <id>2707</id>
    <revision>
      <id>7654</id>
      <timestamp>2006-09-16T06:27:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{User PL1 category description|CSP|CSP}}</comment>
      <text xml:space="preserve">{{User PL1 category description|CSP|CSP}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSS:Experts</title>
    <id>3453</id>
    <revision>
      <id>13577</id>
      <timestamp>2008-05-29T03:28:25Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|CSS|CSS}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSS:Knows</title>
    <id>3263</id>
    <revision>
      <id>11804</id>
      <timestamp>2007-12-08T16:32:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|CSS|CSS}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:CSS:Some</title>
    <id>3454</id>
    <revision>
      <id>13578</id>
      <timestamp>2008-05-29T03:28:44Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|CSS|CSS}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Delphi:Experts</title>
    <id>3432</id>
    <revision>
      <id>13551</id>
      <timestamp>2008-05-29T03:09:06Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|Delphi|Delphi}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Delphi:Knows</title>
    <id>3431</id>
    <revision>
      <id>13550</id>
      <timestamp>2008-05-29T03:08:56Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|Delphi|Delphi}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Delphi:Some</title>
    <id>3262</id>
    <revision>
      <id>11803</id>
      <timestamp>2007-12-08T16:31:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|Delphi|Delphi}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:E:Some</title>
    <id>3264</id>
    <revision>
      <id>11805</id>
      <timestamp>2007-12-08T16:33:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|E|E}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Eiffel:Experts</title>
    <id>1547</id>
    <revision>
      <id>2098</id>
      <timestamp>2006-03-04T09:48:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL3 category description|Eiffel|Eiffel}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Eiffel:Knows</title>
    <id>1548</id>
    <revision>
      <id>2099</id>
      <timestamp>2006-03-04T09:49:10Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL2 category description|Eiffel|Eiffel}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Eiffel:Some</title>
    <id>1546</id>
    <revision>
      <id>2097</id>
      <timestamp>2006-03-04T09:46:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL1 category description|Eiffel|Eiffel}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Erlang:Experts</title>
    <id>1540</id>
    <revision>
      <id>2081</id>
      <timestamp>2006-03-04T07:49:45Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL3 category description|Erlang|Erlang}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Erlang:Knows</title>
    <id>1539</id>
    <revision>
      <id>2079</id>
      <timestamp>2006-03-04T07:49:02Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL1 category description|Erlang|Erlang}}</text>
    </revision>
    <revision>
      <id>2080</id>
      <timestamp>2006-03-04T07:49:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix cat template number</comment>
      <text xml:space="preserve">{{User PL2 category description|Erlang|Erlang}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Erlang:Some</title>
    <id>1538</id>
    <revision>
      <id>2078</id>
      <timestamp>2006-03-04T07:48:43Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL1 category description|Erlang|Erlang}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Forth:Experts</title>
    <id>3226</id>
    <revision>
      <id>10967</id>
      <timestamp>2007-09-20T02:29:24Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Forth|Forth}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Forth:Knows</title>
    <id>3451</id>
    <revision>
      <id>13574</id>
      <timestamp>2008-05-29T03:20:04Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|Forth|Forth}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Forth:Some</title>
    <id>3227</id>
    <revision>
      <id>10968</id>
      <timestamp>2007-09-20T02:30:01Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Forth|Forth}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Fortran:Experts</title>
    <id>2194</id>
    <revision>
      <id>5279</id>
      <timestamp>2006-05-28T14:31:25Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Fortran|Fortran}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Fortran:Knows</title>
    <id>2195</id>
    <revision>
      <id>5280</id>
      <timestamp>2006-05-28T14:31:37Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Fortran|Fortran}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Fortran:Some</title>
    <id>2184</id>
    <revision>
      <id>5259</id>
      <timestamp>2006-05-28T13:09:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Fortran|Fortran}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Groovy:Experts</title>
    <id>2190</id>
    <revision>
      <id>5274</id>
      <timestamp>2006-05-28T14:27:35Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Groovy|Groovy}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Groovy:Knows</title>
    <id>2191</id>
    <revision>
      <id>5275</id>
      <timestamp>2006-05-28T14:28:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Groovy|Groovy}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Groovy:Some</title>
    <id>2192</id>
    <revision>
      <id>5276</id>
      <timestamp>2006-05-28T14:29:23Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Groovy|Groovy}}</text>
    </revision>
    <revision>
      <id>5277</id>
      <timestamp>2006-05-28T14:29:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Groovy|Groovy}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:HTML:Experts</title>
    <id>3404</id>
    <revision>
      <id>13516</id>
      <timestamp>2008-05-29T02:50:49Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|HTML|HTML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:HTML:Knows</title>
    <id>3403</id>
    <revision>
      <id>13515</id>
      <timestamp>2008-05-29T02:50:04Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|HTML|HTML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:HTML:Some</title>
    <id>3405</id>
    <revision>
      <id>13517</id>
      <timestamp>2008-05-29T02:51:14Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|HTML|HTML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Haskell:Experts</title>
    <id>2317</id>
    <revision>
      <id>6165</id>
      <timestamp>2006-06-11T19:24:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Haskell|Haskell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Haskell:Knows</title>
    <id>2316</id>
    <revision>
      <id>6164</id>
      <timestamp>2006-06-11T19:24:15Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Haskell|Haskell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Haskell:Some</title>
    <id>2318</id>
    <revision>
      <id>6166</id>
      <timestamp>2006-06-11T19:24:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Haskell|Haskell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Io:Experts</title>
    <id>3410</id>
    <revision>
      <id>13522</id>
      <timestamp>2008-05-29T02:55:00Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|XML|XML}}</text>
    </revision>
    <revision>
      <id>13523</id>
      <timestamp>2008-05-29T02:55:26Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>Oops</comment>
      <text xml:space="preserve">{{User PL3 category description|Io|Io}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Io:Knows</title>
    <id>3411</id>
    <revision>
      <id>13524</id>
      <timestamp>2008-05-29T02:55:43Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|Io|Io}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Io:Some</title>
    <id>3409</id>
    <revision>
      <id>13521</id>
      <timestamp>2008-05-29T02:54:38Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|Io|Io}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Java:Experts</title>
    <id>1490</id>
    <revision>
      <id>1968</id>
      <timestamp>2006-03-04T01:44:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description template</comment>
      <text xml:space="preserve">{{User PL3 category description|Java|Java}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Java:Knows</title>
    <id>1501</id>
    <revision>
      <id>1990</id>
      <timestamp>2006-03-04T02:13:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+{{User PL2 category description|Java|Java}}</comment>
      <text xml:space="preserve">{{User PL2 category description|Java|Java}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Java:Some</title>
    <id>1525</id>
    <revision>
      <id>2041</id>
      <timestamp>2006-03-04T03:52:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|Java|Java}}</comment>
      <text xml:space="preserve">{{User PL1 category description|Java|Java}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:JavaScript:Experts</title>
    <id>1600</id>
    <revision>
      <id>2304</id>
      <timestamp>2006-03-05T02:25:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL3 category description|JavaScript|JavaScript}}</comment>
      <text xml:space="preserve">{{User PL3 category description|JavaScript|JavaScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:JavaScript:Knows</title>
    <id>1601</id>
    <revision>
      <id>2305</id>
      <timestamp>2006-03-05T02:25:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|JavaScript|JavaScript}}</comment>
      <text xml:space="preserve">{{User PL2 category description|JavaScript|JavaScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:JavaScript:Some</title>
    <id>1599</id>
    <revision>
      <id>2303</id>
      <timestamp>2006-03-05T02:25:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|JavaScript|JavaScript}}</comment>
      <text xml:space="preserve">{{User PL1 category description|JavaScript|JavaScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Javascript:Expert</title>
    <id>1851</id>
    <revision>
      <id>3804</id>
      <timestamp>2006-04-05T10:01:16Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <text xml:space="preserve">Maybe some people with good knowledge of Javascript</text>
    </revision>
    <revision>
      <id>5553</id>
      <timestamp>2006-06-01T13:14:19Z</timestamp>
      <contributor>
        <ip>62.97.249.114</ip>
      </contributor>
      <comment>+ cat Users by programming labguage</comment>
      <text xml:space="preserve">Maybe some people with good knowledge of Javascript

[[Category:Users by programming language]]</text>
    </revision>
    <revision>
      <id>5556</id>
      <timestamp>2006-06-01T16:55:38Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat template</comment>
      <text xml:space="preserve">{{User PL3 category description|JavaScript|JavaScript}}

[[Category:Users by programming language]]</text>
    </revision>
    <revision>
      <id>5557</id>
      <timestamp>2006-06-01T17:11:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>redirect</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Users:JavaScript:Experts]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Javascript:Experts</title>
    <id>1868</id>
    <revision>
      <id>3873</id>
      <timestamp>2006-04-06T01:53:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{User PL3 category description|Javascript|Javascript}}</comment>
      <text xml:space="preserve">{{User PL3 category description|Javascript|Javascript}}</text>
    </revision>
    <revision>
      <id>5561</id>
      <timestamp>2006-06-01T17:14:13Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>redirect</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Users:Javascript:Experts]]</text>
    </revision>
    <revision>
      <id>5580</id>
      <timestamp>2006-06-01T20:38:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Pretty sure you didn't mean to redirect to self</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Users:JavaScript:Experts]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Javascript:Knows</title>
    <id>1867</id>
    <revision>
      <id>3872</id>
      <timestamp>2006-04-06T01:53:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{User PL2 category description|Javascript|Javascript}}</comment>
      <text xml:space="preserve">{{User PL2 category description|Javascript|Javascript}}</text>
    </revision>
    <revision>
      <id>5559</id>
      <timestamp>2006-06-01T17:12:50Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>redirect</comment>
      <text xml:space="preserve">#REDIRECT [[Category:Users:JavaScript:Knows]]</text>
    </revision>
    <revision>
      <id>5560</id>
      <timestamp>2006-06-01T17:13:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>fix link</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Users:JavaScript:Knows]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Javascript:Some</title>
    <id>1866</id>
    <revision>
      <id>3871</id>
      <timestamp>2006-04-06T01:53:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{User PL1 category description|Javascript|Javascript}}</comment>
      <text xml:space="preserve">{{User PL1 category description|Javascript|Javascript}}</text>
    </revision>
    <revision>
      <id>5558</id>
      <timestamp>2006-06-01T17:12:17Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>redirect</comment>
      <text xml:space="preserve">#REDIRECT [[:Category:Users:JavaScript:Some]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:LaTeX:Some</title>
    <id>3261</id>
    <revision>
      <id>11802</id>
      <timestamp>2007-12-08T16:31:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|LaTeX|LaTeX}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Lisp:Experts</title>
    <id>1752</id>
    <revision>
      <id>3103</id>
      <timestamp>2006-03-10T00:08:19Z</timestamp>
      <contributor>
        <username>Gratefulfrog</username>
        <id>40</id>
      </contributor>
      <text xml:space="preserve">User:Gratefulfrog</text>
    </revision>
    <revision>
      <id>3112</id>
      <timestamp>2006-03-10T01:06:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add description</comment>
      <text xml:space="preserve">{{User PL3 category description|Lisp|Lisp}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Lisp:Knows</title>
    <id>1751</id>
    <revision>
      <id>3101</id>
      <timestamp>2006-03-09T23:58:36Z</timestamp>
      <contributor>
        <username>Gratefulfrog</username>
        <id>40</id>
      </contributor>
      <text xml:space="preserve">User:Gratefulfrog</text>
    </revision>
    <revision>
      <id>3113</id>
      <timestamp>2006-03-10T01:06:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|Lisp|Lisp}}</comment>
      <text xml:space="preserve">{{User PL2 category description|Lisp|Lisp}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Lisp:Some</title>
    <id>1756</id>
    <revision>
      <id>3114</id>
      <timestamp>2006-03-10T01:06:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|Lisp|Lisp}}</comment>
      <text xml:space="preserve">{{User PL1 category description|Lisp|Lisp}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Logo:Experts</title>
    <id>3446</id>
    <revision>
      <id>13567</id>
      <timestamp>2008-05-29T03:15:28Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|Logo|Logo}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Logo:Knows</title>
    <id>3447</id>
    <revision>
      <id>13568</id>
      <timestamp>2008-05-29T03:15:38Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|Logo|Logo}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Logo:Some</title>
    <id>3445</id>
    <revision>
      <id>13566</id>
      <timestamp>2008-05-29T03:15:17Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|Logo|Logo}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Lua:Experts</title>
    <id>3349</id>
    <revision>
      <id>12946</id>
      <timestamp>2008-03-31T05:07:41Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat description</comment>
      <text xml:space="preserve">{{User PL3 category description|Lua|Lua}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Lua:Knows</title>
    <id>3350</id>
    <revision>
      <id>12947</id>
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    <title>Category:Users:Maple:Experts</title>
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      <comment>created</comment>
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    <id>1632</id>
    <revision>
      <id>2466</id>
      <timestamp>2006-03-06T03:48:21Z</timestamp>
      <contributor>
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      <text xml:space="preserve">{{User PL3 category description|Mathematica|Mathematica}}</text>
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      <contributor>
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    <id>1559</id>
    <revision>
      <id>2164</id>
      <timestamp>2006-03-04T13:39:06Z</timestamp>
      <contributor>
        <username>Deco</username>
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      <text xml:space="preserve">{{User PL3 category description|Matlab|Matlab}}</text>
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    <title>Category:Users:Matlab:Knows</title>
    <id>1560</id>
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      <id>2165</id>
      <timestamp>2006-03-04T13:39:17Z</timestamp>
      <contributor>
        <username>Deco</username>
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      <timestamp>2006-03-04T13:39:24Z</timestamp>
      <contributor>
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      <id>13532</id>
      <timestamp>2008-05-29T02:58:32Z</timestamp>
      <contributor>
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      <contributor>
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      <contributor>
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      <text xml:space="preserve">{{User PL3 category description|Objective-C|Objective-C}}</text>
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      <contributor>
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      <text xml:space="preserve">{{User PL2 category description|Objective-C|Objective-C}}</text>
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      <contributor>
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      <text xml:space="preserve">{{User PL1 category description|Objective-C|Objective-C}}</text>
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    <title>Category:Users:Oz:Experts</title>
    <id>1628</id>
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      <timestamp>2006-03-06T03:01:37Z</timestamp>
      <contributor>
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{{User PL3 category description|Oz|Oz}}</text>
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      <timestamp>2007-10-25T20:02:51Z</timestamp>
      <contributor>
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    <revision>
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    <revision>
      <id>15741</id>
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      <contributor>
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      <minor/>
      <comment>Reverted edits by [[Special:Contributions/140.113.152.201|140.113.152.201]] ([[User_talk:140.113.152.201|140.113.152.201]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{User PL3 category description|Oz|Oz}}</text>
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      <timestamp>2006-03-06T03:01:17Z</timestamp>
      <contributor>
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    <revision>
      <id>11246</id>
      <timestamp>2007-10-25T08:58:03Z</timestamp>
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{{User PL2 category description|Oz|Oz}}</text>
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      <timestamp>2007-10-25T20:01:49Z</timestamp>
      <contributor>
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      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{User PL2 category description|Oz|Oz}}</text>
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    <revision>
      <id>11749</id>
      <timestamp>2007-11-29T11:01:16Z</timestamp>
      <contributor>
        <ip>217.172.56.130</ip>
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      <timestamp>2008-01-04T02:37:52Z</timestamp>
      <contributor>
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      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.51.208.38|200.51.208.38]] ([[User_talk:200.51.208.38|200.51.208.38]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
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{{User PL2 category description|Oz|Oz}}</text>
    </revision>
    <revision>
      <id>11994</id>
      <timestamp>2008-01-09T16:19:58Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/125.100.97.205|125.100.97.205]] ([[User_talk:125.100.97.205|125.100.97.205]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{User PL2 category description|Oz|Oz}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Oz:Some</title>
    <id>1626</id>
    <revision>
      <id>2447</id>
      <timestamp>2006-03-06T03:00:57Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+cat description</comment>
      <text xml:space="preserve">{{User PL1 category description|Oz|Oz}}</text>
    </revision>
    <revision>
      <id>11247</id>
      <timestamp>2007-10-25T08:59:37Z</timestamp>
      <contributor>
        <ip>66.151.128.155</ip>
      </contributor>
      <text xml:space="preserve">sitliel
{{User PL1 category description|Oz|Oz}}</text>
    </revision>
    <revision>
      <id>11261</id>
      <timestamp>2007-10-25T20:01:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{User PL1 category description|Oz|Oz}}</text>
    </revision>
    <revision>
      <id>11528</id>
      <timestamp>2007-11-10T12:12:45Z</timestamp>
      <contributor>
        <ip>210.82.89.246</ip>
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      <timestamp>2007-11-10T17:24:51Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
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      <minor/>
      <comment>Reverted edits by [[Special:Contributions/210.82.89.246|210.82.89.246]] ([[User_talk:210.82.89.246|210.82.89.246]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{User PL1 category description|Oz|Oz}}</text>
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    <revision>
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      <contributor>
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{{User PL1 category description|Oz|Oz}}</text>
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      <timestamp>2007-12-08T00:44:25Z</timestamp>
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      <text xml:space="preserve">{{User PL1 category description|Oz|Oz}}</text>
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{{User PL1 category description|Oz|Oz}}</text>
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      <text xml:space="preserve">{{User PL3 category description|PHP|PHP}}</text>
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    <id>2187</id>
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        <username>Cpjobling</username>
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      <text xml:space="preserve">{{User PL2 category description|PHP|PHP}}</text>
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    <id>2230</id>
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      <contributor>
        <username>Ahy1</username>
        <id>20</id>
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      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|PHP|PHP}}</text>
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    <id>1593</id>
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      <id>2290</id>
      <timestamp>2006-03-05T01:21:39Z</timestamp>
      <contributor>
        <username>Deco</username>
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      <timestamp>2006-03-05T01:21:49Z</timestamp>
      <contributor>
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      <id>2292</id>
      <timestamp>2006-03-05T01:21:58Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
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      <text xml:space="preserve">{{User PL1 category description|Pascal|Pascal}}</text>
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    <id>1495</id>
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      <id>1974</id>
      <timestamp>2006-03-04T01:47:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
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      <comment>Description template</comment>
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  <page>
    <title>Category:Users:Perl:Knows</title>
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    <revision>
      <id>2019</id>
      <timestamp>2006-03-04T02:28:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
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      <comment>{{User PL2 category description|Perl|Perl}}</comment>
      <text xml:space="preserve">{{User PL2 category description|Perl|Perl}}</text>
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      <comment>{{User PL1 category description|Perl|Perl}}</comment>
      <text xml:space="preserve">{{User PL1 category description|Perl|Perl}}</text>
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    <revision>
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      <contributor>
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      <text xml:space="preserve">laracdro
{{User PL1 category description|Perl|Perl}}</text>
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        <username>Ahy1</username>
        <id>20</id>
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      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{User PL1 category description|Perl|Perl}}</text>
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    <revision>
      <id>11182</id>
      <timestamp>2007-10-13T02:24:05Z</timestamp>
      <contributor>
        <ip>64.27.5.49</ip>
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    <revision>
      <id>11188</id>
      <timestamp>2007-10-13T03:32:07Z</timestamp>
      <contributor>
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      <text xml:space="preserve">{{User PL1 category description|Perl|Perl}}</text>
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      <id>11270</id>
      <timestamp>2007-10-25T20:52:36Z</timestamp>
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{{User PL1 category description|Perl|Perl}}</text>
    </revision>
    <revision>
      <id>11548</id>
      <timestamp>2007-11-12T04:56:50Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/201.134.253.21|201.134.253.21]] ([[User_talk:201.134.253.21|201.134.253.21]]); changed back to last version by [[User:85.176.247.247|85.176.247.247]]</comment>
      <text xml:space="preserve">{{User PL1 category description|Perl|Perl}}</text>
    </revision>
    <revision>
      <id>11626</id>
      <timestamp>2007-11-19T03:06:50Z</timestamp>
      <contributor>
        <ip>216.65.63.45</ip>
      </contributor>
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{{User PL1 category description|Perl|Perl}}</text>
    </revision>
    <revision>
      <id>11627</id>
      <timestamp>2007-11-19T04:38:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/216.65.63.45|216.65.63.45]] ([[User_talk:216.65.63.45|216.65.63.45]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{User PL1 category description|Perl|Perl}}</text>
    </revision>
    <revision>
      <id>13994</id>
      <timestamp>2008-07-17T18:44:41Z</timestamp>
      <contributor>
        <ip>85.185.174.5</ip>
      </contributor>
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{{User PL1 category description|Perl|Perl}}</text>
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        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Smalltalk|Smalltalk}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Smalltalk:Some</title>
    <id>2313</id>
    <revision>
      <id>6161</id>
      <timestamp>2006-06-11T19:22:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|Smalltalk|Smalltalk}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Standard ML:Experts</title>
    <id>2328</id>
    <revision>
      <id>6176</id>
      <timestamp>2006-06-11T19:32:25Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Standard ML|Standard ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Standard ML:Knows</title>
    <id>2327</id>
    <revision>
      <id>6175</id>
      <timestamp>2006-06-11T19:31:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Standard ML|Standard ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Standard ML:Some</title>
    <id>2329</id>
    <revision>
      <id>6177</id>
      <timestamp>2006-06-11T19:32:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Standard ML|Standard ML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Tcl:Experts</title>
    <id>2228</id>
    <revision>
      <id>5587</id>
      <timestamp>2006-06-01T20:47:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL3 category description|Tcl|Tcl}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Tcl:Knows</title>
    <id>2229</id>
    <revision>
      <id>5588</id>
      <timestamp>2006-06-01T20:47:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Tcl|Tcl}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Tcl:Some</title>
    <id>2227</id>
    <revision>
      <id>5586</id>
      <timestamp>2006-06-01T20:46:16Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|Tcl|Tcl}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:TeX:Experts</title>
    <id>3440</id>
    <revision>
      <id>13560</id>
      <timestamp>2008-05-29T03:13:12Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|TeX|TeX}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:TeX:Knows</title>
    <id>3439</id>
    <revision>
      <id>13559</id>
      <timestamp>2008-05-29T03:13:03Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|TeX|TeX}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:TeX:Some</title>
    <id>3441</id>
    <revision>
      <id>13561</id>
      <timestamp>2008-05-29T03:13:24Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|TeX|TeX}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Unlambda:Some</title>
    <id>3896</id>
    <revision>
      <id>16400</id>
      <timestamp>2009-04-17T16:34:31Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Unlambda|Unlambda}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:VBScript:Experts</title>
    <id>3443</id>
    <revision>
      <id>13563</id>
      <timestamp>2008-05-29T03:14:40Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|VBScript|VBScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:VBScript:Knows</title>
    <id>3444</id>
    <revision>
      <id>13564</id>
      <timestamp>2008-05-29T03:14:50Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|VBScript|VBScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:VBScript:Some</title>
    <id>3442</id>
    <revision>
      <id>13562</id>
      <timestamp>2008-05-29T03:13:52Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|VBScript|VBScript}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Visual Basic:Experts</title>
    <id>2331</id>
    <revision>
      <id>6179</id>
      <timestamp>2006-06-11T19:33:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|Visual Basic|Visual Basic}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Visual Basic:Knows</title>
    <id>2330</id>
    <revision>
      <id>6178</id>
      <timestamp>2006-06-11T19:33:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|Visual Basic|Visual Basic}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:Visual Basic:Some</title>
    <id>2332</id>
    <revision>
      <id>6180</id>
      <timestamp>2006-06-11T19:34:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|Visual Basic|Visual Basic}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XML:Experts</title>
    <id>3407</id>
    <revision>
      <id>13519</id>
      <timestamp>2008-05-29T02:53:20Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|XML|XML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XML:Knows</title>
    <id>3408</id>
    <revision>
      <id>13520</id>
      <timestamp>2008-05-29T02:53:33Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|XML|XML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XML:Some</title>
    <id>3406</id>
    <revision>
      <id>13518</id>
      <timestamp>2008-05-29T02:52:50Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|XML|XML}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSL:Experts</title>
    <id>3402</id>
    <revision>
      <id>13513</id>
      <timestamp>2008-05-29T02:48:40Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|XSL|XSL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSL:Knows</title>
    <id>2873</id>
    <revision>
      <id>8381</id>
      <timestamp>2007-01-01T14:43:04Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|XSL|XSL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSL:Some</title>
    <id>3401</id>
    <revision>
      <id>13512</id>
      <timestamp>2008-05-29T02:48:18Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|XSL|XSL}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSLT:Experts</title>
    <id>3416</id>
    <revision>
      <id>13529</id>
      <timestamp>2008-05-29T02:57:52Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL3 category description|XSLT|XSLT}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSLT:Knows</title>
    <id>3417</id>
    <revision>
      <id>13530</id>
      <timestamp>2008-05-29T02:58:03Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|XSLT|XSLT}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:XSLT:Some</title>
    <id>3415</id>
    <revision>
      <id>13528</id>
      <timestamp>2008-05-29T02:57:20Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|XSLT|XSLT}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bash script:Experts</title>
    <id>2320</id>
    <revision>
      <id>6168</id>
      <timestamp>2006-06-11T19:27:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|bash script|bash script}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bash script:Knows</title>
    <id>2321</id>
    <revision>
      <id>6169</id>
      <timestamp>2006-06-11T19:27:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|bash script|bash script}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bash script:Some</title>
    <id>2319</id>
    <revision>
      <id>6167</id>
      <timestamp>2006-06-11T19:26:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|bash script|bash script}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bc:Experts</title>
    <id>2236</id>
    <revision>
      <id>5597</id>
      <timestamp>2006-06-01T20:54:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|bc|bc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bc:Knows</title>
    <id>2237</id>
    <revision>
      <id>5598</id>
      <timestamp>2006-06-01T20:54:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|bc|bc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:bc:Some</title>
    <id>2235</id>
    <revision>
      <id>5596</id>
      <timestamp>2006-06-01T20:53:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|bc|bc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:dc:Experts</title>
    <id>2234</id>
    <revision>
      <id>5594</id>
      <timestamp>2006-06-01T20:52:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL3 category description|dc|dc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:dc:Knows</title>
    <id>2233</id>
    <revision>
      <id>5593</id>
      <timestamp>2006-06-01T20:51:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL2 category description|dc|dc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:dc:Some</title>
    <id>2232</id>
    <revision>
      <id>5592</id>
      <timestamp>2006-06-01T20:51:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{User PL1 category description|dc|dc}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:occam:Experts</title>
    <id>1504</id>
    <revision>
      <id>1994</id>
      <timestamp>2006-03-04T02:15:46Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL3 category description|occam|occam}}</comment>
      <text xml:space="preserve">{{User PL3 category description|occam|occam}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:occam:Knows</title>
    <id>1503</id>
    <revision>
      <id>1993</id>
      <timestamp>2006-03-04T02:15:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL2 category description|occam|occam}}</comment>
      <text xml:space="preserve">{{User PL2 category description|occam|occam}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:occam:Some</title>
    <id>1526</id>
    <revision>
      <id>2042</id>
      <timestamp>2006-03-04T03:53:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{User PL1 category description|occam|occam}}</comment>
      <text xml:space="preserve">{{User PL1 category description|occam|occam}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sed:Experts</title>
    <id>3434</id>
    <revision>
      <id>13553</id>
      <timestamp>2008-05-29T03:09:37Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat5</comment>
      <text xml:space="preserve">{{User PL3 category description|sed|sed}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sed:Knows</title>
    <id>3435</id>
    <revision>
      <id>13554</id>
      <timestamp>2008-05-29T03:09:54Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL2 category description|sed|sed}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sed:Some</title>
    <id>3433</id>
    <revision>
      <id>13552</id>
      <timestamp>2008-05-29T03:09:24Z</timestamp>
      <contributor>
        <username>RossPatterson</username>
        <id>109</id>
      </contributor>
      <comment>+cat</comment>
      <text xml:space="preserve">{{User PL1 category description|sed|sed}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sh script:Experts</title>
    <id>2225</id>
    <revision>
      <id>5583</id>
      <timestamp>2006-06-01T20:42:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL3 category description|sh script|Bourne Shell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sh script:Knows</title>
    <id>2226</id>
    <revision>
      <id>5584</id>
      <timestamp>2006-06-01T20:43:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL2 category description|sh script|Bourne Shell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Users:sh script:Some</title>
    <id>2224</id>
    <revision>
      <id>5581</id>
      <timestamp>2006-06-01T20:41:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">{{User PL1 category description|sh script|Bourne Shell}}</text>
    </revision>
  </page>
  <page>
    <title>Category:Uses library:GMP</title>
    <id>2364</id>
    <revision>
      <id>6398</id>
      <timestamp>2006-06-21T22:59:22Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains code depending on [http://www.swox.se/gmp/ GMP], the GNU Multiple Precision Arithmetic Library.

[[Category:Libraries]]</text>
    </revision>
    <revision>
      <id>6414</id>
      <timestamp>2006-06-22T00:08:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>License note</comment>
      <text xml:space="preserve">This category contains code depending on [http://www.swox.se/gmp/ GMP], the GNU Multiple Precision Arithmetic Library. Because the GMP is released under the LGPL and not the GPL, this code may still be released under the MIT License.

[[Category:Libraries]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Uses library:Gtk2</title>
    <id>2239</id>
    <revision>
      <id>5652</id>
      <timestamp>2006-06-01T22:56:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains code depending on [http://en.wikipedia.org/wiki/Gtk GTK] 2.x.</text>
    </revision>
    <revision>
      <id>5653</id>
      <timestamp>2006-06-01T23:01:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>added '+' to name</comment>
      <text xml:space="preserve">This category contains code depending on [http://en.wikipedia.org/wiki/Gtk GTK+] 2.x.</text>
    </revision>
    <revision>
      <id>6401</id>
      <timestamp>2006-06-21T23:02:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ Category:Libraries</comment>
      <text xml:space="preserve">This category contains code depending on [http://en.wikipedia.org/wiki/Gtk GTK+] 2.x.

[[Category:Libraries]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Uses library:OpenSSL</title>
    <id>2342</id>
    <revision>
      <id>6241</id>
      <timestamp>2006-06-13T15:55:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>created</comment>
      <text xml:space="preserve">This category contains code depending on [http://en.wikipedia.org/wiki/OpenSSL OpenSSL], the open source implementation of SSL and TLS.</text>
    </revision>
    <revision>
      <id>6400</id>
      <timestamp>2006-06-21T23:01:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ Category:Libraries</comment>
      <text xml:space="preserve">This category contains code depending on [http://en.wikipedia.org/wiki/OpenSSL OpenSSL], the open source implementation of SSL and TLS.

[[Category:Libraries]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Van Emde Boas tree</title>
    <id>1990</id>
    <revision>
      <id>4643</id>
      <timestamp>2006-05-13T03:04:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cat</comment>
      <text xml:space="preserve">A [http://en.wikipedia.org/wiki/Van_Emde_Boas_tree van Emde Boas tree] is a data structure that stores ''m''-bit integer keys in a way that permits insertion, lookup, removal, successor, and predecessor operations in O(log ''m'') time. For dense trees this is exponentially better than [[:Category:Balanced tree|balanced trees]].

&lt;noinclude&gt;
[[Category:Data structures]]
&lt;/noinclude&gt;</text>
    </revision>
  </page>
  <page>
    <title>Category:Visitor pattern</title>
    <id>1693</id>
    <revision>
      <id>2699</id>
      <timestamp>2006-03-06T21:22:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Category:Design patterns]]</comment>
      <text xml:space="preserve">[[Category:Design patterns]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Viterbi</title>
    <id>2831</id>
    <revision>
      <id>8205</id>
      <timestamp>2006-11-28T03:13:55Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Viterbi</comment>
      <text xml:space="preserve">This category contains implementaitions of the [http://en.wikipedia.org/wiki/Viterbi_algorithm Viterbi algorithm].

[[Category:Statistics]]
[[Category:Dynamic programming]]</text>
    </revision>
    <revision>
      <id>8312</id>
      <timestamp>2006-12-07T05:31:31Z</timestamp>
      <contributor>
        <ip>68.147.200.92</ip>
      </contributor>
      <comment>sp</comment>
      <text xml:space="preserve">This category contains implementations of the [http://en.wikipedia.org/wiki/Viterbi_algorithm Viterbi algorithm].

[[Category:Statistics]]
[[Category:Dynamic programming]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Wildcards</title>
    <id>2809</id>
    <revision>
      <id>8168</id>
      <timestamp>2006-11-25T19:38:15Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <comment>Category:Wildcards</comment>
      <text xml:space="preserve">This category contains implementations of algorithms for string matching with [http://en.wikipedia.org/wiki/Wildcard_character wildcards].

[[Category: String search algorithms]]</text>
    </revision>
    <revision>
      <id>12045</id>
      <timestamp>2008-01-12T00:10:11Z</timestamp>
      <contributor>
        <username>Fabian Steeg</username>
        <id>114</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">This category contains implementations of algorithms for string matching with [http://en.wikipedia.org/wiki/Wildcard_character wildcards].</text>
    </revision>
  </page>
  <page>
    <title>Category:Word count</title>
    <id>3170</id>
    <revision>
      <id>10556</id>
      <timestamp>2007-06-21T05:57:01Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>lots of word count articles now - enough to warrant a separate cat</comment>
      <text xml:space="preserve">This category contains articles describing code for counting the number of words, lines, and other textual elements in a file.

[[Category:File processing]]</text>
    </revision>
  </page>
  <page>
    <title>Category:Zebra Puzzle</title>
    <id>2384</id>
    <revision>
      <id>6487</id>
      <timestamp>2006-06-26T09:10:14Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains articles on solving [http://en.wikipedia.org/wiki/Zebra_Puzzle Zebra Puzzle]. The Zebra Puzzle is a well-known logic puzzle which is often called &quot;Einstein's Puzzle&quot; or &quot;Einstein's Riddle&quot; 

[[Category:Logic puzzles]]</text>
    </revision>
    <revision>
      <id>6489</id>
      <timestamp>2006-06-26T10:36:19Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This category contains articles on solving [http://en.wikipedia.org/wiki/Zebra_Puzzle Zebra Puzzle]. The Zebra Puzzle is a well-known logic puzzle which is often called &quot;Einstein's Puzzle&quot; or &quot;Einstein's Riddle.&quot; 

==The original puzzle==
Although there are several variants of Zebra Puzzle, we will employ [http://upload.wikimedia.org/wikipedia/en/6/61/Zerba.pdf the first known publication of the puzzle].

:# There are five houses.
:# The Englishman lives in the red house.
:# The Spaniard owns the dog.
:# Coffee is drunk in the green house.
:# The Ukrainian drinks tea.
:# The green house is immediately to the right of the ivory house.
:# The Old Gold smoker owns snails.
:# Kools are smoked in the yellow house.
:# Milk is drunk in the middle house.
:# The Norwegian lives in the first house.
:# The man who smokes Chesterfields lives in the house next to the man with the fox.
:# Kools are smoked in the house next to the house where the horse is kept.
:# The Lucky Strike smoker drinks orange juice.
:# The Japanese smokes Parliaments.
:# The Norwegian lives next to the blue house.

:Now, who drinks water? Who owns the zebra?
In statement 6, ''right'' means ''your'' right. For example, 'House 3' is immediately to the right of the 'House 2.'
 +-----+  +-----+  +-----+  +-----+  +-----+
 |House|  |House|  |House|  |House|  |House| 
 |  1  |  |  2  |  |  3  |  |  4  |  |  5  | 
 +-----+  +-----+  +-----+  +-----+  +-----+

==Solution==
{|
! house
| 1 || 2 || 3 || 4 || 5
|-
! color
| yellow || blue || red || ivory || green
|-
! nationality
| Norwegian || Ukrainian || Englishman || Spaniard || Japanese
|-
! drink
| WATER || tea || milk || orange juice || coffee
|-
! smoke
| Kools || Chesterfield || Old Gold || Lucky Strike || Parliament
|-
! pet
| fox || horse || snails || dog || ZEBRA
|}

[[Category:Logic puzzles]]</text>
    </revision>
  </page>
  <page>
    <title>Chatterbot (QBASIC)</title>
    <id>3956</id>
    <revision>
      <id>16811</id>
      <timestamp>2010-08-18T03:18:11Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>code dump of chatterbot</comment>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=QBASIC&gt;
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM

Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that WikiChat has already seen
  DIM Alternatives$(DictionarySize) 'The characters that WikiChat may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes WikiChat more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;WIKICHAT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16812</id>
      <timestamp>2010-08-18T03:20:06Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM

Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that WikiChat has already seen
  DIM Alternatives$(DictionarySize) 'The characters that WikiChat may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes WikiChat more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;WIKICHAT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16813</id>
      <timestamp>2010-08-18T03:26:23Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Add some text</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM

Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that WikiChat has already seen
  DIM Alternatives$(DictionarySize) 'The characters that WikiChat may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes WikiChat more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;WIKICHAT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN
&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
Human: hello there
Computer:
Human: hello
Computer:
Human: how are you
Computer:
Human: fine thanks how are you
Computer: fine thanks how are you
Human: fine thanks
Computer:
Human:

(Session 2) 
Human: hello
Computer: how are you
Human: fine thanks how are you
Computer: fine thanks
Human: glad to hear it
Computer:
Human:

(Session 3) 
Human: hello
Computer: how are you
Human: fine thanks
Computer: glad to hear it
Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16814</id>
      <timestamp>2010-08-18T03:27:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* QChatt learning sessions */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM

Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that WikiChat has already seen
  DIM Alternatives$(DictionarySize) 'The characters that WikiChat may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes WikiChat more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;WIKICHAT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN
&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16815</id>
      <timestamp>2010-08-18T04:00:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>save progress so far</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you these are just procedures with access to the global variables.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many, using the variable ContextLength, and use the array, Context$, to track the last six together with the array Alternatives$, to keep track of characters which can follow the last six. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? 

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16816</id>
      <timestamp>2010-08-18T04:01:34Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many, using the variable ContextLength, and use the array, Context$, to track the last six together with the array Alternatives$, to keep track of characters which can follow the last six. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? 

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16817</id>
      <timestamp>2010-08-18T04:03:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? 

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16818</id>
      <timestamp>2010-08-18T04:17:36Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16819</id>
      <timestamp>2010-08-18T04:36:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

&lt;codeblock language=QBASIC&gt;
StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16820</id>
      <timestamp>2010-08-18T04:56:14Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData routine and StoreData just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16821</id>
      <timestamp>2010-08-18T04:57:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">{{codedump}}

==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16822</id>
      <timestamp>2010-08-18T05:01:43Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>not just a codedump now</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

==QChatt learning sessions==
The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16823</id>
      <timestamp>2010-08-18T05:25:42Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16824</id>
      <timestamp>2010-08-18T05:26:22Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1.

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16825</id>
      <timestamp>2010-08-18T05:27:52Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */ oops</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN

&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN

&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN

&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN

&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN

&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN

&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN

&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1.

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16826</id>
      <timestamp>2010-08-18T05:30:30Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */ tweak</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN
&lt;/codeblock&gt;

This main routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN
&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN
&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN
&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN
&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN
&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN
&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1.

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16828</id>
      <timestamp>2010-08-24T00:07:33Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN
&lt;/codeblock&gt;

The Converse routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN
&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN
&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN
&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN
&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN
&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN
&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1.

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
    <revision>
      <id>16829</id>
      <timestamp>2010-08-24T00:09:01Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* A simple Chatterbot example */</comment>
      <text xml:space="preserve">==A simple Chatterbot example==
In principle a chatterbot can be a very short program. For instance the following program implements a chatterbot which will learn phrases in any language by repetition in much the same way that a parrot does.

The first section just calls a set of routines in order. The routines have been named to make their function reasonably obvious. Don't let the GOSUBs worry you. These are just procedures with access to the global variables and every variable in this short program is global.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Main&gt;&gt;=
QChatt:
  DEFINT A-Z
  GOSUB Initialise
  GOSUB LoadData
  GOSUB Converse
  GOSUB StoreData
  SYSTEM
&lt;/codeblock&gt;

First we set up a couple of items. This chatbot works by keeping track of the last six (or whatever) characters and using them to predict the next character. So we need to say how many to track, using the variable ContextLength, and use the array, Context$, to store the resulting text fragments together with the array, Alternatives$, to keep track of characters which can follow a particular text fragment. The DictionaryFile$ variable specifies the name of a file which can be used as permanent storage of the results of sessions to date.

The purpose of RANDOMIZE TIMER is just to ensure that the random number generator has been properly seeded, so that the RND calls later in the program produce &quot;unexpected&quot; results.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Initialise&gt;&gt;=
Initialise:
  LET DictionarySize = 1000
  DIM Context$(DictionarySize) 'The character sequences that QChatt has already seen
  DIM Alternatives$(DictionarySize) 'The characters that QChatt may print after recognising a sequence.
  LET EmptyRow = 0
  LET EndOfResponseCharacter$ = CHR$(180)
  LET ContextLength = 6  'A bigger value makes QChatt more grammatical but slower learning.
  LET CurrentContext$ = STRING$(ContextLength, EndOfResponseCharacter$)
  LET DictionaryFile$ = &quot;QCHATT.MEM&quot;
  RANDOMIZE TIMER
  RETURN
&lt;/codeblock&gt;

The Converse routine runs the top level sentence/response loop. It passes anything that the Human says to an analysis routine, MemoriseHumanResponse, which picks it apart and uses it as raw material for future possible computer responses. It then prints a Computer response created by the GenerateComputerResponse routine which uses the results of previous analyses if any of them are appropriate. If not it just waits for more Human responses. When it doesn't get any it stops.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Converse&gt;&gt;=
Converse:
  DO
    LINE INPUT &quot;Human: &quot;; Response$
    IF Response$ = &quot;&quot; THEN EXIT DO
    LET Response$ = Response$ + EndOfResponseCharacter$
    GOSUB MemoriseHumanResponse
    LET Response$ = &quot;&quot;
    GOSUB GenerateComputerResponse
    PRINT &quot;Computer: &quot;; Response$
  LOOP
  RETURN
&lt;/codeblock&gt;

So how does the computer analyse the Human responses? Well it uses the CurrentContext$ variable to keep track of the last few characters, however many are specified by ContextLength, by running through the Human's response character by character and adding it to the right end while dropping whichever character is on the left end of CurrentContext$. To begin with CurrentContext$ normally has the last few characters of the Computer response. This is what links the responses together so that the GenerateComputerResponse routine has a chance of coming up with something halfway sensible for a given Human sentence.

The character in the CurrentCharacter$ variable is basically what should be predicted by the CurrentContext$ text fragment in the GenerateComputerResponse procedure, so the InsertCharacter procedure records the fact that this particular CurrentCharacter$ can follow that CurrentContext$.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;=
MemoriseHumanResponse:
  DO WHILE Response$ &gt; &quot;&quot;
    LET CurrentCharacter$ = LEFT$(Response$, 1)
    LET Response$ = MID$(Response$, 2)
    GOSUB InsertCharacter
    LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
  LOOP
  RETURN
&lt;/codeblock&gt;

So now that we know how to analyse the text, how do we use the results to generate the Computer response? Well we basically use the CurrentContext$ variable in the same way that we did for the analysis. The difference is that we use it to retrieve the possible following characters stored in Alternative$, instead of recording the current character from the Human response. When we retrieve the alternatives, we may find that there is more than one possible character that can follow this particular CurrentContext$ text fragment. If so, we pick one at random. We may also find that a particular CurrentContext$ text fragment doesn't have any following characters recorded in Alternatives$. In that case we just stop the generation and return the result.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;=
GenerateComputerResponse:
   DO
     GOSUB Lookup
     LET CurrentCharacter$ = MID$(Alternatives$(DictionaryIndex), INT(RND * LEN(Alternatives$(DictionaryIndex))) + 1, 1)
     IF CurrentCharacter$ = &quot;&quot; THEN
       EXIT DO
     ELSE
       LET CurrentContext$ = MID$(CurrentContext$, 2) + CurrentCharacter$
       IF CurrentCharacter$ = EndOfResponseCharacter$ THEN
         EXIT DO
       ELSE
         LET Response$ = Response$ + CurrentCharacter$
       END IF
     END IF
   LOOP
   RETURN
&lt;/codeblock&gt;

Now for a few utility routines. Firstly the InsertCharacter routine. It's called that because it records a new possible following character for a particular CurrentContext$ text fragment but only if it hasn't already been recorded. To ensure that it adds the character to the correct set of Alternatives$, the Lookup procedure converts the CurrentContext$ text fragment into an array index stored in the DictionaryIndex variable.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InsertCharacter&gt;&gt;=
InsertCharacter:
  GOSUB Lookup
  IF INSTR(Alternatives$(DictionaryIndex), CurrentCharacter$) = 0 THEN
    LET Alternatives$(DictionaryIndex) = Alternatives$(DictionaryIndex) + CurrentCharacter$
  END IF
  RETURN
&lt;/codeblock&gt;

In this simple version of the QChatt program the Lookup routine is implemented as a linear lookup. The CurrentContext$ text fragment is compared against all the stored Context$ and if a matching one is found, its DictionaryIndex is returned. This is the least efficient part of the program. In other versions of QChatt I have replaced it with a hash array or with a Trie which allows much larger amounts of data to be handled. However in this article I have gone for simplicity over efficiency. 

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Lookup&gt;&gt;=
Lookup:
  LET Context$(EmptyRow) = CurrentContext$
  LET DictionaryIndex = 0
  DO WHILE CurrentContext$ &lt;&gt; Context$(DictionaryIndex)
    LET DictionaryIndex = DictionaryIndex + 1
  LOOP
  IF DictionaryIndex = EmptyRow AND DictionaryIndex &lt; DictionarySize THEN
    LET Alternatives$(EmptyRow) = &quot;&quot;
    LET EmptyRow = DictionaryIndex + 1
  END IF
  RETURN
&lt;/codeblock&gt;

The LoadData and StoreData routines just do what it says on the tin. They are included to make sure that QChatt doesn't forget everything when you close the program down.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;=
LoadData:
  OPEN DictionaryFile$ FOR APPEND AS #1
  CLOSE #1
  OPEN DictionaryFile$ FOR INPUT AS #1
  DO WHILE EmptyRow &lt; DictionarySize AND NOT EOF(1)
    LINE INPUT #1, Context$(EmptyRow)
    LINE INPUT #1, Alternatives$(EmptyRow)
    LET EmptyRow = EmptyRow + 1
  LOOP
  CLOSE #1
  RETURN

StoreData:
  OPEN DictionaryFile$ FOR OUTPUT AS #1
  FOR DictionaryIndex = 0 TO EmptyRow - 1
    PRINT #1, Context$(DictionaryIndex)
    PRINT #1, Alternatives$(DictionaryIndex)
  NEXT
  CLOSE #1
  RETURN
&lt;/codeblock&gt;

So putting it all together as ...

&lt;codeblock language=QBASIC&gt;
&lt;&lt;QChatt.bas&gt;&gt;=
&lt;&lt;Main&gt;&gt;
&lt;&lt;Initialise&gt;&gt;
&lt;&lt;Converse&gt;&gt;
&lt;&lt;MemoriseHumanResponse&gt;&gt;
&lt;&lt;GenerateComputerResponse&gt;&gt;
&lt;&lt;InsertCharacter&gt;&gt;
&lt;&lt;Lookup&gt;&gt;
&lt;&lt;LoadAndStoreData&gt;&gt;
&lt;/codeblock&gt;

... we end up with a program which can be interpreted by QBASIC or compiled by QuickBASIC 4.5 or VBDOS 1.

==QChatt learning sessions==
Note that to begin with, this chatterbot knows nothing and therefore says nothing. However if one uses simple conversation with it, like a parrot it will begin to reply as it starts to find responses that are appropriate for the immediately preceding sentence.

The following sessions show how to teach QChatt some simple conversation. Note that sessions are started by running the QChatt program and ended by pressing the return key without giving a response to the computer. They show QChatt being taught a basic conversational pattern in English.

(Session 1) 
:Human: hello there
:Computer:
:Human: hello
:Computer:
:Human: how are you
:Computer:
:Human: fine thanks how are you
:Computer: fine thanks how are you
:Human: fine thanks
:Computer:
:Human:

(Session 2) 
:Human: hello
:Computer: how are you
:Human: fine thanks how are you
:Computer: fine thanks
:Human: glad to hear it
:Computer:
:Human:

(Session 3) 
:Human: hello
:Computer: how are you
:Human: fine thanks
:Computer: glad to hear it
:Human:

The responses will be stored for the next session, so that there is no need to reteach them but it should be noted that while this example chatterbot will create &quot;original&quot; sentences after a little teaching, it has a very limited capacity and works best with short sentences.

[[Category:Environment:Windows]]
[[Category:Programming language:QBASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Chemical equations balancer (Python)</title>
    <id>3016</id>
    <revision>
      <id>9058</id>
      <timestamp>2007-02-13T10:53:49Z</timestamp>
      <contributor>
        <username>Djura</username>
        <id>141</id>
      </contributor>
      <comment>{Codecump} under {Develop}ment</comment>
      <text xml:space="preserve">{{Codedump}}
{{Develop}}

&lt;codeblock language=Python&gt;
#! /usr/bin/env python

class Equ:
	def __init__(self):
		self.Eq = [[], []]
		self.Atoms = set()
		self.LS = 0
		self.PS = 1
	def addMolek(self, molek, side):
		self.Atoms = self.Atoms.union(molek.keys())
		self.Eq[side].append([molek, 1])
		return True
	def countAtom(self, atom):
		cl, cp = (None, None)
		for xat in self.Eq:
			count = 0
			for mlk in xat:
				   count += mlk[0].get(atom, 0)
			if cl == None:
				cl = count
			else:
				cp = count
		return (cl, cp)
	def multiRci(self, atom, nmbrs = (1, 1)):
		ls, ps = nmbrs
		print nmbrs
#		print ls, ps
		for xsd in xrange(len(self.Eq)):
			if xsd == self.LS:
				mtp = ls
			else:
				mtp = ps
			for xmolek in xrange(len(self.Eq[xsd])):
				if self.Eq[xsd][xmolek][0].get(atom, 0) != 0:
					for xother in self.Eq[xsd][xmolek][0].keys():
						self.Eq[xsd][xmolek][0][xother] *= mtp
					self.Eq[xsd][xmolek][1] *= mtp
		return True
	def isEq(self):
		a = []
		for at in self.Atoms:
			ls, ps = self.countAtom(at)
			print 'atom: ', at, ' left: ', ls, ' right: ', ps
			if ls != ps:
				a.append([at, (ls, ps)])
			else:
		if len(a) == 0:
			return True
		else:
			print 'vracim: ', a, '\n\n'
			return a
	def mkEq(self):	
		at = self.isEq()
		if at == True:
			return True
		else:
			for dsf in xrange(2):
				at = self.isEq()
				mn = ['',(float(&quot;infinity&quot;), float(&quot;infinity&quot;))]
				for at in at:
					if nsd(mn[1]) &gt; nsd(at[1]):
						mn[1] = at[1]
						mn[0] = at[0]
				print mn
				print nsn(mn[1]), ' / ', (mn[1][0]), ' , ', nsn(mn[1]), ' / ', (mn[1][1])
				self.multiRci(mn[0], (nsn(mn[1])/(mn[1][0]), nsn(mn[1])/(mn[1][1])))

def nsn((first, second)):
	return (first * second) / nsd((first, second))
def nsd((first, second)):
	if first == float(&quot;infinity&quot;) or second == float(&quot;infinity&quot;):
		return float(&quot;infinity&quot;)
	if second == 0:
		return first
	return nsd((second, first%second))

rce = Equ()
rce.addMolek(dict(H=2, O=0), rce.LS)
rce.addMolek(dict(H=0, O=2), rce.LS)
rce.addMolek(dict(H=2, O=1), rce.PS)
print rce.Atoms
rce.mkEq()
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9059</id>
      <timestamp>2007-02-13T10:56:44Z</timestamp>
      <contributor>
        <username>Djura</username>
        <id>141</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Codedump}}
{{Develop}}

&lt;codeblock language=Python&gt;
#! /usr/bin/env python

class Equ:
	def __init__(self):
		self.Eq = [[], []]
		self.Atoms = set()
		self.LS = 0
		self.PS = 1
	def addMolek(self, molek, side):
		self.Atoms = self.Atoms.union(molek.keys())
		self.Eq[side].append([molek, 1])
		return True
	def countAtom(self, atom):
		cl, cp = (None, None)
		for xat in self.Eq:
			count = 0
			for mlk in xat:
				   count += mlk[0].get(atom, 0)
			if cl == None:
				cl = count
			else:
				cp = count
		return (cl, cp)
	def multiRci(self, atom, nmbrs = (1, 1)):
		ls, ps = nmbrs
		print nmbrs
#		print ls, ps
		for xsd in xrange(len(self.Eq)):
			if xsd == self.LS:
				mtp = ls
			else:
				mtp = ps
			for xmolek in xrange(len(self.Eq[xsd])):
				if self.Eq[xsd][xmolek][0].get(atom, 0) != 0:
					for xother in self.Eq[xsd][xmolek][0].keys():
						self.Eq[xsd][xmolek][0][xother] *= mtp
					self.Eq[xsd][xmolek][1] *= mtp
		return True
	def isEq(self):
		a = []
		for at in self.Atoms:
			ls, ps = self.countAtom(at)
			print 'atom: ', at, ' left: ', ls, ' right: ', ps
			if ls != ps:
				a.append([at, (ls, ps)])
			else:
		if len(a) == 0:
			return True
		else:
			print 'vracim: ', a, '\n\n'
			return a
	def mkEq(self):	
		at = self.isEq()
		if at == True:
			return True
		else:
			for dsf in xrange(2):  # hack, works only with 02 + H2 -&gt; H20 reaction
				at = self.isEq()
				mn = ['',(float(&quot;infinity&quot;), float(&quot;infinity&quot;))]
				for at in at:
					if nsd(mn[1]) &gt; nsd(at[1]):
						mn[1] = at[1]
						mn[0] = at[0]
				print mn
				print nsn(mn[1]), ' / ', (mn[1][0]), ' , ', nsn(mn[1]), ' / ', (mn[1][1])
				self.multiRci(mn[0], (nsn(mn[1])/(mn[1][0]), nsn(mn[1])/(mn[1][1])))

def nsn((first, second)):
	return (first * second) / nsd((first, second))
def nsd((first, second)):
	if first == float(&quot;infinity&quot;) or second == float(&quot;infinity&quot;):
		return float(&quot;infinity&quot;)
	if second == 0:
		return first
	return nsd((second, first%second))

rce = Equ()
rce.addMolek(dict(H=2, O=0), rce.LS)
rce.addMolek(dict(H=0, O=2), rce.LS)
rce.addMolek(dict(H=2, O=1), rce.PS)
print rce.Atoms
rce.mkEq()
&lt;/codeblock&gt;</text>
    </revision>
  </page>
  <page>
    <title>Ciphersaber (BASIC)</title>
    <id>2630</id>
    <revision>
      <id>7266</id>
      <timestamp>2006-08-13T20:01:39Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>[[Ciphersaber (BASIC)]] moved to [[Ciphersaber (QBASIC)]]: More specific about language</comment>
      <text xml:space="preserve">#REDIRECT [[Ciphersaber (QBASIC)]]</text>
    </revision>
  </page>
  <page>
    <title>Ciphersaber (QBASIC)</title>
    <id>2605</id>
    <revision>
      <id>7127</id>
      <timestamp>2006-08-07T06:55:17Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>experiment</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
1 DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
2 RANDOMIZE TIMER 
3 INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
4 OPEN MID$(fin$, 2) FOR BINARY AS #1 
5 OPEN fout$ FOR BINARY AS #2 
6 LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
7 IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
8 LET ky$ = ky$ + q$ 
9 FOR j% = 0 TO 255 
10    LET s%(j%) = j% 
11 NEXT 
12 FOR i% = 0 TO 255 
13    LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
14    SWAP s%(j%), s%(i%) 
15 NEXT 
16 LET ky$ = &quot; &quot; 
17 FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
18    LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
19    SWAP s%(i%), s%(j&amp; MOD 256) 
20    GET #1, , ky$ 
21    LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
22    PUT #2, , ky$ 
23 NEXT 
24 CLOSE
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7128</id>
      <timestamp>2006-08-07T06:56:46Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
1 DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
2 RANDOMIZE TIMER 
3 INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
4 OPEN MID$(fin$, 2) FOR BINARY AS #1 
5 OPEN fout$ FOR BINARY AS #2 
6 LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
7 IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
8 LET ky$ = ky$ + q$ 
9 FOR j% = 0 TO 255 
10    LET s%(j%) = j% 
11 NEXT 
12 FOR i% = 0 TO 255 
13    LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
14    SWAP s%(j%), s%(i%) 
15 NEXT 
16 LET ky$ = &quot; &quot; 
17 FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
18    LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
19    SWAP s%(i%), s%(j&amp; MOD 256) 
20    GET #1, , ky$ 
21    LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
22    PUT #2, , ky$ 
23 NEXT 
24 CLOSE
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7129</id>
      <timestamp>2006-08-07T06:58:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>remove unnecessary line numbers</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER 
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7131</id>
      <timestamp>2006-08-07T07:14:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER 
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7132</id>
      <timestamp>2006-08-07T07:15:12Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER 
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7139</id>
      <timestamp>2006-08-08T02:16:42Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER 
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography:BASIC]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7140</id>
      <timestamp>2006-08-08T02:17:08Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER 
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7141</id>
      <timestamp>2006-08-08T02:28:56Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>More practice</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Algorithm==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix character have been used to specifiy the variable types.

&lt;codeblock language=BASIC&gt;
&lt;&lt;init&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock

&lt;codeblock language=BASIC&gt;
&lt;&lt;input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock

&lt;codeblock language=BASIC&gt;
&lt;process&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock

&lt;codeblock language=BASIC&gt;
&lt;&lt;output&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;init&gt;&gt;
&lt;input&gt;&gt;
&lt;&lt;process&gt;
&lt;&lt;output&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7142</id>
      <timestamp>2006-08-08T02:31:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Algorithm==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix character have been used to specifiy the variable types.

&lt;codeblock language=BASIC&gt;
&lt;&lt;init&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell us whether we encoding or decoding and which file we are interested in.
&lt;codeblock language=BASIC&gt;
&lt;&lt;input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;process&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we've got to print it out in a new file.
&lt;codeblock language=BASIC&gt;
&lt;&lt;output&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;init&gt;&gt;
&lt;input&gt;&gt;
&lt;&lt;process&gt;
&lt;&lt;output&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7143</id>
      <timestamp>2006-08-08T02:32:21Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Algorithm==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix character have been used to specifiy the variable types.

&lt;codeblock language=BASIC&gt;
&lt;&lt;init&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell us whether we encoding or decoding and which file we are interested in.
&lt;codeblock language=BASIC&gt;
&lt;&lt;input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;process&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we've got to print it out in a new file.
&lt;codeblock language=BASIC&gt;
&lt;&lt;output&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;init&gt;&gt;
&lt;input&gt;&gt;
&lt;&lt;process&gt;
&lt;&lt;output&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7144</id>
      <timestamp>2006-08-08T02:33:09Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Algorithm==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix character have been used to specifiy the variable types.

&lt;codeblock language=BASIC&gt;
&lt;&lt;init&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell us whether we encoding or decoding and which file we are interested in.
&lt;codeblock language=BASIC&gt;
&lt;&lt;input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;process&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we've got to print it out in a new file.
&lt;codeblock language=BASIC&gt;
&lt;&lt;output&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;init&gt;&gt;
&lt;&lt;input&gt;&gt;
&lt;&lt;process&gt;&gt;
&lt;&lt;output&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7145</id>
      <timestamp>2006-08-08T03:36:32Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Algorithm */ Add stuff</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix character have been used to specifiy the variable types.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell us whether we encoding or decoding and which file we are interested in. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character random sequence. The sequence ensures that the key is at least 10 characters long. The sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7146</id>
      <timestamp>2006-08-08T03:39:05Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell us whether we encoding or decoding and which file we are interested in. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character random sequence. The sequence ensures that the key is at least 10 characters long. The sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7147</id>
      <timestamp>2006-08-08T03:40:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character random sequence. The sequence ensures that the key is at least 10 characters long. The sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7148</id>
      <timestamp>2006-08-08T03:42:11Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character random sequence. The sequence ensures that the key is at least 10 characters long. The sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7149</id>
      <timestamp>2006-08-08T03:43:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string wqhen they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character random sequence. The sequence ensures that the key is at least 10 characters long. The sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7150</id>
      <timestamp>2006-08-08T03:45:07Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string wqhen they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The psuedorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7151</id>
      <timestamp>2006-08-08T03:46:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string wqhen they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)coding. The RC4 coding method which we are using is symmetrical. In other words we encode and decode a file the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)code it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it altogether et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7152</id>
      <timestamp>2006-08-08T03:49:39Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 algorithm which has now been superceded by the Ciphersaber-2 algorithm.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it all together et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7154</id>
      <timestamp>2006-08-08T04:38:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it all together et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7157</id>
      <timestamp>2006-08-08T04:55:24Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>tweak</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

Finally put it all together et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7158</id>
      <timestamp>2006-08-08T04:56:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the encoding phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7159</id>
      <timestamp>2006-08-08T04:57:23Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, fout$, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Input&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
OPEN MID$(fin$, 2) FOR BINARY AS #1 
OPEN fout$ FOR BINARY AS #2 
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #1, , q$ ELSE PUT #2, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(1) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #1, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #2, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #0
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;Input&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7160</id>
      <timestamp>2006-08-08T05:03:47Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */ tweak</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a decent key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7161</id>
      <timestamp>2006-08-08T05:05:00Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>/* Description */ tweak</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:QBASIC]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7173</id>
      <timestamp>2006-08-09T02:34:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>cat</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The Ciphersaber strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7189</id>
      <timestamp>2006-08-10T10:49:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>WP link</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The [http://en.wikipedia.org/wiki/CipherSaber Ciphersaber] strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7265</id>
      <timestamp>2006-08-13T20:01:39Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>[[Ciphersaber (BASIC)]] moved to [[Ciphersaber (QBASIC)]]: More specific about language</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The [http://en.wikipedia.org/wiki/CipherSaber Ciphersaber] strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|BASIC]]</text>
    </revision>
    <revision>
      <id>7273</id>
      <timestamp>2006-08-13T20:05:07Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>recat</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The [http://en.wikipedia.org/wiki/CipherSaber Ciphersaber] strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=BASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=BASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=BASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=BASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:QBASIC]]
[[Category:Environment:DOS]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|QBASIC]]</text>
    </revision>
    <revision>
      <id>7512</id>
      <timestamp>2006-08-29T08:11:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>language=QBASIC</comment>
      <text xml:space="preserve">The dialect of BASIC used for this program is QBASIC. Thus it runs on the QBASIC interpreter and can be compiled by QuickBASIC 4.5, PDS 7.1 or Visual BASIC for DOS 1.0. The [http://en.wikipedia.org/wiki/CipherSaber Ciphersaber] strong encryption project is described on [http://ciphersaber.gurus.com/ the Ciphersaber website] which should be read for more information.

The program itself can be used to encipher and decipher files. It uses the Ciphersaber-1 version of the RC4 algorithm which has now been superceded by the Ciphersaber-2 version.

==Description==
Firstly it is necessary to declare all the variables and initialise them. Here the standard postfix characters have been used to specify the variable types. The &quot;$&quot; means that the variable is for strings, the &quot;%&quot; means that the variable is for 16-bit signed integers and the &quot;&amp;&quot; means that the variable is for 32-bit signed integers. String variables are automatically initialised to the empty string when they are declared and integers are initialised to zero. The RANDOMIZE TIMER statement ensures that a unique pseudorandom sequence is generated when that is required later in the program.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;DeclarationAndInitialisation&gt;&gt;=
DIM fin$, f1%, fout$, f2%, ky$, q$, i%, j%, j&amp;, s%(255) 
RANDOMIZE TIMER
&lt;/codeblock&gt;

We need to get user input to tell the program whether encoding is intended or decoding, which file we are interested in, and what the key phrase is supposed to be. We also need to open the two files which we are going to work on: one for input; one for output. As this program was originally written to be as short as possible a minimal method of indicating whether we wish to encode a file or decode it is used: in short the input filename is prefixed with &quot;+&quot; when the intention is to encrypt and with &quot;-&quot; when the intention is to decrypt.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;InputOutput&gt;&gt;=
INPUT &quot;Input File (+Encode, -Decode), Output File, Key: &quot;, fin$, fout$,ky$ 
LET f1% = FREEFILE
OPEN MID$(fin$, 2) FOR BINARY AS #f1% 
LET f2% = FREEFILE
OPEN fout$ FOR BINARY AS #f2%
&lt;/codeblock&gt;

A ciphersaber key consists of a user chosen section and a 10 character pseudorandom sequence. The sequence ensures that the key is at least 10 characters long. The pseudorandom sequence is stored as the first part of a Ciphersaber encoded file so that it can be retrieved when the decoding is done later on.  

&lt;codeblock language=QBASIC&gt;
&lt;&lt;KeyCreation&gt;&gt;=
LET q$ = CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) + CHR$(RND * 256) 
IF LEFT$(fin$, 1) = &quot;-&quot; THEN GET #f1%, , q$ ELSE PUT #f2%, , q$ 
LET ky$ = ky$ + q$ 
&lt;/codeblock&gt;

Once we have a long enough key the next step is to use it to create a coding array which will be used in the (de)crypting phase.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;=
FOR j% = 0 TO 255 
   LET s%(j%) = j% 
NEXT 
FOR i% = 0 TO 255 
   LET j% = (j% + s%(i%) + ASC(MID$(ky$, i% MOD LEN(ky$) + 1, 1))) MOD 256 
   SWAP s%(j%), s%(i%) 
NEXT 
&lt;/codeblock&gt;

Now we're ready to do the (de)crypting. The RC4 coding method which we are using is symmetrical. In other words we encrypt and decrypt a file in the same way, so we can use the same program to do either job. The following section shows how. Basically we read the input file one character at a time, use it to update the coding array, (de)crypt it and print it out in the new file.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;Transformation&gt;&gt;=
LET ky$ = &quot; &quot; 
FOR j&amp; = 1 TO LOF(f1%) + (LEFT$(fin$, 1) = &quot;-&quot;) * 10 
   LET i% = (i% + s%(j&amp; MOD 256)) MOD 256 
   SWAP s%(i%), s%(j&amp; MOD 256) 
   GET #f1%, , ky$ 
   LET ky$ = CHR$(ASC(ky$) XOR s%((s%(j&amp; MOD 256) + s%(i%)) MOD 256)) 
   PUT #f2%, , ky$ 
NEXT 
&lt;/codeblock&gt;

Finally it's time to go home. We close down the open files and return to the operating system.

&lt;codeblock language=QBASIC&gt;
&lt;&lt;FinishUp&gt;&gt;=
CLOSE #f1%, f2%
SYSTEM
&lt;/codeblock&gt;

So we put it all together, et voila!

&lt;codeblock language=BASIC&gt;
&lt;&lt;csabre.bas&gt;&gt;=
&lt;&lt;DeclarationAndInitialisation&gt;&gt;
&lt;&lt;InputOutput&gt;&gt;
&lt;&lt;KeyCreation&gt;&gt;
&lt;&lt;CodingArrayInitialisation&gt;&gt;
&lt;&lt;Transformation&gt;&gt;
&lt;&lt;FinishUp&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:QBASIC]]
[[Category:Environment:DOS]]
[[Category:Cryptography]]
[[Category:Ciphersaber-1|QBASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Combinatorial Geometry in MATLAB</title>
    <id>3079</id>
    <revision>
      <id>9533</id>
      <timestamp>2007-03-21T07:55:41Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 
1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X)) 
+repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;pre&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Pre plot&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]&lt;/pre&gt;&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9534</id>
      <timestamp>2007-03-21T07:56:26Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Plot of the solution */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 
1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X)) 
+repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]&lt;/pre&gt;&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9535</id>
      <timestamp>2007-03-21T07:56:55Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* All the code */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 
1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X)) 
+repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9536</id>
      <timestamp>2007-03-21T07:58:28Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* All the code */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 
1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X)) 
+repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9538</id>
      <timestamp>2007-03-21T08:02:37Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* All the code */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 
1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X)) 
+repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9540</id>
      <timestamp>2007-03-21T11:21:46Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Data generation */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 1).*repmat(b,1,length(X))) - min(repmat(a,1,length(X))+ repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9541</id>
      <timestamp>2007-03-21T11:22:02Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Data generation */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 1).*repmat(b,1,length(X))) - ...
              min(repmat(a,1,length(X))+ repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)- 
repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9542</id>
      <timestamp>2007-03-21T11:22:14Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Crossings */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 1).*repmat(b,1,length(X))) - ...
              min(repmat(a,1,length(X))+ repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)-repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9543</id>
      <timestamp>2007-03-21T11:29:14Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* All the code */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 1).*repmat(b,1,length(X))) - ...
              min(repmat(a,1,length(X))+ repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)-repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

====Another option===

It is possible to use the fsolve function directly.

At first the function to optimize has to be entered:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;mimafun&gt;&gt;=
function y=mimafun(x,a,b) 
%a,b = columns 
V=a+b*x; 
V(:,2)=-V; 
y=sum(max(V));
&lt;/codeblock&gt;

And then directly used:
&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;fsolve direct use&gt;&gt;=
[X, Y]=fsolve(@(x) mimafun(x,a,b),0)
&lt;/codeblock&gt;


[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>9556</id>
      <timestamp>2007-03-22T08:15:37Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* =Another option */</comment>
      <text xml:space="preserve">==Arrangement of hyperplanes==

===Minimal range of an arrangement of lines===

Following a question on the [http://groups.google.com/group/comp.soft-sys.matlab/browse_frm/thread/d6dc2b631f42a156/ MATLAB newsgroup]:

 An interesting problem came up recently. 
 It probably has a simple solution that I'm 
 coming up blank on. 

Given a pair of (real) vectors, &lt;math&gt;a&lt;/math&gt; and &lt;math&gt;b&lt;/math&gt;, each of length &lt;math&gt;n&lt;/math&gt;. 

Find &lt;math&gt;X&lt;/math&gt; (a real scalar) that minimizes the expression 

&lt;math&gt;Y = \max(a+X \, b) - \min(a+X \, b)&lt;/math&gt;

Here is a MATLAB implemented solution:

====Data generation====
Here the data are randomly generated, and the function to minimize is defined:

 f_crit - the scalar version of the criteria

 F_crit - the vectorized version of the criteria


&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Data Generation&gt;&gt;=
n = 5; 
a = rand(n,1); 
b = rand(n,1); 
f_crit = @(X) max(a+X*b) - min(a+X*b); 
F_crit = @(X) max(repmat(a,1,length(X))+repmat(X',length(a), 1).*repmat(b,1,length(X))) - ...
              min(repmat(a,1,length(X))+ repmat(X',length(a),1).*repmat(b,1,length(X))); 
&lt;/codeblock&gt;

====Crossings====
The crossings between all possible pairs of lines are computed.
The crossing between lines &lt;math&gt;y=a+b\,x&lt;/math&gt; and &lt;math&gt;y=A+B\,x&lt;/math&gt; is defined by

&lt;math&gt;x(a,b;A,B)=-\,\frac{a-A}{b-B}&lt;/math&gt;

Note how the upper triangular elements of the matrix are selected, they are sorted only for the pollowing plot.

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Crossings&gt;&gt;=
crossings = -(repmat(a,1,n)-repmat(a',n,1))./(repmat(b,1,n)-repmat(b',n,1)); 
triu_id   = cumsum(eye(n),2)-eye(n); 
crossings = sort(crossings(logical(triu_id))); 
crossingy = F_crit(crossings)'; 
[Y,idX]   = min(crossingy); 
X         = crossings(idX); 
&lt;/codeblock&gt;

====Plot of the solution====

To plot the solution, some computations have to be made first:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Preprocess for plots&gt;&gt;=
domainx = [min(crossings), max(crossings)]; 
domainy = [a+b*domainx(1), a+b*domainx(2)]; 
miax = [min(domainy(:)), max(domainy(:))]'; 
allx = [repmat(crossings,1,2), repmat(nan,length(crossings),1)]'; 
ally = repmat([miax; NaN],1,length(crossings)); 
&lt;/codeblock&gt;

They the solution is plotted in two stages:
* the arrangement of lines and their corssings
* the criteria, on which the crossing are plotted, and the overall minimum

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Plot arrangement&gt;&gt;=
figure('color', [1 1 1]); 
a1=subplot(2,1,1); 
plot(domainx, domainy, 'linewidth',2); 
hold on 
plot(allx(:),ally(:),':k'); 
hold off 
title('All lines'); 
a2=subplot(2,1,2); 
plot(crossings,crossingy,'-', 'linewidth',2); 
hold on 
plot(X, Y, 'or', 'Markerfacecolor', [1 0 0]); 
plot(crossings,crossingy,'.k'); 
hold off 
text(X,Y,sprintf('  X=%5.2f, Y=%5.2f', X, Y), 'rotation', 90) 
title('Minimum'); 
linkaxes([a1,a2],'x');
&lt;/codeblock&gt;

====All the code====
[[Image:Arrangement-min-lines.png]]

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;Arrangement_of_lines.m&gt;&gt;=

&lt;&lt;Data Generation&gt;&gt;

&lt;&lt;Crossings&gt;&gt;

&lt;&lt;Preprocess for plots&gt;&gt;

&lt;&lt;Plot arrangement&gt;&gt;
&lt;/codeblock&gt;

====Another option====

It is possible to use the fsolve function directly.

At first the function to optimize has to be entered:

&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;mimafun&gt;&gt;=
function y=mimafun(x,a,b) 
%a,b = columns 
V=a+b*x; 
V(:,2)=-V; 
y=sum(max(V));
&lt;/codeblock&gt;

And then directly used:
&lt;codeblock language=&quot;matlab&quot;&gt;
&lt;&lt;fsolve direct use&gt;&gt;=
[X, Y]=fsolve(@(x) mimafun(x,a,b),0)
&lt;/codeblock&gt;


[[Category:Mathematics]]
[[Category:Programming language:MATLAB]]</text>
    </revision>
  </page>
  <page>
    <title>Complex Numbers (Ruby)</title>
    <id>1797</id>
    <revision>
      <id>3327</id>
      <timestamp>2006-03-15T11:00:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Complex Numbers (Ruby) moved to Complex numbers (Ruby): Match category</comment>
      <text xml:space="preserve">#redirect [[Complex numbers (Ruby)]]</text>
    </revision>
  </page>
  <page>
    <title>Complex numbers (C Plus Plus)</title>
    <id>1799</id>
    <revision>
      <id>3331</id>
      <timestamp>2006-03-16T15:13:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial data, arithmetic, conjugate, norm, exp, etc.</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs-&gt;getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.re());
    double b = c.im();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3332</id>
      <timestamp>2006-03-16T15:16:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Division */ Note on division by zero</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs-&gt;getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.re());
    double b = c.im();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3333</id>
      <timestamp>2006-03-16T15:20:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add source files</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs-&gt;getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.re());
    double b = c.im();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3334</id>
      <timestamp>2006-03-16T15:21:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Bad static</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs-&gt;getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.re());
    double b = c.im();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3335</id>
      <timestamp>2006-03-16T15:23:47Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Kill extra decl, other compiler fixes</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3354</id>
      <timestamp>2006-03-17T11:55:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+&lt;&lt;complex inline basic operations&gt;&gt;</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>3356</id>
      <timestamp>2006-03-17T12:02:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Forgot two inlines</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part, using ''this'' explicitly for clarity:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex(double re, double im);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex(double re, double im) {
    this-&gt;real = re;
    this-&gt;imag = im;
}
&lt;/codeblock&gt;

We also provide a default constructor yielding complex zero, a conversion constructor from a single real number (this is marked ''explicit'' to avoid confusing implicit coercions from &lt;code&gt;double&lt;/code&gt; to &lt;code&gt;complex&lt;/code&gt;):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex();
explicit complex(double re);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex::complex() {
    this-&gt;real = 0.0;
    this-&gt;imag = 0.0;
}

inline complex::complex(double re) {
    this-&gt;real = re;
    this-&gt;imag = 0.0;
}
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
inline complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>5367</id>
      <timestamp>2006-05-29T22:15:19Z</timestamp>
      <contributor>
        <ip>68.238.86.68</ip>
      </contributor>
      <comment>/* Constructors */</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part.  The values are initialized in the member initialization list; this is analogous to writing &lt;code&gt;double real = re;&lt;/code&gt; as opposed to &lt;code&gt;double real; real = re;&lt;/code&gt;, which is what happens if &lt;code&gt;real&lt;/code&gt; is initialized in the constructor body, with &lt;code&gt;{ this-&gt;real = re; }&lt;/code&gt;.  Additionally, the constructor is given default arguments of 0.0 for both &lt;code&gt;re&lt;/code&gt; and &lt;code&gt;im&lt;/code&gt;.  This means that if the constructor is called without any arguments, it will produce complex zero, if called with one argument it will produce a conversion from a real number to a complex number, and if given both arguments it produces a complete complex number.  The constructor is marked &lt;code&gt;explicit&lt;/code&gt; to prevent automatic conversion from a &lt;code&gt;double&lt;/code&gt; to a &lt;code&gt;complex&lt;/code&gt;.  The values are initialized :

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
explicit complex(double = 0.0, double = 0.0);
&lt;&lt;complex inline constructors&gt;&gt;=
explicit inline complex::complex(double re, double im) : real(re), imag(im) { }
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
inline static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef _COMPLEX_H_
#define _COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>12752</id>
      <timestamp>2008-03-09T13:30:03Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>/* Class and files */ names starting with underscore and capital letter are reserved for the implementation</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part.  The values are initialized in the member initialization list; this is analogous to writing &lt;code&gt;double real = re;&lt;/code&gt; as opposed to &lt;code&gt;double real; real = re;&lt;/code&gt;, which is what happens if &lt;code&gt;real&lt;/code&gt; is initialized in the constructor body, with &lt;code&gt;{ this-&gt;real = re; }&lt;/code&gt;.  Additionally, the constructor is given default arguments of 0.0 for both &lt;code&gt;re&lt;/code&gt; and &lt;code&gt;im&lt;/code&gt;.  This means that if the constructor is called without any arguments, it will produce complex zero, if called with one argument it will produce a conversion from a real number to a complex number, and if given both arguments it produces a complete complex number.  The constructor is marked &lt;code&gt;explicit&lt;/code&gt; to prevent automatic conversion from a &lt;code&gt;double&lt;/code&gt; to a &lt;code&gt;complex&lt;/code&gt;.  The values are initialized :

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
explicit complex(double = 0.0, double = 0.0);
&lt;&lt;complex inline constructors&gt;&gt;=
explicit inline complex::complex(double re, double im) : real(re), imag(im) { }
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
inline static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef COMPLEX_H_
#define COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef _COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>12753</id>
      <timestamp>2008-03-09T13:31:07Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>/* Class and files */ oops, overlooked mention of macro name in comment</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part.  The values are initialized in the member initialization list; this is analogous to writing &lt;code&gt;double real = re;&lt;/code&gt; as opposed to &lt;code&gt;double real; real = re;&lt;/code&gt;, which is what happens if &lt;code&gt;real&lt;/code&gt; is initialized in the constructor body, with &lt;code&gt;{ this-&gt;real = re; }&lt;/code&gt;.  Additionally, the constructor is given default arguments of 0.0 for both &lt;code&gt;re&lt;/code&gt; and &lt;code&gt;im&lt;/code&gt;.  This means that if the constructor is called without any arguments, it will produce complex zero, if called with one argument it will produce a conversion from a real number to a complex number, and if given both arguments it produces a complete complex number.  The constructor is marked &lt;code&gt;explicit&lt;/code&gt; to prevent automatic conversion from a &lt;code&gt;double&lt;/code&gt; to a &lt;code&gt;complex&lt;/code&gt;.  The values are initialized :

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
explicit complex(double = 0.0, double = 0.0);
&lt;&lt;complex inline constructors&gt;&gt;=
explicit inline complex::complex(double re, double im) : real(re), imag(im) { }
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
inline static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+b) + (c+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-b) + (c-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef COMPLEX_H_
#define COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>16673</id>
      <timestamp>2010-03-17T09:47:26Z</timestamp>
      <contributor>
        <username>Jona0497</username>
        <id>2002</id>
      </contributor>
      <minor/>
      <comment>/* Arithmetic operations */</comment>
      <text xml:space="preserve">This article implements a C++ class for representing complex numbers. Although this is a common introductory exercise, in most real programming situations the standard &lt;code&gt;std::complex&lt;/code&gt; class should be preferred.

== Data ==

We choose to use the fixed built-in IEEE floating-point type &lt;code&gt;double&lt;/code&gt; to represent the real and imaginary parts of the number. We choose this form instead of another representation such as polar form because it is the only form that makes all four basic arithmetic operations both simple and efficient.

Although we could template the class over the type used for each part, this could make some operations such as division act strangely with certain argument types. The data is made accessible via four accessor methods. We choose &quot;Re&quot; and &quot;Im&quot; after the mathematical operators &quot;Re&quot; and &quot;Im&quot;, standing for &quot;real part&quot; and &quot;imaginary part&quot;, respectively.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex data members&gt;&gt;=
double real;
double imag;

&lt;&lt;complex declarations&gt;&gt;=
double getRe();
double getIm();
void setRe(double value);
void setIm(double value);

&lt;&lt;complex inline accessors&gt;&gt;=
inline double complex::getRe() { return real; }
inline double complex::getIm() { return imag; }
inline void complex::setRe(double value) { real = value; }
inline void complex::setIm(double value) { imag = value; }
&lt;/codeblock&gt;

== Constructors ==

We provide one obvious constructor for &lt;code&gt;complex&lt;/code&gt;, based on its real and imaginary part.  The values are initialized in the member initialization list; this is analogous to writing &lt;code&gt;double real = re;&lt;/code&gt; as opposed to &lt;code&gt;double real; real = re;&lt;/code&gt;, which is what happens if &lt;code&gt;real&lt;/code&gt; is initialized in the constructor body, with &lt;code&gt;{ this-&gt;real = re; }&lt;/code&gt;.  Additionally, the constructor is given default arguments of 0.0 for both &lt;code&gt;re&lt;/code&gt; and &lt;code&gt;im&lt;/code&gt;.  This means that if the constructor is called without any arguments, it will produce complex zero, if called with one argument it will produce a conversion from a real number to a complex number, and if given both arguments it produces a complete complex number.  The constructor is marked &lt;code&gt;explicit&lt;/code&gt; to prevent automatic conversion from a &lt;code&gt;double&lt;/code&gt; to a &lt;code&gt;complex&lt;/code&gt;.  The values are initialized :

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
explicit complex(double = 0.0, double = 0.0);
&lt;&lt;complex inline constructors&gt;&gt;=
explicit inline complex::complex(double re, double im) : real(re), imag(im) { }
&lt;/codeblock&gt;

Finally, we provide a static method initializing a complex object from the polar form (radius and angle in the plane). It uses this formula to convert to the internal rectangular form:

: &lt;math&gt;re^{i\theta} = r\cos \theta + (r\sin \theta)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
static complex fromPolar(double radius, double angle);
&lt;&lt;complex inline constructors&gt;&gt;=
inline static complex complex::fromPolar(double radius, double angle) {
    return complex(radius*cos(angle), radius*sin(angle));
}
&lt;/codeblock&gt;

We need math.h for sine and cosine on doubles:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Arithmetic operations ==

We will implement the four simple arithmetic operations: add, subtract, multiply, and divide. We start with the first three of these, making use of the usual formulas, shown below. C++'s operator overloading makes it relatively simple to make these operations available using the same binary infix syntax used in mathematical notation.

:&lt;math&gt;(a + bi) + (c + di) = (a+c) + (b+d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) - (c + di) = (a-c) + (b-d)i&lt;/math&gt;
:&lt;math&gt;(a + bi) \times (c + di) = (ac - bd) + (ad + bc)i&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(complex rhs);
complex operator-(complex rhs);
complex operator*(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(complex rhs) {
    return complex(this-&gt;real + rhs.real, this-&gt;imag + rhs.imag);
}
inline complex complex::operator-(complex rhs) {
    return complex(this-&gt;real - rhs.real, this-&gt;imag - rhs.imag);
}
inline complex complex::operator*(complex rhs) {
    return complex(this-&gt;real*rhs.real - this-&gt;imag*rhs.imag,
                   this-&gt;real*rhs.imag + this-&gt;imag*rhs.real);
}
&lt;/codeblock&gt;

These operations, especially multiplication, are simpler when one operand is a real number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator+(double rhs);
complex operator-(double rhs);
complex operator*(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator+(double rhs) {
    return complex(this-&gt;real + rhs, this-&gt;imag);
}
inline complex complex::operator-(double rhs) {
    return complex(this-&gt;real - rhs, this-&gt;imag);
}
inline complex complex::operator*(double rhs) {
    return complex(this-&gt;real * rhs, this-&gt;imag * rhs);
}
&lt;/codeblock&gt;

We also define named methods for the frequently-used operations of taking the complex conjugate and finding the norm (denoted abs(''z'') or |''z''|) of a complex number:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex conjugate();
double norm();
&lt;&lt;complex inline basic operations&gt;&gt;=
inline double complex::norm() {
    return this-&gt;real*this-&gt;real + this-&gt;imag*this-&gt;imag;
}
inline complex complex::conjugate() {
    return complex(this-&gt;real, -this-&gt;imag);
}
&lt;/codeblock&gt;

=== Division ===

Division is a bit more complicated. Although there is a general formula, we prefer to simplify things by first defining division by a real number, which, like multiplication by a real number, simply scales each part:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(double rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(double rhs) {
    return complex(this-&gt;real/rhs, this-&gt;imag/rhs);
}
&lt;/codeblock&gt;

Now, we can combine complex multiplication, division by reals, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using this formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex declarations&gt;&gt;=
complex operator/(complex rhs);
&lt;&lt;complex inline arithmetic methods&gt;&gt;=
inline complex complex::operator/(complex rhs) {
    return (*this)*rhs.conjugate()/rhs.norm();
}
&lt;/codeblock&gt;

Note that division by the real or complex number zero is not allowed and will store a floating-point result such as NaN or infinity in the part values, but division by a complex number with only the real or imaginary component zero is okay.

=== Left-hand side reals ===

All that remains is the case where doubles are on the left hand side and complex numbers are on the right. However, because the object can only appear on the left-hand side of operator methods that are members of that object, and because we cannot extend built-in types, we must use global (top-level) methods to handle this case. It's a common practice to make such methods ''friend'' functions of the class, but this is unneccessary in this case, as they just delegate to previously defined public operations:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex operator+(double lhs, complex rhs);
complex operator-(double lhs, complex rhs);
complex operator*(double lhs, complex rhs);
complex operator/(double lhs, complex rhs);

&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;=
inline complex operator+(double lhs, complex rhs) {
    return rhs + lhs;
}
inline complex operator-(double lhs, complex rhs) {
    return complex(lhs - rhs.getRe(), rhs.getIm());
}
inline complex operator*(double lhs, complex rhs) {
    return rhs * lhs;
}
inline complex operator/(double lhs, complex rhs) {
    return rhs.conjugate()*lhs/rhs.norm();
}
&lt;/codeblock&gt;

The main simplification possible for division given a real first argument is that we can use the version of multiplication taking a real argument.

== Other operations ==

Complex number computations often make use of certain [http://en.wikipedia.org/wiki/Holomorphic_function holomorphic functions] that generalize real functions. The simplest is the [http://en.wikipedia.org/wiki/Exponential_function exponential function], an entire function that can be defined in terms of real-valued functions by:

: &lt;math&gt;e^{a + bi} = e^a(\cos b) + e^a(\sin b)i&lt;/math&gt;

where ''a'',''b'' are real. This can be implemented using some additional functions from math.h:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex top-level declarations&gt;&gt;=
complex exp(complex c);
&lt;&lt;exp function&gt;&gt;=
complex exp(complex c) {
    double e_to_a = exp(c.getRe());
    double b = c.getIm();
    return complex(e_to_a*cos(b), e_to_a*sin(b));
}
&lt;/codeblock&gt;

== Class and files ==

Here's our complete class and files produced so far:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;complex.h&gt;&gt;=
#ifndef COMPLEX_H_
#define COMPLEX_H_

&lt;&lt;header files&gt;&gt;

class complex {
public:
    &lt;&lt;complex declarations&gt;&gt;
private:
    &lt;&lt;complex data members&gt;&gt;
};

&lt;&lt;complex top-level declarations&gt;&gt;

&lt;&lt;complex inline accessors&gt;&gt;
&lt;&lt;complex inline constructors&gt;&gt;
&lt;&lt;complex inline arithmetic methods&gt;&gt;
&lt;&lt;complex inline basic operations&gt;&gt;
&lt;&lt;complex inline top-level arithmetic operations&gt;&gt;

#endif // #ifndef COMPLEX_H_

&lt;&lt;complex.cpp&gt;&gt;=
#include &quot;complex.h&quot;

&lt;&lt;exp function&gt;&gt;

&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
  </page>
  <page>
    <title>Complex numbers (Java)</title>
    <id>1955</id>
    <revision>
      <id>4426</id>
      <timestamp>2006-05-07T02:38:09Z</timestamp>
      <contributor>
        <ip>222.107.225.30</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;==
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;==
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;==
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;==
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex Conjugate&gt;&gt;==
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four Basic Arithmetic Operations&gt;&gt;==
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar Form&gt;&gt;==
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String Representation&gt;&gt;==
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;==
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four Basic Arithmetic Operations&gt;&gt;
  &lt;&lt;Polar Form&gt;&gt;
  &lt;&lt;Complex Conjugate&gt;&gt;  
  &lt;&lt;String Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4427</id>
      <timestamp>2006-05-07T02:42:52Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Constructors */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;==
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;==
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;==
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;==
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex Conjugate&gt;&gt;==
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four Basic Arithmetic Operations&gt;&gt;==
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar Form&gt;&gt;==
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String Representation&gt;&gt;==
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;==
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four Basic Arithmetic Operations&gt;&gt;
  &lt;&lt;Polar Form&gt;&gt;
  &lt;&lt;Complex Conjugate&gt;&gt;  
  &lt;&lt;String Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4428</id>
      <timestamp>2006-05-07T02:45:03Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Test */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;==
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;==
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;==
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;==
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex Conjugate&gt;&gt;==
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four Basic Arithmetic Operations&gt;&gt;==
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar Form&gt;&gt;==
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String Representation&gt;&gt;==
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;==
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four Basic Arithmetic Operations&gt;&gt;
  &lt;&lt;Polar Form&gt;&gt;
  &lt;&lt;Complex Conjugate&gt;&gt;  
  &lt;&lt;String Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4429</id>
      <timestamp>2006-05-07T02:51:48Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* The Whole Class */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;==
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;==
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;==
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;==
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex Conjugate&gt;&gt;==
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four Basic Arithmetic Operations&gt;&gt;==
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar Form&gt;&gt;==
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String Representation&gt;&gt;==
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;==
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;==
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four Basic Arithmetic Operations&gt;&gt;
  &lt;&lt;Polar Form&gt;&gt;
  &lt;&lt;Complex Conjugate&gt;&gt;  
  &lt;&lt;String Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4432</id>
      <timestamp>2006-05-07T03:13:42Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;==
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;==
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;==
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;==
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;==
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;==
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar_Form&gt;&gt;==
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;==
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;==
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;==
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4435</id>
      <timestamp>2006-05-07T05:05:12Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>fix codeblock ids</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock&gt;
  &lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;
== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4436</id>
      <timestamp>2006-05-07T05:07:42Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Polar Form */ fix codeblock id</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot;
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      }
      else {
        return(this.re + &quot;+ &quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4439</id>
      <timestamp>2006-05-07T06:14:47Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* String Representation */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / op.getNorm());
    result.setIm(result.getIm() / op.getNorm());
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4440</id>
      <timestamp>2006-05-07T06:38:07Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Four Basic Arithmetic Operations */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }
  
  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4442</id>
      <timestamp>2006-05-07T06:44:32Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Four Basic Arithmetic Operations */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(1, 0);
    Complex b = new Complex(0, 1);
    Complex c = new Complex(1, 1);
    Complex d = new Complex(3, 4);
    System.out.println(a);
    System.out.println(b);
    System.out.println(a.add(b));
    System.out.println(b.getAngle());
    System.out.println(d.getNorm());
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4444</id>
      <timestamp>2006-05-07T06:45:52Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Test */</comment>
      <text xml:space="preserve">{{develop}}
Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>4445</id>
      <timestamp>2006-05-07T06:48:24Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>remove develop tag</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>5283</id>
      <timestamp>2006-05-28T14:38:01Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Getter and Setter where wrong way around</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>12302</id>
      <timestamp>2008-01-24T06:42:18Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>14660</id>
      <timestamp>2008-09-19T21:44:39Z</timestamp>
      <contributor>
        <ip>64.20.168.21</ip>
      </contributor>
      <comment>/* Polar Form */</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    if (this.re == 0) {
        return 0;
    }
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>14661</id>
      <timestamp>2008-09-19T21:46:38Z</timestamp>
      <contributor>
        <ip>64.20.168.21</ip>
      </contributor>
      <comment>/* Polar Form */</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    if (this.im == 0) {
        if (this.re &lt; 0) {
            return Math.PI;
        }
        return 0;
    }
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>14662</id>
      <timestamp>2008-09-19T21:47:02Z</timestamp>
      <contributor>
        <ip>64.20.168.21</ip>
      </contributor>
      <comment>/* Polar Form */</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    if (this.im == 0) {
        if (this.re &lt; 0) {
            return Math.PI;
        }
        return 0;
    }
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>14668</id>
      <timestamp>2008-09-20T17:24:30Z</timestamp>
      <contributor>
        <ip>71.147.13.131</ip>
      </contributor>
      <comment>undo edits by 64.20.168.21; unnecessary as Math.atan2 already does that</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16042</id>
      <timestamp>2009-01-26T14:11:54Z</timestamp>
      <contributor>
        <ip>195.37.1.145</ip>
      </contributor>
      <comment>/* Four Basic Arithmetic Operations */</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
    result.setRe(result.getRe() / (op.getNorm() * op.getNorm()));
    result.setIm(result.getIm() / (op.getNorm() * op.getNorm()));
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||^2}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16043</id>
      <timestamp>2009-01-26T14:31:14Z</timestamp>
      <contributor>
        <ip>195.37.1.145</ip>
      </contributor>
      <comment>Division using op.getNorm()*op.getNorm() was very inefficient.</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
   double opNormSq = op.getRe()*op.getRe()+op.getIm()*op.getIm();
    result.setRe(result.getRe() / opNormSq);
    result.setIm(result.getIm() / opNormSq);
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||^2}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16044</id>
      <timestamp>2009-01-26T14:35:09Z</timestamp>
      <contributor>
        <ip>195.37.1.145</ip>
      </contributor>
      <comment>added test of division by multiplying afterwards again.</comment>
      <text xml:space="preserve">Java does not support standard complex number library. However, it is not difficult to write a complex number class. Also, Apache Commons Math has a [http://commons.apache.org/math/apidocs/org/apache/commons/math/complex/Complex.html Complex] class.

== Data ==
A complex number is composed of two part - a real part &lt;code&gt;re&lt;/code&gt; and an imaginary part &lt;code&gt;im&lt;/code&gt;. We use IEEE floating-point type &lt;code&gt;double&lt;/code&gt; for both part.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Data&gt;&gt;=
  private double re;
  private double im;
&lt;/codeblock&gt;

== Constructors ==
There are three constructors.
# Without any argument, it initializes a zero complex number.
# Otherwise, it initializes a complex number for given real part and imaginary part. 
# We also copy a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Constructor&gt;&gt;=
  public Complex () {
    this.re = 0;
    this.im = 0;
  }
  
  public Complex(double re, double im) {
    this.re = re;
    this.im = im;
  }
  
  public Complex(Complex input) {
    this.re = input.getRe();
    this.im = input.getIm();
  }
&lt;/codeblock&gt;

== Getter and Setter ==
The implementation of both getter and setter are quite straightforward.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Setter&gt;&gt;=
  public void setRe(double re) {
    this.re = re;
  }
  
  public void setIm(double im) {
    this.im = im;
  }   
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Getter&gt;&gt;=
  public double getRe() {
    return this.re;
  }
  
  public double getIm() {
    return this.im;
  }
&lt;/codeblock&gt;

==Complex Conjugate==
The &lt;code&gt;getConjugate&lt;/code&gt; method returns the complex conjugate of a given complex number.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex_Conjugate&gt;&gt;=
  public Complex getConjugate() {
    return new Complex(this.re, this.im * (-1));
  }
&lt;/codeblock&gt;

== Four Basic Arithmetic Operations ==
Addition, Subtraction, multiplication, and division are four basic arithmetic operations.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;=
  public Complex add(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re + op.getRe());
    result.setIm(this.im + op.getIm());
    return result;
  }
  
  public Complex sub(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re - op.getRe());
    result.setIm(this.im - op.getIm());
    return result;
  }
  
  public Complex mul(Complex op) {
    Complex result = new Complex();
    result.setRe(this.re * op.getRe() - this.im * op.getIm());
    result.setIm(this.re * op.getIm() + this.im * op.getRe());
    return result;
  }

  public Complex div(Complex op) {
    Complex result = new Complex(this);
    result = result.mul(op.getConjugate());
   double opNormSq = op.getRe()*op.getRe()+op.getIm()*op.getIm();
    result.setRe(result.getRe() / opNormSq);
    result.setIm(result.getIm() / opNormSq);
    return result;
  }
&lt;/codeblock&gt;  
The division method (&lt;code&gt;div&lt;/code&gt;) is the only method which is non-trivial. We can combine complex multiplication, division, and the complex conjugate and norm operations to perform division of arbitrary complex numbers using the following formula:

:&lt;math&gt;\frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(a + bi)(c - di)}{||c + di||^2}.&lt;/math&gt;

== Polar Form ==
&lt;codeblock language=java&gt;
&lt;&lt;Polar_Form&gt;&gt;=
  public Complex fromPolar(double magnitude, double angle) {
    Complex result = new Complex();
    result.setRe(magnitude * Math.cos(angle));
    result.setIm(magnitude * Math.sin(angle));
    return result;
  }

  public double getNorm() {
    return Math.sqrt(this.re * this.re + this.im * this.im);
  }
  
  public double getAngle() {
    return Math.atan2(this.im, this.re);
  }
&lt;/codeblock&gt;

== String Representation ==
This chunk returns string representation of a given complex number. We use &lt;code&gt;i&lt;/code&gt; for the imaginary unit. If one part of a given complex number is zero, we omit it without printing &quot;0.&quot; We also take the negative imaginary part into consideration.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;String_Representation&gt;&gt;=
  public String toString() {
    if (this.re == 0) {
      if (this.im == 0) {
        return &quot;0&quot;;
      } else {
        return (this.im + &quot;i&quot;);
      }
    } else {
      if (this.im == 0) {
        return String.valueOf(this.re);
      } else if (this.im &lt; 0) {
        return(this.re + &quot; &quot; + this.im + &quot;i&quot;);
      } else {
        return(this.re + &quot; +&quot; + this.im + &quot;i&quot;);
      }
    }
  }
&lt;/codeblock&gt;

== Test ==
This chunk is used to test.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test&gt;&gt;=
  public static void main(String argv[]) {
    Complex a = new Complex(3, 4);
    Complex b = new Complex(1, -100);
    System.out.println(a.getNorm());
    System.out.println(b.getAngle());
    System.out.println(a.mul(b));
    System.out.println(a.div(b));
    System.out.println(a.div(b).mul(b));
  }
&lt;/codeblock&gt;

== The Whole Class ==
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Complex.java&gt;&gt;=
public class Complex {
  &lt;&lt;Constructor&gt;&gt;
  &lt;&lt;Getter&gt;&gt;
  &lt;&lt;Setter&gt;&gt;
  &lt;&lt;Four_Basic_Arithmetic_Operations&gt;&gt;
  &lt;&lt;Polar_Form&gt;&gt;
  &lt;&lt;Complex_Conjugate&gt;&gt;  
  &lt;&lt;String_Representation&gt;&gt;
  &lt;&lt;Data&gt;&gt;
  &lt;&lt;Test&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
  </page>
  <page>
    <title>Complex numbers (Ruby)</title>
    <id>1795</id>
    <revision>
      <id>3318</id>
      <timestamp>2006-03-14T23:51:40Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>Starting out</comment>
      <text xml:space="preserve">{{develop}}

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a
    @imag = b
  when :polar
    @magnitude = a
    @theta = b
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.real * other,
      self.imag * other
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.real / other,
      self.imag / other
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 6 )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 4 )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta (1.0 / 3.0), z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3 )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(0.5), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z4.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3319</id>
      <timestamp>2006-03-14T23:53:45Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>Removed the duplication of class Complex in complex.rb</comment>
      <text xml:space="preserve">{{develop}}

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a
    @imag = b
  when :polar
    @magnitude = a
    @theta = b
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.real * other,
      self.imag * other
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.real / other,
      self.imag / other
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 6 )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 4 )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta (1.0 / 3.0), z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3 )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(0.5), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z4.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3320</id>
      <timestamp>2006-03-14T23:54:38Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>Resolved warning in complex_test.rb</comment>
      <text xml:space="preserve">{{develop}}

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a
    @imag = b
  when :polar
    @magnitude = a
    @theta = b
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.real * other,
      self.imag * other
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.real / other,
      self.imag / other
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 6 )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3 )
  z2 = Complex.new( 2, Math::PI / 4 )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3 )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(0.5), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z4.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3321</id>
      <timestamp>2006-03-15T00:13:33Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>Bug fixing</comment>
      <text xml:space="preserve">{{develop}}

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3322</id>
      <timestamp>2006-03-15T00:15:21Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <minor/>
      <comment>Done!</comment>
      <text xml:space="preserve">== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3324</id>
      <timestamp>2006-03-15T00:24:31Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <minor/>
      <comment>Added to category &quot;Complex numbers&quot;</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3326</id>
      <timestamp>2006-03-15T11:00:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Complex Numbers (Ruby) moved to Complex numbers (Ruby)</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    raise NotImplementedError
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

''[Exponentiation with a complex exponent is yet to be implemented]''

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3340</id>
      <timestamp>2006-03-16T19:34:42Z</timestamp>
      <contributor>
        <username>Lukfugl</username>
        <id>8</id>
      </contributor>
      <comment>/* Exponentiation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation. To implement exponentiation with a complex exponent, we'll make use of a change in base:

:&lt;math&gt;q^z = e^{z \ln q}&lt;/math&gt;

Letting &lt;math&gt;a = \Re(z \ln q)&lt;/math&gt; and &lt;math&gt;b = \Im(z \ln q)&lt;/math&gt;, we can derive:

:&lt;math&gt;q^z = e^{a + ib}&lt;/math&gt;
:&lt;math&gt;q^z = e^a e^{ib}&lt;/math&gt;
:&lt;math&gt;|q^z| = e^a&lt;/math&gt;
:&lt;math&gt;\theta(q^z) = b&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    log = &lt;&lt;log&gt;&gt;
    z_prime = other * log
    Complex.new(
      Math.exp(z_prime.real),
      z_prime.imag,
      :polar
    )
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

To calculate the logarithm of &lt;math&gt;q&lt;/math&gt; when &lt;math&gt;q&lt;/math&gt; is complex, we utilize the polar/phasor representation:

:&lt;math&gt;\ln q = \ln re^{i\theta} = \ln r + i\theta&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;log&gt;&gt;=
Complex.new(
  Math.ln(self.magnitude),
  self.theta,
  :coordinate
)
&lt;/codeblock&gt;

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>6696</id>
      <timestamp>2006-07-11T12:41:45Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Complex numbers (Ruby)]] moved to [[Complex numbers (Ruby) on Wheels]]</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation. To implement exponentiation with a complex exponent, we'll make use of a change in base:

:&lt;math&gt;q^z = e^{z \ln q}&lt;/math&gt;

Letting &lt;math&gt;a = \Re(z \ln q)&lt;/math&gt; and &lt;math&gt;b = \Im(z \ln q)&lt;/math&gt;, we can derive:

:&lt;math&gt;q^z = e^{a + ib}&lt;/math&gt;
:&lt;math&gt;q^z = e^a e^{ib}&lt;/math&gt;
:&lt;math&gt;|q^z| = e^a&lt;/math&gt;
:&lt;math&gt;\theta(q^z) = b&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    log = &lt;&lt;log&gt;&gt;
    z_prime = other * log
    Complex.new(
      Math.exp(z_prime.real),
      z_prime.imag,
      :polar
    )
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

To calculate the logarithm of &lt;math&gt;q&lt;/math&gt; when &lt;math&gt;q&lt;/math&gt; is complex, we utilize the polar/phasor representation:

:&lt;math&gt;\ln q = \ln re^{i\theta} = \ln r + i\theta&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;log&gt;&gt;=
Complex.new(
  Math.ln(self.magnitude),
  self.theta,
  :coordinate
)
&lt;/codeblock&gt;

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>6872</id>
      <timestamp>2006-07-11T14:16:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Complex numbers (Ruby) on Wheels]] moved to [[Complex numbers (Ruby)]]: revert</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= @real**2 + @imag**2
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation. To implement exponentiation with a complex exponent, we'll make use of a change in base:

:&lt;math&gt;q^z = e^{z \ln q}&lt;/math&gt;

Letting &lt;math&gt;a = \Re(z \ln q)&lt;/math&gt; and &lt;math&gt;b = \Im(z \ln q)&lt;/math&gt;, we can derive:

:&lt;math&gt;q^z = e^{a + ib}&lt;/math&gt;
:&lt;math&gt;q^z = e^a e^{ib}&lt;/math&gt;
:&lt;math&gt;|q^z| = e^a&lt;/math&gt;
:&lt;math&gt;\theta(q^z) = b&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    log = &lt;&lt;log&gt;&gt;
    z_prime = other * log
    Complex.new(
      Math.exp(z_prime.real),
      z_prime.imag,
      :polar
    )
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

To calculate the logarithm of &lt;math&gt;q&lt;/math&gt; when &lt;math&gt;q&lt;/math&gt; is complex, we utilize the polar/phasor representation:

:&lt;math&gt;\ln q = \ln re^{i\theta} = \ln r + i\theta&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;log&gt;&gt;=
Complex.new(
  Math.ln(self.magnitude),
  self.theta,
  :coordinate
)
&lt;/codeblock&gt;

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>15719</id>
      <timestamp>2009-01-01T23:28:01Z</timestamp>
      <contributor>
        <username>Peterhil</username>
        <id>1762</id>
      </contributor>
      <comment>/* Accessors */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= Math.hypot(@real, @imag)
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation. To implement exponentiation with a complex exponent, we'll make use of a change in base:

:&lt;math&gt;q^z = e^{z \ln q}&lt;/math&gt;

Letting &lt;math&gt;a = \Re(z \ln q)&lt;/math&gt; and &lt;math&gt;b = \Im(z \ln q)&lt;/math&gt;, we can derive:

:&lt;math&gt;q^z = e^{a + ib}&lt;/math&gt;
:&lt;math&gt;q^z = e^a e^{ib}&lt;/math&gt;
:&lt;math&gt;|q^z| = e^a&lt;/math&gt;
:&lt;math&gt;\theta(q^z) = b&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    log = &lt;&lt;log&gt;&gt;
    z_prime = other * log
    Complex.new(
      Math.exp(z_prime.real),
      z_prime.imag,
      :polar
    )
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

To calculate the logarithm of &lt;math&gt;q&lt;/math&gt; when &lt;math&gt;q&lt;/math&gt; is complex, we utilize the polar/phasor representation:

:&lt;math&gt;\ln q = \ln re^{i\theta} = \ln r + i\theta&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;log&gt;&gt;=
Complex.new(
  Math.ln(self.magnitude),
  self.theta,
  :coordinate
)
&lt;/codeblock&gt;

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>15720</id>
      <timestamp>2009-01-01T23:29:42Z</timestamp>
      <contributor>
        <username>Peterhil</username>
        <id>1762</id>
      </contributor>
      <comment>/* Accessors */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the &lt;code&gt;Complex&lt;/code&gt; class. This class includes initialization and accessors for to query and build the complex number as well as basic arithmetic functions:

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;initialization&gt;&gt;
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We will provide access to both the coordinate and polar/phasor representations of the complex number.

=== Initialization ===

The initialization method will store only the starting representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;initialization&gt;&gt;=
def initialize( a, b, type=:coordinate )
  case type
  when :coordinate
    @real = a.to_f
    @imag = b.to_f
  when :polar
    @magnitude = a.to_f
    @theta = b.to_f
  else
    raise ArgumentError, &quot;unknown type '#{type}'&quot;
  end
end
&lt;/codeblock&gt;

=== Accessors ===

Access to a representation other than the original is provided on demand, with caching:

&lt;codeblock language=Ruby&gt;
&lt;&lt;accessors&gt;&gt;=
def real
  @real ||= @magnitude * Math.cos(@theta)
end

def imag
  @imag ||= @magnitude * Math.sin(@theta)
end

def magnitude
  @magnitude ||= Math.hypot(@real, @imag)
end

def theta
  @theta ||= Math.atan2(@imag, @real)
end
&lt;/codeblock&gt;

== Arithmetic ==

Core arithmetic operations provided are addition, subtraction, multiplication, division and exponentiation. The arithmetic interface is unified to accept either complex or real arguments, with any necessary distinction made in the method itself.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;addition&gt;&gt;=
def +( other )
  if Complex === other
    Complex.new(
      self.real + other.real,
      self.imag + other.imag
    )
  else
    Complex.new(
      self.real + other,
      self.imag
    )
  end
end

&lt;&lt;subtraction&gt;&gt;=
def -( other )
  if Complex === other
    Complex.new(
      self.real - other.real,
      self.imag - other.imag
    )
  else
    Complex.new(
      self.real - other,
      self.imag
    )
  end

end
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar/phasor representation:

&lt;codeblock language=Ruby&gt;
&lt;&lt;multiplication&gt;&gt;=
def *( other )
  if Complex === other
    Complex.new(
      self.magnitude * other.magnitude,
      self.theta + other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude * other,
      self.theta,
      :polar
    )
  end
end

&lt;&lt;division&gt;&gt;=
def /( other )
  if Complex === other
    Complex.new(
      self.magnitude / other.magnitude,
      self.theta - other.theta,
      :polar
    )
  else
    Complex.new(
      self.magnitude / other,
      self.theta,
      :polar
    )
  end
end
&lt;/codeblock&gt;

=== Exponentiation ===

Exponentiation with a real exponent is easy using the polar/phasor representation. To implement exponentiation with a complex exponent, we'll make use of a change in base:

:&lt;math&gt;q^z = e^{z \ln q}&lt;/math&gt;

Letting &lt;math&gt;a = \Re(z \ln q)&lt;/math&gt; and &lt;math&gt;b = \Im(z \ln q)&lt;/math&gt;, we can derive:

:&lt;math&gt;q^z = e^{a + ib}&lt;/math&gt;
:&lt;math&gt;q^z = e^a e^{ib}&lt;/math&gt;
:&lt;math&gt;|q^z| = e^a&lt;/math&gt;
:&lt;math&gt;\theta(q^z) = b&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;exponentiation&gt;&gt;=
def **( other )
  if Complex === other
    log = &lt;&lt;log&gt;&gt;
    z_prime = other * log
    Complex.new(
      Math.exp(z_prime.real),
      z_prime.imag,
      :polar
    )
  else
    Complex.new(
      self.magnitude ** other,
      self.theta * other,
      :polar
    )
  end
end
&lt;/codeblock&gt;

To calculate the logarithm of &lt;math&gt;q&lt;/math&gt; when &lt;math&gt;q&lt;/math&gt; is complex, we utilize the polar/phasor representation:

:&lt;math&gt;\ln q = \ln re^{i\theta} = \ln r + i\theta&lt;/math&gt;

&lt;codeblock language=Ruby&gt;
&lt;&lt;log&gt;&gt;=
Complex.new(
  Math.ln(self.magnitude),
  self.theta,
  :coordinate
)
&lt;/codeblock&gt;

== Test Suite ==

To build a test suite for this class we'll use the &lt;code&gt;Test::Unit&lt;/code&gt; library. First we place the class in a file, then include that class and build a &lt;code&gt;TestCase&lt;/code&gt;.

&lt;codeblock language=Ruby&gt;
&lt;&lt;complex.rb&gt;&gt;=
&lt;&lt;complex class&gt;&gt;

&lt;&lt;complex_test.rb&gt;&gt;=
require 'test/unit'
require './complex'

class TestComplex &lt; Test::Unit::TestCase
  &lt;&lt;define tolerance&gt;&gt;
  &lt;&lt;test initialization from coordinates&gt;&gt;
  &lt;&lt;test initialization from polar&gt;&gt;
  &lt;&lt;test polar access from coordinates&gt;&gt;
  &lt;&lt;test coordinate access from polar&gt;&gt;
  &lt;&lt;test addition&gt;&gt;
  &lt;&lt;test subtraction&gt;&gt;
  &lt;&lt;test multiplication&gt;&gt;
  &lt;&lt;test division&gt;&gt;
  &lt;&lt;test real exponentiation&gt;&gt;
end
&lt;/codeblock&gt;

=== Initialization ===

First we'll test that initialization works as expected:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test initialization from coordinates&gt;&gt;=
def test_initialization_from_coordinates
  z = Complex.new( 1, 2 )
  assert_equal 1, z.real
  assert_equal 2, z.imag
end

&lt;&lt;test initialization from polar&gt;&gt;=
def test_initialization_from_polar
  z = Complex.new( 1, 2, :polar )
  assert_equal 1, z.magnitude
  assert_equal 2, z.theta
end
&lt;/codeblock&gt;

=== Accessors ===

Next we verify that our on-demand accessors work correctly. These and the arithmetic checks all require that we define a tolerance first:

&lt;codeblock language=Ruby&gt;
&lt;&lt;define tolerance&gt;&gt;=
TOLERANCE = 0.001

&lt;&lt;test polar access from coordinates&gt;&gt;=
def test_polar_access_from_coordinates
  z = Complex.new( 1, 1 )
  assert_in_delta Math.sqrt(2), z.magnitude, TOLERANCE
  assert_in_delta Math::PI/4, z.theta, TOLERANCE
end

&lt;&lt;test coordinate access from polar&gt;&gt;=
def test_coordinates_access_from_polar
  z = Complex.new( 1, Math::PI / 4, :polar )
  assert_in_delta Math.sqrt(0.5), z.real, TOLERANCE
  assert_in_delta Math.sqrt(0.5), z.imag, TOLERANCE
end
&lt;/codeblock&gt;

=== Arithmetic ===

Finally we'll check all of our arithmetic methods:

&lt;codeblock language=Ruby&gt;
&lt;&lt;test addition&gt;&gt;=
def test_addition
  z1 = Complex.new( 1, 2 )
  z2 = Complex.new( 3, 4 )

  z3 = z1 + z2
  assert_equal 4, z3.real
  assert_equal 6, z3.imag

  z4 = z1 + 5
  assert_equal 6, z4.real
  assert_equal 2, z4.imag
end

&lt;&lt;test subtraction&gt;&gt;=
def test_subtraction
  z1 = Complex.new( 3, 4 )
  z2 = Complex.new( 2, 1 )

  z3 = z1 - z2
  assert_equal 1, z3.real
  assert_equal 3, z3.imag

  z4 = z1 - 2
  assert_equal 1, z4.real
  assert_equal 4, z4.imag
end

&lt;&lt;test multiplication&gt;&gt;=
def test_multiplication
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 6, :polar )

  z3 = z1 * z2
  assert_equal 2, z3.magnitude
  assert_in_delta Math::PI / 2, z3.theta, TOLERANCE

  z4 = z1 * 5
  assert_equal 5, z4.magnitude
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test division&gt;&gt;=
def test_division
  z1 = Complex.new( 1, Math::PI / 3, :polar )
  z2 = Complex.new( 2, Math::PI / 4, :polar )

  z3 = z1 / z2
  assert_in_delta 0.5, z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 12, z3.theta, TOLERANCE

  z4 = z1 / 3
  assert_in_delta 1.0/3.0, z4.magnitude, TOLERANCE
  assert_equal Math::PI / 3, z4.theta
end

&lt;&lt;test real exponentiation&gt;&gt;=
def test_exponentiation
  z1 = Complex.new( 2, Math::PI / 3, :polar )

  z2 = z1 ** 3
  assert_equal 8, z2.magnitude
  assert_in_delta Math::PI, z2.theta, TOLERANCE

  z3 = z1 ** 0.5
  assert_in_delta Math.sqrt(2), z3.magnitude, TOLERANCE
  assert_in_delta Math::PI / 6, z3.theta, TOLERANCE
end
&lt;/codeblock&gt;</text>
    </revision>
  </page>
  <page>
    <title>Complex numbers (Scala)</title>
    <id>3242</id>
    <revision>
      <id>11343</id>
      <timestamp>2007-10-28T20:26:48Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>11344</id>
      <timestamp>2007-10-28T20:27:09Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11345</id>
      <timestamp>2007-10-28T20:33:57Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;

We provide two concrete subclasses to easily create a complex number with its rectangular coordinates or polar coordinates.

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11346</id>
      <timestamp>2007-10-28T20:34:31Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions.

We provide two concrete subclasses to easily create a complex number with its rectangular coordinates or polar coordinates.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end
&lt;/codeblock&gt;


[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11347</id>
      <timestamp>2007-10-28T20:40:56Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;



[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11348</id>
      <timestamp>2007-10-28T20:41:26Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;



[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11349</id>
      <timestamp>2007-10-28T20:45:57Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

== Accessors ==
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11350</id>
      <timestamp>2007-10-28T20:54:55Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic are defined in the abstract Complex base class.

  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11351</id>
      <timestamp>2007-10-28T20:55:19Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11352</id>
      <timestamp>2007-10-28T21:00:20Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11353</id>
      <timestamp>2007-10-28T21:01:15Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;&lt;exponentiation&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11354</id>
      <timestamp>2007-10-28T21:01:54Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11355</id>
      <timestamp>2007-10-28T21:57:45Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=c&gt;
&lt;&lt;foo.c&gt;&gt;=
int main() { return 0; }
&lt;/codeblock&gt;



[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11356</id>
      <timestamp>2007-10-28T21:58:18Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11357</id>
      <timestamp>2007-10-28T22:05:35Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;CountingSortTest.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11358</id>
      <timestamp>2007-10-28T22:08:05Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11359</id>
      <timestamp>2007-10-28T22:11:01Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;polar complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11360</id>
      <timestamp>2007-10-28T22:13:15Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;polar complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangular complex class&gt;&gt;
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}
&lt;&lt;polar complex class&gt;&gt;
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11361</id>
      <timestamp>2007-10-28T22:14:00Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

&lt;&lt;polar complex class&gt;&gt;=
class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}
&lt;&lt;polar complex class&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11362</id>
      <timestamp>2007-10-28T22:15:16Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangular complex class&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}
&lt;&lt;polar complex class&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11363</id>
      <timestamp>2007-10-28T22:15:41Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11364</id>
      <timestamp>2007-10-28T22:16:07Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;initialization&gt;&gt;=

class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11365</id>
      <timestamp>2007-10-28T22:16:50Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11366</id>
      <timestamp>2007-10-28T22:18:22Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;rectangle initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;polar initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11367</id>
      <timestamp>2007-10-28T22:18:55Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
end

class RectComplex
  &lt;&lt;rectangle initialization&gt;&gt;
end

class PolarComplex
  &lt;&lt;polar initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11368</id>
      <timestamp>2007-10-28T22:20:15Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;


class RectComplex
  &lt;&lt;rectangle initialization&gt;&gt;


class PolarComplex
  &lt;&lt;polar initialization&gt;&gt;
end
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11369</id>
      <timestamp>2007-10-28T22:20:34Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;


class RectComplex
  &lt;&lt;rectangle initialization&gt;&gt;


class PolarComplex
  &lt;&lt;polar initialization&gt;&gt;

&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11370</id>
      <timestamp>2007-10-28T22:22:12Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;


&lt;&lt;rectangle initialization&gt;&gt;

&lt;&lt;polar initialization&gt;&gt;

&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11371</id>
      <timestamp>2007-10-28T22:23:10Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;

&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11372</id>
      <timestamp>2007-10-28T22:25:58Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;

&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)

&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)

&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)

&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)

&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11373</id>
      <timestamp>2007-10-28T22:27:12Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;

&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11374</id>
      <timestamp>2007-10-28T22:28:06Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}
&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11375</id>
      <timestamp>2007-10-28T22:28:44Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;

=== Addition and subtraction ===

Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11376</id>
      <timestamp>2007-10-28T22:30:02Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Code ==
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11377</id>
      <timestamp>2007-10-28T22:31:02Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <comment>/* Code */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Code ==
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex;
  &lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11378</id>
      <timestamp>2007-10-28T22:31:38Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Code */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Code ==
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex;

&lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11380</id>
      <timestamp>2007-10-28T22:32:41Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;complex class&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==

== Downloadable Code ==
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex;

&lt;&lt;complex class&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11381</id>
      <timestamp>2007-10-28T22:35:37Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11382</id>
      <timestamp>2007-10-28T22:36:18Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11383</id>
      <timestamp>2007-10-28T22:37:45Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11384</id>
      <timestamp>2007-10-28T22:44:43Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex
&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11385</id>
      <timestamp>2007-10-28T22:45:36Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11386</id>
      <timestamp>2007-10-28T22:48:29Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11387</id>
      <timestamp>2007-10-28T22:49:44Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Util */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11388</id>
      <timestamp>2007-10-28T22:59:49Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11389</id>
      <timestamp>2007-10-28T23:01:55Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11390</id>
      <timestamp>2007-10-28T23:03:17Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Subtraction */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11391</id>
      <timestamp>2007-10-28T23:03:46Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Multiplication */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11392</id>
      <timestamp>2007-10-28T23:04:06Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Division */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;Complex.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11393</id>
      <timestamp>2007-10-28T23:05:47Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11394</id>
      <timestamp>2007-10-28T23:13:30Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Addition and subtraction */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;  

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11395</id>
      <timestamp>2007-10-28T23:13:51Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Multiplication and division */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Test ==
&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11396</id>
      <timestamp>2007-10-28T23:15:14Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the text is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11397</id>
      <timestamp>2007-10-28T23:15:38Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11398</id>
      <timestamp>2007-10-28T23:17:05Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Arithmetic */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11399</id>
      <timestamp>2007-10-28T23:18:25Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Representation */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>11401</id>
      <timestamp>2007-10-28T23:21:13Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Run */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ComjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11402</id>
      <timestamp>2007-10-28T23:22:00Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ComjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ComjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11403</id>
      <timestamp>2007-10-28T23:22:38Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <minor/>
      <comment>/* Test Conjugate */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ComjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11404</id>
      <timestamp>2007-10-28T23:22:54Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test Run */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ConjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11405</id>
      <timestamp>2007-10-28T23:23:24Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <comment>/* Test */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test conjugate&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ConjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11406</id>
      <timestamp>2007-10-28T23:28:37Z</timestamp>
      <contributor>
        <username>Oscarpica</username>
        <id>1523</id>
      </contributor>
      <text xml:space="preserve">[[Category:Complex_numbers]]

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor that behave differently, these classes share exactly the same behavior.

Take notice that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test conjugate&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ConjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>12135</id>
      <timestamp>2008-01-22T06:40:18Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>grammar cleanup</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

This article presents an set of classes for representing complex numbers in the [http://en.wikipedia.org/wiki/Scala_(programming_language) Scala] multiparadigm programming language.

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number, as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor, which behaves differently, these classes share exactly the same behavior.

Note that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan(i / r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test conjugate&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ConjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16655</id>
      <timestamp>2010-02-12T20:54:16Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Initialization */</comment>
      <text xml:space="preserve">[[Category:Complex_numbers]]

This article presents an set of classes for representing complex numbers in the [http://en.wikipedia.org/wiki/Scala_(programming_language) Scala] multiparadigm programming language.

== Representation ==

We will represent a complex number with the abstract &lt;code&gt;Complex&lt;/code&gt; class. This class includes accessors to query the complex number, as well as basic arithmetic functions. 

We provide two concrete subclasses to construct a complex number either with its rectangular coordinates (RectComplex) or its polar coordinates (PolarComplex). Except for their constructor, which behaves differently, these classes share exactly the same behavior.

Note that these complex numbers are immutable.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexNumber.scala&gt;&gt;=
package complex

class Complex {
  &lt;&lt;accessors&gt;&gt;
  &lt;&lt;arithmetic&gt;&gt;
  &lt;&lt;conjugate&gt;&gt;
}

&lt;&lt;rectangle initialization&gt;&gt;
&lt;&lt;polar initialization&gt;&gt;
&lt;/codeblock&gt;

=== Accessors ===
The accessors are defined in the Complex abstract base class. 
 
&lt;codeblock language=Scala&gt;
&lt;&lt;accessors&gt;&gt;=
  val real:      double
  val imag:      double
  val magnitude: double
  val angle:     double  
&lt;/codeblock&gt;

=== Initialization ===
Initialization is done in the concrete subclasses.

&lt;codeblock language=Scala&gt;
&lt;&lt;rectangle initialization&gt;&gt;=
class RectComplex(r: double, i: double) extends Complex {
  val real = r
  val imag = i
  val magnitude = Math.sqrt(r*r + i*i)
  val angle = Math.atan2(i, r)
}

&lt;&lt;polar initialization&gt;&gt;=
class PolarComplex(m: double, a: double) extends Complex {
  val real = m * Math.cos(a)
  val imag = m * Math.sin(a)
  val magnitude = m
  val angle = a
}
&lt;/codeblock&gt;

== Arithmetic ==
Core arithmetic operations provided are addition, subtraction, multiplication, division. The arithmetic operations are defined in the abstract Complex base class.

&lt;codeblock language=Ruby&gt;
&lt;&lt;arithmetic&gt;&gt;=
&lt;&lt;addition&gt;&gt;
&lt;&lt;subtraction&gt;&gt;
&lt;&lt;multiplication&gt;&gt;
&lt;&lt;division&gt;&gt;
&lt;/codeblock&gt;
=== Addition and Subtraction ===
Addition and subtraction are implemented using the coordinate representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;addition&gt;&gt;=
  def +(that: Complex) = new RectComplex(real + that.real, imag + that.imag)
&lt;&lt;subtraction&gt;&gt;=
  def -(that: Complex) = new RectComplex(real - that.real, imag - that.imag)
&lt;/codeblock&gt;

=== Multiplication and Division ===

Multiplication and division are implemented using the polar representation:

&lt;codeblock language=Scala&gt;
&lt;&lt;multiplication&gt;&gt;=
  def *(that: Complex) = new PolarComplex(magnitude * that.magnitude, angle + that.angle)
&lt;&lt;division&gt;&gt;=
  def /(that: Complex) = new PolarComplex(magnitude / that.magnitude, angle - that.angle)
&lt;/codeblock&gt;

== Complex Conjugate ==
&lt;codeblock language=Scala&gt;
&lt;&lt;conjugate&gt;&gt;=
  def conjugate = new RectComplex(real, -imag)
&lt;/codeblock&gt;

== Test ==
Here where test our complex numbers. As you can see the code is much longer than our complex number implementation itself.

&lt;codeblock language=Scala&gt;
&lt;&lt;ComplexTestSuite.scala&gt;&gt;=
package complex

&lt;&lt;test initialization&gt;&gt;
&lt;&lt;test util&gt;&gt;
&lt;&lt;test rectangular constructor&gt;&gt;
&lt;&lt;test polar constructor&gt;&gt;
&lt;&lt;test addition&gt;&gt;
&lt;&lt;test subtraction&gt;&gt;
&lt;&lt;test multiplication&gt;&gt;
&lt;&lt;test division&gt;&gt;
&lt;&lt;test conjugate&gt;&gt;
&lt;&lt;test run&gt;&gt;
&lt;/codeblock&gt;

=== Test Initialization ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test initialization&gt;&gt;=
  import scala.testing.SUnit._
  val tr = new TestResult
  val tolerance = 0.000001
&lt;/codeblock&gt;

=== Test Util ===
A util base class for the individual test objects.
&lt;codeblock language=Scala&gt;
&lt;&lt;test util&gt;&gt;=
  abstract class UtilTest(title: String) extends TestCase(title) with Assert {
    def assertInDelta(exp: double, found: double) = {
      val delta = Math.abs(exp - found)
      if (delta &gt; tolerance) fail(&quot;Expected delta to be less than &quot; + tolerance + &quot;. Was &quot; + delta)
    }
  }
&lt;/codeblock&gt;

=== Test Rectangular Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test rectangular constructor&gt;&gt;=
  object RectConstructorTest extends UtilTest(&quot;Testing rectangular complex number constructor&quot;) {
    override def runTest = {
      val c = new RectComplex(1, 1)
      assertEquals(1, c.real)
      assertEquals(1, c.imag)
      assertInDelta(Math.sqrt(2.0), c.magnitude)
      assertInDelta(Math.Pi / 4, c.angle)
    }
  }

&lt;/codeblock&gt;

=== Test Polar Constructor ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test polar constructor&gt;&gt;=
  object PolarConstructorTest extends UtilTest(&quot;Testing polar complex number constructor&quot;) {
    override def runTest = {
      val c = new PolarComplex(1, Math.Pi / 4)
      assertInDelta(Math.sqrt(2.0) / 2, c.real)
      assertInDelta(Math.sqrt(2.0) / 2, c.imag)
      assertEquals(1, c.magnitude)
      assertEquals(Math.Pi / 4, c.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Addition ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test addition&gt;&gt;=
  object AdditionTest extends UtilTest(&quot;Testing complex addition&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 + z2
      assertEquals(1 + 3, z3.real)
      assertEquals(2 + 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Subtraction ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test subtraction&gt;&gt;=
  object SubractionTest extends UtilTest(&quot;Testing complex subtraction&quot;) {
    override def runTest = {
      val z1 = new RectComplex(1, 2)
      val z2 = new RectComplex(3, 4)
      val z3 = z1 - z2
      assertEquals(1 - 3, z3.real)
      assertEquals(2 - 4, z3.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Multiplication ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test multiplication&gt;&gt;=
  object MultiplicationTest extends UtilTest(&quot;Testing complex multiplication&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(3, Math.Pi / 6)
      val z3 = z1 * z2
      assertEquals(1 * 3, z3.magnitude)
      assertEquals(Math.Pi / 2, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Division ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test division&gt;&gt;=
  object DivisionTest extends UtilTest(&quot;Testing complex division&quot;) {
    override def runTest = {
      val z1 = new PolarComplex(1, Math.Pi / 3)
      val z2 = new PolarComplex(2, Math.Pi / 6)
      val z3 = z1 / z2
      assertEquals(1.0 / 2, z3.magnitude)
      assertEquals(Math.Pi / 6, z3.angle)
    }
  }
&lt;/codeblock&gt;

=== Test Conjugate ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test conjugate&gt;&gt;=
  object ConjugateTest extends UtilTest(&quot;Testing complex conjugate&quot;) {
    override def runTest = {
      val z = new RectComplex(1, 2).conjugate
      assertEquals(1, z.real)
      assertEquals(-2, z.imag)
    }
  }
&lt;/codeblock&gt;

=== Test Run ===
&lt;codeblock language=Scala&gt;
&lt;&lt;test run&gt;&gt;=
  new TestSuite(RectConstructorTest, 
                PolarConstructorTest, 
                AdditionTest,
                SubractionTest, 
                MultiplicationTest, 
                DivisionTest,
                ConjugateTest
                ).run(tr)
  for(f &lt;- tr.failures) {
    println(f)
  }
&lt;/codeblock&gt;

[[Category:Complex numbers]]
[[Category:Environment:Portable]]
[[Category:Programming language:Scala]]</text>
    </revision>
  </page>
  <page>
    <title>Conversion between numbers and strings</title>
    <id>2993</id>
    <revision>
      <id>8904</id>
      <timestamp>2007-02-08T19:22:23Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Draft of introduction - please don't dive in just yet!</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* ''0xBABE'' (hexadecimal)
* ''0177'' (octal)
* ''%01101101'' (binary)
* ''42'' (decimal)
into an integer that will converted (if necessary) into a twos-complement binary value and stored inside the computer. Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing.</text>
    </revision>
    <revision>
      <id>8905</id>
      <timestamp>2007-02-08T20:32:34Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Article stub complete</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* &lt;code&gt;0x2A&lt;/code&gt; (hexadecimal)
* &lt;code&gt;052&lt;/code&gt; (octal)
* &lt;code&gt;%101010&lt;/code&gt; (binary)
* &lt;code&gt;42&lt;/code&gt; (decimal)
into a number that will converted (if necessary) into a twos-complement binary value and stored inside the computer. 

Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing. For example within the statements: 
&lt;codeblock&gt;1: int i = 42
2: print i;&lt;/codeblock&gt;
line 2 will cause a string conversion function to be called which converts the 32-bit twos-complement binary value &lt;code&gt;00000000000000000000000000101010&lt;/code&gt; to be converted into the decimal number 42, and the digits of this number to be converted into the characters &lt;code&gt;'4'&lt;/code&gt; and &lt;code&gt;'2'&lt;/code&gt; before being printed. 

An understanding of the algorithms needed for this is fundamental to understanding the computer representation of numeric quantities, and is also fairly instructive in its own right. The algorithms themselves can be adapted to create a general library for the conversion and display of numbers in any base.

== Reference ==

The article is, in part, inspired by Randall Hyde, ''Write Greate Code'' (Volume 1), No Starch Press, 2004.</text>
    </revision>
    <revision>
      <id>8906</id>
      <timestamp>2007-02-08T20:33:51Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added categories</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* &lt;code&gt;0x2A&lt;/code&gt; (hexadecimal)
* &lt;code&gt;052&lt;/code&gt; (octal)
* &lt;code&gt;%101010&lt;/code&gt; (binary)
* &lt;code&gt;42&lt;/code&gt; (decimal)
into a number that will converted (if necessary) into a twos-complement binary value and stored inside the computer. 

Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing. For example within the statements: 
&lt;codeblock&gt;1: int i = 42
2: print i;&lt;/codeblock&gt;
line 2 will cause a string conversion function to be called which converts the 32-bit twos-complement binary value &lt;code&gt;00000000000000000000000000101010&lt;/code&gt; to be converted into the decimal number 42, and the digits of this number to be converted into the characters &lt;code&gt;'4'&lt;/code&gt; and &lt;code&gt;'2'&lt;/code&gt; before being printed. 

An understanding of the algorithms needed for this is fundamental to understanding the computer representation of numeric quantities, and is also fairly instructive in its own right. The algorithms themselves can be adapted to create a general library for the conversion and display of numbers in any base.

== Reference ==

The article is, in part, inspired by Randall Hyde, ''Write Greate Code'' (Volume 1), No Starch Press, 2004.

[[Category:Convert Integer to String]]
[[Category:Introductory Examples]]</text>
    </revision>
    <revision>
      <id>8910</id>
      <timestamp>2007-02-08T20:51:30Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Reference */</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* &lt;code&gt;0x2A&lt;/code&gt; (hexadecimal)
* &lt;code&gt;052&lt;/code&gt; (octal)
* &lt;code&gt;%101010&lt;/code&gt; (binary)
* &lt;code&gt;42&lt;/code&gt; (decimal)
into a number that will converted (if necessary) into a twos-complement binary value and stored inside the computer. 

Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing. For example within the statements: 
&lt;codeblock&gt;1: int i = 42
2: print i;&lt;/codeblock&gt;
line 2 will cause a string conversion function to be called which converts the 32-bit twos-complement binary value &lt;code&gt;00000000000000000000000000101010&lt;/code&gt; to be converted into the decimal number 42, and the digits of this number to be converted into the characters &lt;code&gt;'4'&lt;/code&gt; and &lt;code&gt;'2'&lt;/code&gt; before being printed. 

An understanding of the algorithms needed for this is fundamental to understanding the computer representation of numeric quantities, and is also fairly instructive in its own right. The algorithms themselves can be adapted to create a general library for the conversion and display of numbers in any base.

== Reference ==

&lt;ref name=&quot;hyde&quot;&gt;Randall Hyde, ''Write Great Code'' (Volume 1), No Starch Press, 2004&lt;/ref&gt;

&lt;references /&gt;

[[Category:Convert Integer to String]]
[[Category:Introductory Examples]]</text>
    </revision>
    <revision>
      <id>8911</id>
      <timestamp>2007-02-08T20:51:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Reference */</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* &lt;code&gt;0x2A&lt;/code&gt; (hexadecimal)
* &lt;code&gt;052&lt;/code&gt; (octal)
* &lt;code&gt;%101010&lt;/code&gt; (binary)
* &lt;code&gt;42&lt;/code&gt; (decimal)
into a number that will converted (if necessary) into a twos-complement binary value and stored inside the computer. 

Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing. For example within the statements: 
&lt;codeblock&gt;1: int i = 42
2: print i;&lt;/codeblock&gt;
line 2 will cause a string conversion function to be called which converts the 32-bit twos-complement binary value &lt;code&gt;00000000000000000000000000101010&lt;/code&gt; to be converted into the decimal number 42, and the digits of this number to be converted into the characters &lt;code&gt;'4'&lt;/code&gt; and &lt;code&gt;'2'&lt;/code&gt; before being printed. 

An understanding of the algorithms needed for this is fundamental to understanding the computer representation of numeric quantities, and is also fairly instructive in its own right. The algorithms themselves can be adapted to create a general library for the conversion and display of numbers in any base.

== Reference ==

Randall Hyde, ''Write Great Code'' (Volume 1), No Starch Press, 2004


[[Category:Convert Integer to String]]
[[Category:Introductory Examples]]</text>
    </revision>
    <revision>
      <id>8912</id>
      <timestamp>2007-02-08T20:53:35Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Minor edits</comment>
      <text xml:space="preserve">{{develop}}
This is a placeholder for a general discussion of the fundamental algorithms that are used to convert numbers to strings and strings to numbers. These algorithms are used by nearly all programming language compilers and assemblers in order to convert a numeric literal such as:
* &lt;code&gt;0x2A&lt;/code&gt; (hexadecimal)
* &lt;code&gt;052&lt;/code&gt; (octal)
* &lt;code&gt;%101010&lt;/code&gt; (binary)
* &lt;code&gt;42&lt;/code&gt; (decimal)
into a number that will converted (if necessary) into a twos-complement binary value and stored inside the computer. 

Most programming
languages also provide functions that transparently convert from the internal twos-complement form to binary, octal, hexadecimal, decimal, character (or whatever) for printing. For example within the statements: 
&lt;codeblock&gt;1: int i = 42
2: print i;&lt;/codeblock&gt;
line 2 will cause a string conversion function to be called which converts the 32-bit twos-complement binary value &lt;code&gt;00000000000000000000000000101010&lt;/code&gt; to be converted into the decimal number 42, and the digits of this number to be converted into the characters &lt;code&gt;'4'&lt;/code&gt; and &lt;code&gt;'2'&lt;/code&gt; before being printed. 

An understanding of the algorithms needed for these conversions is fundamental to understanding the computer representation of numeric quantities, and is also fairly instructive in its own right. The algorithms themselves can be adapted to create a general library for the conversion and display of numbers in any base.

== Reference ==

Randall Hyde, ''Write Great Code'' (Volume 1), No Starch Press, 2004


[[Category:Convert Integer to String]]
[[Category:Introductory Examples]]</text>
    </revision>
  </page>
  <page>
    <title>Convert Integer to String</title>
    <id>2395</id>
    <revision>
      <id>6555</id>
      <timestamp>2006-06-30T11:21:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>[[Convert Integer to String]] moved to [[Convert Integer to String (Java)]]: Created as a category page but now a placeholder for first example of the category Convert Integer to String</comment>
      <text xml:space="preserve">#REDIRECT [[Convert Integer to String (Java)]]</text>
    </revision>
  </page>
  <page>
    <title>Convert Integer to String (BASIC)</title>
    <id>2632</id>
    <revision>
      <id>7270</id>
      <timestamp>2006-08-13T20:03:34Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>[[Convert Integer to String (BASIC)]] moved to [[Convert Integer to String (QBASIC)]]: More specific dialect</comment>
      <text xml:space="preserve">#REDIRECT [[Convert Integer to String (QBASIC)]]</text>
    </revision>
  </page>
  <page>
    <title>Convert Integer to String (Java)</title>
    <id>2874</id>
    <revision>
      <id>8384</id>
      <timestamp>2007-01-01T14:58:01Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <comment>created with an initial codebase</comment>
      <text xml:space="preserve">There are a lot of different possibilities to convert a integer number into a String-object.

In Java you can convert any primitiv-type into a String-object, by appeding an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitiv type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot;+i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ===

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++) {
        System.out.println(convertInteger(i)+&quot; &lt;=&gt; &quot;+convertSimple(i));
    }
}
&lt;/codeblock&gt;


== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8385</id>
      <timestamp>2007-01-01T14:59:38Z</timestamp>
      <contributor>
        <username>Kajk</username>
        <id>127</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">There are a lot of different possibilities to convert a integer number into a String-object.

In Java you can convert any primitiv-type into a String-object, by appeding an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitiv type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot;+i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++) {
        System.out.println(convertInteger(i)+&quot; &lt;=&gt; &quot;+convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8885</id>
      <timestamp>2007-02-08T17:16:01Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>corrected spelling error</comment>
      <text xml:space="preserve">There are a lot of different possibilities to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appeding an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot;+i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++) {
        System.out.println(convertInteger(i)+&quot; &lt;=&gt; &quot;+convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8886</id>
      <timestamp>2007-02-08T17:24:06Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>More minor proof-reading corrections. Spaced out the operators to make code more readable</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>8898</id>
      <timestamp>2007-02-08T18:59:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added category</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[Category:Convert Integer to String|Java]</text>
    </revision>
    <revision>
      <id>8899</id>
      <timestamp>2007-02-08T19:00:55Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Corrected categories</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Convert Integer to String|Java]]
[[Category:Introductory Examples|Java]]</text>
    </revision>
    <revision>
      <id>8900</id>
      <timestamp>2007-02-08T19:03:10Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The class */</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Convert Integer to String|Java]]
[[Category:Introductory Examples]]</text>
    </revision>
    <revision>
      <id>8901</id>
      <timestamp>2007-02-08T19:05:07Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>/* The class */</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Convert Integer to String]]
[[Category:Introductory Examples]]</text>
    </revision>
    <revision>
      <id>8902</id>
      <timestamp>2007-02-08T19:07:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Convert Integer to String]]</text>
    </revision>
    <revision>
      <id>15071</id>
      <timestamp>2008-10-17T06:14:59Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>added another method</comment>
      <text xml:space="preserve">There are a number of different ways to convert a integer number into a String-object.

In Java you can convert any primitive-type into a String-object, by appending an empty String (&lt;code&gt;&quot;&quot;&lt;/code&gt;) to the beginning or the end of the variable (of a primitive type).
&lt;codeblock language=java&gt;
&lt;&lt;built-in convert&gt;&gt;=
public static String convertSimple(int i) {
    return &quot;&quot; + i;
}
&lt;/codeblock&gt;

To use the static-&lt;code&gt;toString&lt;/code&gt; Method of the &lt;code&gt;Integer&lt;/code&gt;-class can make the code more (sometimes also less) readable.
&lt;codeblock language=java&gt;
&lt;&lt;integer convert&gt;&gt;=
public static String convertInteger(int i) {
    return Integer.toString(i);
}
&lt;/codeblock&gt;

Technically you can also use the Formatter (like C's &quot;sprintf&quot;), although it is kind of overkill.
&lt;codeblock language=java&gt;
&lt;&lt;format convert&gt;&gt;=
public static String convertFormat(int i) {
    return String.format(&quot;%d&quot;, i);
}
&lt;/codeblock&gt;

== Testing the methods ==

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i = 0; i &lt;= 46; i++) {
        System.out.println(convertInteger(i) + &quot; &lt;=&gt; &quot; + convertSimple(i) + &quot; &lt;=&gt; &quot; + convertFormat(i));
    }
}
&lt;/codeblock&gt;

== The class ==

&lt;codeblock language=java&gt;
&lt;&lt;ConvertInt2Str.java&gt;&gt;=
public class ConvertInt2Str {
        &lt;&lt;built-in convert&gt;&gt;
        &lt;&lt;integer convert&gt;&gt;
        &lt;&lt;format convert&gt;&gt;
        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Convert Integer to String]]</text>
    </revision>
  </page>
  <page>
    <title>Convert Integer to String (QBASIC)</title>
    <id>2816</id>
    <revision>
      <id>8179</id>
      <timestamp>2006-11-26T17:23:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Convert Integer to String (QBASIC)]] moved to [[Convert integer to English words (QBASIC)]]: Better name - convert integer to string connotes 12 -&gt; &quot;12&quot;, not 12 -&gt; &quot;twelve&quot;</comment>
      <text xml:space="preserve">#REDIRECT [[Convert integer to English words (QBASIC)]]</text>
    </revision>
    <revision>
      <id>8195</id>
      <timestamp>2006-11-28T00:24:00Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>relink</comment>
      <text xml:space="preserve">#REDIRECT [[Convert integer to words (QBASIC)]]</text>
    </revision>
  </page>
  <page>
    <title>Convert Object to String (Java)</title>
    <id>2995</id>
    <revision>
      <id>8926</id>
      <timestamp>2007-02-09T00:40:33Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Started the article and sketched its scope. No code yet!</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/string&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behavious allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It may also be worth mentioning the automated string builder functions provided for Jakarta Commons which use reflection to automate the creation of a toString method.

[[Category:Convert Object to String|Java]]
[[Category:Introductory Examples|Java]]
[[Category:Fundamentals|Java]]</text>
    </revision>
    <revision>
      <id>8927</id>
      <timestamp>2007-02-09T00:44:03Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Adjusted categories</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/string&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behavious allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It may also be worth mentioning the automated string builder functions provided for Jakarta Commons which use reflection to automate the creation of a toString method.

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8928</id>
      <timestamp>2007-02-09T00:45:54Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/string&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behavious allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It may also be worth mentioning the automated string builder functions provided for Jakarta Commons which use reflection to automate the creation of a toString method.

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Convert numbers to string (Java)]]</text>
    </revision>
    <revision>
      <id>8929</id>
      <timestamp>2007-02-09T00:46:59Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/string&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behavious allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It may also be worth mentioning the automated string builder functions provided for Jakarta Commons which use reflection to automate the creation of a toString method.

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8930</id>
      <timestamp>2007-02-09T00:50:15Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behavious allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8934</id>
      <timestamp>2007-02-09T00:52:34Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 

This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8942</id>
      <timestamp>2007-02-09T10:43:58Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Starting to develop the &quot;print primitives&quot; section</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Covnerting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList numbers = new ArrayList();
Boolean wflag = new Boolean(b); numbers.add(wflag);
Character wc = new Character(c); numbers.add(wc);
Byte wb = new Byte(b); numbers.add(wb);
Short ws = new Short(s); numbers.add(ws);
Integer wi = new Integer(i); numbers.add(wi);
Long wl = new Long(l); numbers.add(wl);
Float wf = new Float(f); numbers.add(wf);
Double wd = new Double(d); numbers.add(wd);
&lt;/codeblock&gt;


You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CovertPrimitiveToStrings.java&gt;&gt;=
class CovertPrimitivesToStrings {
  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;     
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]


== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8944</id>
      <timestamp>2007-02-09T15:18:28Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Class incompete but ready for first testing</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(b); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; i &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.class);
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
}
&lt;/codeblock&gt;
You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CovertPrimitiveToStrings.java&gt;&gt;=
class CovertPrimitivesToStrings {
  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8945</id>
      <timestamp>2007-02-09T15:24:38Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(b); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; i &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.class);
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CovertPrimitiveToStrings.java&gt;&gt;=
class CovertPrimitivesToStrings {
  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8946</id>
      <timestamp>2007-02-09T15:29:06Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(b); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; i &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.class);
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CovertPrimitiveToStrings.java&gt;&gt;=
class CovertPrimitivesToStrings {

  import java.util.ArrayList;

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8947</id>
      <timestamp>2007-02-09T15:40:04Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Code corrections to correct compiler errors</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(b); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; i &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.class);
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8948</id>
      <timestamp>2007-02-09T15:41:27Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Correction to code...</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; i &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8949</id>
      <timestamp>2007-02-09T15:53:22Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Correction to code...</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot; to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]</text>
    </revision>
    <revision>
      <id>8950</id>
      <timestamp>2007-02-09T15:56:07Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Code compiles and is ready for further refinement. Think of this as a check-in.</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

To demonstrate this behaviour, let's create a set of primitives
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make testing easier, let's create wrapper classes for each of these cases and add them to an array list.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;


===Stubs===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;    
  }
}
&lt;/codeblock&gt;


== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8951</id>
      <timestamp>2007-02-09T16:34:41Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Next iteration...</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. We will postulate instead that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt;

     static String coerceWrappedPrimitiveValueToString(Object o) {
       return &quot;&quot;;
     }
    
  }
}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which is turned off by default. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a Java 1.4 or later JDK using the &lt;code&gt;-ea&lt;/code&gt; argument present:
&lt;codeblock&gt;
javac -ea ConvertPrimitivesToStrings.java
java ConvertPrimitivesToStrings
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8952</id>
      <timestamp>2007-02-09T16:40:57Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. We will postulate instead that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  static String coerceWrappedPrimitiveValueToString(Object o) {
       return &quot;&quot;;
  }
}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which is turned off by default. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a Java 1.4 or later JDK using the &lt;code&gt;-ea&lt;/code&gt; argument present:
&lt;codeblock&gt;
javac -ea ConvertPrimitivesToStrings.java
java ConvertPrimitivesToStrings
&lt;/codeblock&gt;



You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8953</id>
      <timestamp>2007-02-09T18:03:37Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Almost complete ... won't pass noweb yet though!</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   String coercedString = &quot;&quot;;
   &lt;&lt;coerce primitive to string according to type&gt;&gt;
   return coercedString;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. Let us begin by determining the class of the wrapper:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;determine the class of the wrapper object&gt;&gt;=
Class wrapperClass = o.getClass();
&lt;/codeblock&gt;

We will need to identify the wrapper class before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;decision tree&gt;&gt;=
if (wrapperClass instanceOf Boolean) {
  &lt;&lt;coerce value of Boolean to String&gt;&gt;
}
else if (wrapperClass instanceof Character) {
  &lt;&lt;coerce value of Character to String&gt;&gt;
}
else if (wrapperClass instanceof Byte) {
  &lt;&lt;coerce value of Byte to String&gt;&gt;
}
else if (wrapperClass instanceof Short) {
  &lt;&lt;coerce value of Short to String&gt;&gt;
}
else if (wrapperClass instanceof Integer) {
  &lt;&lt;coerce value of Integer to String&gt;&gt;
}
else if (wrapperClass instanceof Long) {
  &lt;&lt;coerce value of Long to String&gt;&gt;
}
else if (wrapperClass instanceof Float) {
  &lt;&lt;coerce value of Float to String&gt;&gt;
}
else if (wrapperClass instanceof Double) {
  &lt;&lt;coerce value of Double to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: use toString&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;coerce value of Long to String&gt;&gt;=
Long lvalue = (Long)o.longValue();
coercedString = coercedString + lvalue;
&lt;/codeblock&gt;

The other types follow the same pattern.

:

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: use toString&gt;&gt;=
coercedString = coercedString + o;
&lt;/codeblock&gt;

You can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's behaviour allows you to write clearer and cleaner code. 



This article will present more detail on how this is done with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. 

Here's the final program

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8954</id>
      <timestamp>2007-02-09T18:27:40Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Check in midway ...</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. 

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;return primitive coerced to string according to type&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. Let us begin by determining the class of the wrapper:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;determine the class of the wrapper object&gt;&gt;=
Class wrapperClass = o.getClass();
&lt;/codeblock&gt;

We will need to identify the wrapper class before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;decision tree&gt;&gt;=
if (wrapperClass instanceOf Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
return &quot;&quot; + (Long)o.longValue();
&lt;/codeblock&gt;

The other types follow the same pattern [to be completed ...]

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;


== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8963</id>
      <timestamp>2007-02-09T19:21:22Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Primitive testing code complete...ready for testing</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;return primitive coerced to string according to type&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. Let us begin by determining the class of the wrapper:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;determine the class of the wrapper object&gt;&gt;=
Class wrapperClass = o.getClass();
&lt;/codeblock&gt;

We will need to identify the wrapper class before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;decision tree&gt;&gt;=
if (wrapperClass instanceOf Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
return &quot;&quot; + (Long)o.longValue();
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
return &quot;&quot; + (Boolean)o.booleanValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
return &quot;&quot; + (Character)o.charValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
return &quot;&quot; + (Byte)o.byteValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
return &quot;&quot; + (Short)o.longValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
return &quot;&quot; + (Integer)o.intValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
return &quot;&quot; + (Float)o.floatValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
return &quot;&quot; + (Double)o.doubleValue();
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;


== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8965</id>
      <timestamp>2007-02-09T19:24:39Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Needed a final chunk</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;return primitive coerced to string according to type&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. Let us begin by determining the class of the wrapper:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;determine the class of the wrapper object&gt;&gt;=
Class wrapperClass = o.getClass();
&lt;/codeblock&gt;

We will need to identify the wrapper class before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;decision tree&gt;&gt;=
if (wrapperClass instanceOf Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (wrapperClass instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
return &quot;&quot; + (Long)o.longValue();
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
return &quot;&quot; + (Boolean)o.booleanValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
return &quot;&quot; + (Character)o.charValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
return &quot;&quot; + (Byte)o.byteValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
return &quot;&quot; + (Short)o.longValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
return &quot;&quot; + (Integer)o.intValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
return &quot;&quot; + (Float)o.floatValue();
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
return &quot;&quot; + (Double)o.doubleValue();
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

Having put all the pieces into place, the coercion methods becomes:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return primitive coerced to string according to type&gt;&gt;=
&lt;&lt;determine the class of the wrapper object&gt;&gt;
&lt;&lt;decision tree&gt;&gt;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8966</id>
      <timestamp>2007-02-09T19:40:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>corrected compilation errors</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;return primitive coerced to string according to type&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. 

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;decision tree&gt;&gt;=
if (o instanceOf Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte byte = ((Byte)o).byteValue();
return &quot;&quot; + byte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i; 
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

Having put all the pieces into place, the coercion methods becomes:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return primitive coerced to string according to type&gt;&gt;=
&lt;&lt;determine the class of the wrapper object&gt;&gt;
&lt;&lt;decision tree&gt;&gt;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8967</id>
      <timestamp>2007-02-09T19:43:06Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Done I think!</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. 

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceOf Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte byte = ((Byte)o).byteValue();
return &quot;&quot; + byte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i; 
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8969</id>
      <timestamp>2007-02-09T23:34:32Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Validating the auto string coercion */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. 

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte byte = ((Byte)o).byteValue();
return &quot;&quot; + byte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i; 
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8970</id>
      <timestamp>2007-02-09T23:36:07Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Validating the auto string coercion */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.


== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. 

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i; 
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>8978</id>
      <timestamp>2007-02-10T13:13:05Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added section for Object toString</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string. 

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that is
somehow related to the data that the object represents. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;. But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

Will demostrate &lt;code&gt;toString&lt;/code&gt; for this built-in types as well as user defined types.

== Converting Java Primitives to Strings ==

For primitives, the Java compiler will insert code to wrap the primitive in an instance of its wrapper class, and call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method. Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understant, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt; 

     &lt;&lt;Test primitive to string conversion&gt;&gt; 
  }
  
  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run 
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;. 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string. 

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern: 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i; 
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

Clearly can also call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9114</id>
      <timestamp>2007-02-17T14:02:32Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
int x = 1; int y = 2;
System.out.println(&quot;x + y = &quot; + (x + y));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  x + y = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;x + y = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;x + y = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;x + y&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = x + y;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(x + y).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print x + y the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;x + y = &quot; + (x + y)).equals(arg.toString());
&lt;/codeblock&gt;

=== Why the parenthesis? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;x + y = &quot; + (x + y)&lt;/code&gt;. This is to force the compiler to perform the
integer summation before the string concatenation. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + x + y);
&lt;/codeblock&gt;
would print the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + (new Integer(x).toString()) + (new Integer(y).toString()));
&lt;/code&gt;
which would result in
 x + y = 12
rather than the expected
 x + y = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9115</id>
      <timestamp>2007-02-17T14:07:20Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>clarification</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
int x = 1; int y = 2;
System.out.println(&quot;x + y = &quot; + (x + y));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  x + y = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;x + y = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;x + y = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;x + y&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = x + y;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(x + y).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print x + y the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;x + y = &quot; + (x + y)).equals(arg.toString());
&lt;/codeblock&gt;

=== Why the parenthesis? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;x + y = &quot; + (x + y)&lt;/code&gt;
and may be wondering why. The reason is to force the compiler to perform the
integer summation before the string concatenation. If we instead relied on operator precedence and instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + x + y);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + (new Integer(x).toString()) + (new Integer(y).toString()));
&lt;/code&gt;
printing
 x + y = 12
rather than the expected
 x + y = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9116</id>
      <timestamp>2007-02-17T14:08:10Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Why the parenthesis? */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
int x = 1; int y = 2;
System.out.println(&quot;x + y = &quot; + (x + y));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  x + y = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;x + y = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;x + y = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;x + y&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = x + y;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(x + y).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print x + y the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;x + y = &quot; + (x + y)).equals(arg.toString());
&lt;/codeblock&gt;

=== Why the parenthesis? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;x + y = &quot; + (x + y)&lt;/code&gt;
and may be wondering why. The reason is to force the compiler to perform the
integer summation before the string concatenation. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + x + y);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + (new Integer(x).toString()) + (new Integer(y).toString()));
&lt;/code&gt;
printing
 x + y = 12
rather than the expected
 x + y = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;ConvertPrimitivesToStrings&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac ConvertPrimitivesToStrings.java
java -ea ConvertPrimitivesToStrings
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9117</id>
      <timestamp>2007-02-17T14:09:18Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Defining the test */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
int x = 1; int y = 2;
System.out.println(&quot;x + y = &quot; + (x + y));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  x + y = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;x + y = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;x + y = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;x + y&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = x + y;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(x + y).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print x + y the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;x + y = &quot; + (x + y)).equals(arg.toString());
&lt;/codeblock&gt;

=== Why the parenthesis? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;x + y = &quot; + (x + y)&lt;/code&gt;
and may be wondering why. The reason is to force the compiler to perform the
integer summation before the string concatenation. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + x + y);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + (new Integer(x).toString()) + (new Integer(y).toString()));
&lt;/code&gt;
printing
 x + y = 12
rather than the expected
 x + y = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9118</id>
      <timestamp>2007-02-17T14:11:27Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Why the parenthesis? */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
int x = 1; int y = 2;
System.out.println(&quot;x + y = &quot; + (x + y));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  x + y = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;x + y = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;x + y = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;x + y&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = x + y;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(x + y).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print x + y the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;x + y = &quot; + (x + y)).equals(arg.toString());
&lt;/codeblock&gt;

=== Why the parenthesis? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;x + y = &quot; + (x + y)&lt;/code&gt;
and may be wondering why. The reason is to force the compiler to perform the
integer summation before the string concatenation. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + x + y);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;x + y = &quot; + (new Integer(x).toString()) + (new Integer(y).toString()));
&lt;/codeblock&gt;
printing
 x + y = 12
rather than the expected
 x + y = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9119</id>
      <timestamp>2007-02-17T14:32:43Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  1 + 2 = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;x + y = &quot; + x + y).equals(&quot;x + y = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print x + y the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9120</id>
      <timestamp>2007-02-17T14:34:23Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  1 + 2 = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9122</id>
      <timestamp>2007-02-17T15:19:26Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== Converting Java Reference Types to Strings ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  1 + 2 = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9123</id>
      <timestamp>2007-02-17T15:24:29Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Changed title of section</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

=== Behavioural description of String literals ===

Consider this simple example:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  1 + 2 = 3

Which is very convenient, but what is really happening behind the scenes?

When this code is compiled, the Java compiler notes the signature of the method &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the argument must be converted to a &lt;code&gt;String&lt;/code&gt;. The first part of the expression is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the string, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use an assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9124</id>
      <timestamp>2007-02-17T15:54:48Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Strengthened the introduction and modified the explanation a little.</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

Which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9125</id>
      <timestamp>2007-02-17T15:55:49Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Automatic Conversion of Objects to String in String Literals */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

Which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9126</id>
      <timestamp>2007-02-17T15:56:31Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Automatic Conversion of Objects to String in String Literals */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;1 + 2 = &quot; + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.


=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9127</id>
      <timestamp>2007-02-17T15:58:44Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>corrected &quot;Not the way to do it&quot;</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 1 + 2 = 12
rather than the expected
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9128</id>
      <timestamp>2007-02-17T15:59:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* When is 1 + 2 = 12? */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9129</id>
      <timestamp>2007-02-17T16:01:23Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* When is 1 + 2 = 12? */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method. 
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects. 

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor: 
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;)
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9130</id>
      <timestamp>2007-02-17T16:07:10Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the String constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream.
Thus the final expression is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9132</id>
      <timestamp>2007-02-17T16:20:45Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9133</id>
      <timestamp>2007-02-17T16:24:14Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added section title for second example program</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit code from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java API override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in String coercion methods with examples of converting both the primitive and built-in reference types to &lt;code&gt;String&lt;/code&gt; (including &lt;code&gt;Object&lt;/code&gt; and &lt;code&gt;String&lt;/code&gt;) as well as an example of a user defined type's default behaviour and behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. In this way we hope to illustrate some of the background to Java's automated
string coercion and illustrate some of the problems with a language which makes a distinction between ''object'' types and ''primitives''.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example. Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== When is 1 + 2 = 12? ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== Reference ==

Bruce Eckel, ''Thinking in Java'', 3rd Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9134</id>
      <timestamp>2007-02-17T16:45:04Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

=== Object ===

=== String ===

=== Class ===

=== A Selection of Examples from the API ===


== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9137</id>
      <timestamp>2007-02-17T17:07:17Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

=== String ===

=== Class ===

=== A Selection of Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9138</id>
      <timestamp>2007-02-17T17:39:50Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt; followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of useful classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public void printTableOfNumbers() {

}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers()
&lt;/codeblock&gt;

The result should be:

  Table of the Java Numbers

  Primitive Type	Size in Bits	Minimum Value	Maximum Value
  ==============    =============	=============	==============
  byte				8				-128			127
  short				16
  int				32
  double			64
  float				32
  double			64
  ==============	=============	=============	==============

=== Printing Booleans and Characters ===

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9139</id>
      <timestamp>2007-02-17T17:48:24Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt; followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of useful classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public void printTableOfNumbers() {
  String table = &quot;Table of the Java Numbers&quot; +
     &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\tMaximum Value&quot; +
     &quot;==============\t=============\t============\t=============\t=============&quot;;
  table += &quot;byte\t&quot; + 8 + &quot;\t&quot; + (byte)5 + &quot;\t&quot; + Byte.MIN_VALUE + &quot;\t&quot; + Byte.MAX_VALUE;
  table +=
      &quot;==============\t=============\t============\t=============\t=============&quot;;
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers()
&lt;/codeblock&gt;

The result should be:

  Table of the Java Numbers
  Primitive Type	Size in Bits	Minimum Value	Maximum Value
  ==============    =============	=============	==============
  byte				8				-128			127
  short				16
  int				32
  double			64
  float				32
  double			64
  ==============	=============	=============	==============

=== Printing Booleans and Characters ===

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9140</id>
      <timestamp>2007-02-17T17:56:43Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt; followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of useful classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
	     &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\tMaximum Value\n&quot; +
	     &quot;==============\t=============\t============\t=============\t=============\n&quot;;
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	table +=
	      &quot;==============\t=============\t============\t=============\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

  Table of the Java Numbers
  Primitive Type	Size in Bits	Minimum Value	Maximum Value
  ==============    =============	=============	==============
  byte				8				-128			127
  short				16
  int				32
  double			64
  float				32
  double			64
  ==============	=============	=============	==============

=== Printing Booleans and Characters ===

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9141</id>
      <timestamp>2007-02-17T18:02:33Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt; followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of useful classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
	     &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\tMaximum Value\n&quot; +
	     &quot;==============\t=============\t============\t=============\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t\t&quot; + Long.MIN_VALUE + &quot;\t\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t\t&quot; + Float.MIN_VALUE + &quot;\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	      &quot;==============\t=============\t============\t=============\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

  Table of the Java Numbers
  Primitive Type	Size in Bits	Minimum Value	Maximum Value
  ==============    =============	=============	==============
  byte				8				-128			127
  short				16
  int				32
  double			64
  float				32
  double			64
  ==============	=============	=============	==============

=== Printing Booleans and Characters ===

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9142</id>
      <timestamp>2007-02-17T18:13:26Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt; followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of useful classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9143</id>
      <timestamp>2007-02-17T18:28:07Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the exclusive OR operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  table = &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:



=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9144</id>
      <timestamp>2007-02-17T18:30:42Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added printTruthTable</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the exclusive OR operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  table = &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:



=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
        &lt;&lt;print truth table&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9145</id>
      <timestamp>2007-02-17T18:31:55Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Program 2 */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the exclusive OR operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  table = &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:



=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
        &lt;&lt;XOR table&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 2 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9146</id>
      <timestamp>2007-02-17T18:35:45Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the exclusive OR operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========


=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9147</id>
      <timestamp>2007-02-17T18:49:10Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 13 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   for (int i = 0; i &lt; letters.length; i ++) {
   		char letter = letters[i];
   		letter + 13;
   	}
   	String cypherText = new String(letters);
   	return cypherText;
}
&lt;/codeblock&gt;

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9148</id>
      <timestamp>2007-02-17T18:51:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added simple cypher to example</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 13 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   for (int i = 0; i &lt; letters.length; i ++) {
   		char letter = letters[i];
   		letter + 13;
   	}
   	String cypherText = new String(letters);
   	return cypherText;
}
&lt;/codeblock&gt;

=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
        &lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9149</id>
      <timestamp>2007-02-17T19:08:20Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 13 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += (byte)13;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

Here is the result:

  [|?-v?-?ur-?vzr-s|⌂-nyy-t||q-zr{-?|-p|zr-?|-?ur-nvq-|s-?ur-}n⌂??


=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9150</id>
      <timestamp>2007-02-17T19:12:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

Here is the result:

  [|?-v?-?ur-?vzr-s|⌂-nyy-t||q-zr{-?|-p|zr-?|-?ur-nvq-|s-?ur-}n⌂??


=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9151</id>
      <timestamp>2007-02-17T19:16:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, '' '', Sun Microsystems Press, 200x.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9152</id>
      <timestamp>2007-02-17T19:21:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added Bloch's Effective Java</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9153</id>
      <timestamp>2007-02-17T19:22:46Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added place holder</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9154</id>
      <timestamp>2007-02-17T19:25:00Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added summary of future section</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9155</id>
      <timestamp>2007-02-17T19:28:25Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Summary of what is to come</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

=== Writing Your Own toString Method ===

=== Using Jakarta Commons ===

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9157</id>
      <timestamp>2007-02-17T19:40:04Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added summaries of future sections</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@1223445&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>9159</id>
      <timestamp>2007-02-17T19:44:02Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Looks like object addresses are actually 24 bits long!</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics how how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============


=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10184</id>
      <timestamp>2007-05-16T18:35:48Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Corrected a typo</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10185</id>
      <timestamp>2007-05-16T18:37:16Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Printing Strings */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10186</id>
      <timestamp>2007-05-16T18:37:55Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Printing Metaclass information */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10187</id>
      <timestamp>2007-05-16T18:38:35Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* A Selection of further Examples from the API */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;
== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10188</id>
      <timestamp>2007-05-16T18:40:36Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Program 2 */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of ''Printing Objects with'' &lt;code&gt;Object.toString{)&lt;/code&gt;.

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10189</id>
      <timestamp>2007-05-16T18:41:35Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Program 2 */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10190</id>
      <timestamp>2007-05-16T18:43:02Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Converting Java Primitives to Strings */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simple call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to polymorphism.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;



=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10191</id>
      <timestamp>2007-05-16T18:45:53Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added a wikipedia link to polymorphism article.</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10192</id>
      <timestamp>2007-05-16T18:47:19Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* The Default behaviour */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [Jakarta Commons http://jakarta.apache.org/commons/] comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>10193</id>
      <timestamp>2007-05-16T18:49:22Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>/* Using Jakarta Commons */</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [http://jakarta.apache.org/commons/ Apache Jakarta Commons] library comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

'''Complete Me'''

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>11485</id>
      <timestamp>2007-11-07T16:01:23Z</timestamp>
      <contributor>
        <ip>124.30.203.6</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>11486</id>
      <timestamp>2007-11-07T20:22:50Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/124.30.203.6|124.30.203.6]] ([[User_talk:124.30.203.6|124.30.203.6]]); changed back to last version by [[User:Cpjobling|Cpjobling]]</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the &quot;address&quot; of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [http://jakarta.apache.org/commons/ Apache Jakarta Commons] library comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

'''Complete Me'''

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>15181</id>
      <timestamp>2008-10-21T01:22:33Z</timestamp>
      <contributor>
        <ip>132.234.251.211</ip>
      </contributor>
      <comment>the numbers in toString() are a hashcode, not an address</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected, will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the hashcode representation of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [http://jakarta.apache.org/commons/ Apache Jakarta Commons] library comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

'''Complete Me'''

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
    <revision>
      <id>15484</id>
      <timestamp>2008-11-25T18:56:47Z</timestamp>
      <contributor>
        <ip>204.185.119.88</ip>
      </contributor>
      <comment>grammar fix</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the hashcode representation of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [http://jakarta.apache.org/commons/ Apache Jakarta Commons] library comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

'''Complete Me'''

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
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      <comment>3</comment>
      <text xml:space="preserve">o1W3jB  &lt;a href=&quot;http://svaimhxqrtps.com/&quot;&gt;svaimhxqrtps&lt;/a&gt;, [url=http://lrtyfvzohvro.com/]lrtyfvzohvro[/url], [link=http://nengcsscsydf.com/]nengcsscsydf[/link], http://rfykoxlypdfy.com/</text>
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      <minor/>
      <comment>Reverted edits by [[Special:Contributions/77.242.20.18|77.242.20.18]] ([[User_talk:77.242.20.18|77.242.20.18]]); changed back to last version by [[User:204.185.119.88|204.185.119.88]]</comment>
      <text xml:space="preserve">{{develop}}

Because of a neat compiler trick, any Java reference type or primitive that appears where a &lt;code&gt;String&lt;/code&gt; is expected will be converted
into a string.

For an reference type (object), this is done by inserting code to call &lt;code&gt;String toString()&lt;/code&gt; on the reference. All reference types inherit this method from &lt;code&gt;java.lang.Object&lt;/code&gt;, and most (if not all) classes provided in the standard Java Application Programmer's Interface (API) override this method to produce a string that represents
the data in a form suitable for printing. To provide this service for Java's primitive types, the compiler must wrap the type in
a so-called ''wrapper'' class, and call the wrapper class's &lt;code&gt;toString&lt;/code&gt; method.

Other classes, for example those that you write yourself, will inherit the standard &lt;code&gt;Object.toString()&lt;/code&gt; which produces something like &lt;code&gt;&quot;ClassName@123456&quot;&lt;/code&gt; (where the number is the hashcode representation of the object). Thus even user-defined classes will print something!
If you want something friendlier, you have to provide a method with the signature &lt;code&gt;public String toString()&lt;/code&gt;.
But once you have done so, you get the &quot;print friendly&quot; behaviour of the built-in Java classes for free.

This article will present more detail on Java's built-in string conversion methods with examples of converting and concatenating literal strings, creating strings from the reference types provided in the standard Java APIs,
and the use of the wrapper classes to print the primitive types. In doing so we will present a description of the &lt;code&gt;Object.toString&lt;/code&gt; method which is responsible for most of the ''magic'' that the Java compiler
performs to convert things to strings. The article concludes with a description of a user defined type's default printing behaviour and its behaviour after introduction of a custom &lt;code&gt;toString&lt;/code&gt; method. It is hoped that the article will illustrate some of the background to Java's automated string coercion. It also illustrates some of the extra complexity that a language which makes a distinction between ''object'' types and ''primitives'' creates for itself.

== The Automatic Conversion of Objects to String in String Literals ==

The developers of the Java language recognized that the manipulation of strings would be important to the developers
of Java programs. They thus wanted to make the representation and manipulation of strings as straightforward and
transparent as possible.  They provided
language support for the representation of strings as literals; compiler support for the automatic transparent conversion of
string literals into &lt;code&gt;String&lt;/code&gt; objects; and the automatic conversion from any ''reference type'' (that is any subclass of class &lt;code&gt;Object&lt;/code&gt;
which is more informally called an ''object'') into a printable string by use of the &lt;code&gt;Object.toString&lt;/code&gt; method.
Despite this extra syntactical support for string literals and automatic object-to-string conversion, &lt;code&gt;String&lt;/code&gt; literals and literal expressions
are still represented
and manipulated internally by the Java run-time system as &lt;code&gt;String&lt;/code&gt; objects.

We shall demonstrate this behaviour by means of a simple example.

=== 1 + 2 = 3 ===

Consider the print statements:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;automatic call to toString&gt;&gt;=
System.out.println(&quot;Proof that 1 + 2 = 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + (1 + 2));
&lt;/codeblock&gt;

When you run this code it prints to the console:

  Proof that 1 + 2 = 3
  1 + 2 = 3

which, despite Java's wordy ''print statement'' &lt;code&gt;System.out.println&lt;/code&gt;, is very convenient.

When this code is compiled, the Java compiler notes the signature of the method calls to the print statement is &lt;code&gt;System.out.toString(String arg)&lt;/code&gt;. It therefore
knows that the arguments must be converted to a &lt;code&gt;String&lt;/code&gt;. In the first expression, &lt;code&gt;String arg&lt;/code&gt; is the string literal
&lt;code&gt;&quot;Proof that 1 + 2 = 3&quot;&lt;/code&gt; and it is converted to a String object by a call to the &lt;code&gt;String&lt;/code&gt; constructor:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String literal = new String(&quot;Proof that 1 + 2 = 3&quot;);
&lt;/codeblock&gt;
The first part of the second print statement is a string literal &lt;code&gt;&quot;1 + 2 = &quot;&lt;/code&gt;
and is effectively converted to the java expression:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert string literal to String object&gt;&gt;=
String arg0 = new String(&quot;1 + 2 = &quot;);
&lt;/codeblock&gt;

The next part of the expression is the &lt;code&gt;+&lt;/code&gt; operator which
in the ''string context'' means ''concatenation''. The right-hand argument of the concatenation operator is an expression &lt;code&gt;1 + 2&lt;/code&gt;
which has value equivalent to the expression &lt;code&gt;int arg1 = 1 + 2;&lt;/code&gt;. This expression is of type &lt;code&gt;int&lt;/code&gt; and must be converted to
a &lt;code&gt;String&lt;/code&gt; before the concatenation can be performed. To convert &lt;code&gt;int&lt;/code&gt; to &lt;code&gt;String&lt;/code&gt; we must call upon
the services of the ''wrapper class'' Integer (discussed further later in this article). The &lt;code&gt;Integer&lt;/code&gt; class has a method
&lt;code&gt;toString&lt;/code&gt; which can convert
an &lt;code&gt;int&lt;/code&gt; value into a &lt;code&gt;String&lt;/code&gt;. Thus the compiler will generate code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;convert int to String object&gt;&gt;=
String arg1 = new Integer(1 + 2).toString();
&lt;/codeblock&gt;
Now the expression is reduced to
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;concatenate arguments&gt;&gt;=
String arg = arg0 + arg1;
&lt;/codeblock&gt;
To actually print the strings, &lt;code&gt;System.out.println&lt;/code&gt; will call &lt;code&gt;String.toString()&lt;/code&gt; and pass the resulting bytes to the console's output stream:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print String objects using toString&gt;&gt;=
System.out.println(literal.toString());
System.out.println(arg.toString());
&lt;/codeblock&gt;

Putting all of this together, the long way to print a pair of &lt;code&gt;String&lt;/code&gt; literals is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;=
&lt;&lt;convert string literal to String object&gt;&gt;
&lt;&lt;convert int to String object&gt;&gt;
&lt;&lt;concatenate arguments&gt;&gt;
&lt;&lt;print String objects using toString&gt;&gt;
&lt;/codeblock&gt;
It is perhaps important to note that this code is close to the code that the compiler actually creates and
that Java virtual machine (JVM) must execute to perform this simple operation (although compiler optimization
is able to do some simplifications).

To prove this we use a pair of assertions:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;proof that 1 + 2 = 3&gt;&gt;=
assert (&quot;Proof that 1 + 2 = 3&quot;).equals(literal.toString());
assert (&quot;1 + 2 = &quot; + (1 + 2)).equals(arg.toString());
&lt;/codeblock&gt;

=== In String-world 1 + 2 sometimes equals 12 ===

The observant reader will have noted the use of parenthesis in the expression &lt;code&gt;&quot;1 + 2 = &quot; + (1 + 2)&lt;/code&gt;
and may be wondering why. If we instead wrote:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(&quot;Proof that sometimes 1 + 2 does not make 3&quot;);
System.out.println(&quot;1 + 2 = &quot; + 1 + 2);
&lt;/codeblock&gt;
the result would be the equivalent of:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;not the way to do it&gt;&gt;=
System.out.println(new String(&quot;Proof that sometimes 1 + 2 does not make 3&quot;).toString());
System.out.println((new String(&quot;1 + 2 = &quot;).toString()) + (new Integer(1).toString()) + (new Integer(2).toString()));
&lt;/codeblock&gt;
printing
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 12
rather than the expected
 Proof that sometimes 1 + 2 does not make 3
 1 + 2 = 3

We can ask the compiler to prove this with another assertion:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;=
assert (&quot;1 + 2 = &quot; + 1 + 2).equals(&quot;1 + 2 = 12&quot;);
&lt;/codeblock&gt;

The technical reason for this, perhaps, counterintuitive behaviour is that under the standard Java operator precedence rules, the concatenation operator binds tighter than the addition operator. Thus the compiler sees &lt;code&gt;&quot;1 + 2 = &quot; + 1 + 2&lt;/code&gt; as
a sequence of string concatenations. We need the parenthesis to force Java to perform addition
rather than concatenation on the arguments &lt;code&gt;1 + 2&lt;/code&gt;.

=== Program 1 ===

Here is the code for the first example in executable form:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;StringLiterals.java&gt;&gt;=

public class StringLiterals {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for string literals\n&quot; +
        &quot;relies on the toString method and string concatenation&quot;);

     &lt;&lt;automatic call to toString&gt;&gt;

     &lt;&lt;print 1 + 2 = 3 the long way&gt;&gt;

     &lt;&lt;proof that 1 + 2 = 3&gt;&gt;

     &lt;&lt;not the way to do it&gt;&gt;

     &lt;&lt;counter proof that 1 + 2 doesn't always make 3&gt;&gt;

  }

}
&lt;/codeblock&gt;

You should note that the test relies on the &lt;code&gt;assert&lt;/code&gt; keyword, which was added to Java in JDK 1.4. To run this code
you will need to compile the class &lt;code&gt;StringLiterals&lt;/code&gt; using a compiler from JDK 1.4 or later.
The code for assertion checking is usually turned off, so to have the &lt;code&gt;assert&lt;/code&gt; statement executed, the compiler class must be run
using the &lt;code&gt;-ea&lt;/code&gt; argument:
&lt;codeblock&gt;
javac StringLiterals.java
java -ea StringLiterals
&lt;/codeblock&gt;

We will use the &lt;code&gt;assert&lt;/code&gt; keyword in the other programs in this article, and they all must be compiled and run in the same way.

== More about Object.toString() ==

As demonstrated in the previous section, much of the magic of string literal manipulation is performed
behind the scenes by the &lt;code&gt;String toString()&lt;/code&gt; method that all Java reference types, or ''objects'', inherit from &lt;code&gt;java.lang.Object&lt;/code&gt;. To illustrate this, let's examine the string generated by
&lt;code&gt;Object&lt;/code&gt; itself.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
Object o = new Object();
System.out.println(&quot;Object printed with toString: &quot; + o);
&lt;/codeblock&gt;
An easy and elegant way to force an object to become a string is to concatenate it with a prepended empty string literal as in:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
String objectAsString = &quot;&quot; + o;
System.out.println(&quot;Object as a string literal: &quot; + objectAsString);
&lt;/codeblock&gt;
Of course, because both expressions will eventually call &lt;code&gt;o.toString()&lt;/code&gt;, we'd expect the two to be equivalent. We use an assertion to prove that they are:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
assert objectAsString.equals(o.toString());
&lt;/codeblock&gt;

A typical run of the program will produce:

  Object printed with toString: java.lang.Object@3e25a5
  Object as a string literal: java.lang.Object@3e25a5

As you can see, the default behaviour of the &lt;code&gt;Object.toString&lt;/code&gt; method is to return the fully qualified name of the calling class (in this case &lt;code&gt;java.lang.Object&lt;/code&gt;) followed by an hexadecimal code representing the &quot;address&quot; of the object in Java's run-time heap store. The code &lt;code&gt;@3e25a5&lt;/code&gt; that follows the class name will not necessarily be the same when you run the program, or even between program runs.

It is usual for class designers to override the &lt;code&gt;Object.toString&lt;/code&gt; method so that classes are able to print useful information about themselves. In the remainder of this section, we shall examine how the designers
of the Java API have chosen to override &lt;code&gt;toString&lt;/code&gt; for a selection of the most commonly used classes.

=== Printing Numbers ===

In Java, numbers are not objects, but instead, perhaps for performance reasons, are represented by so-called
''primitive'' values. The following simple function uses automatic string conversion to produce the table of numbers that often accompanies Java textbooks. The mechanics of how this is done is discussed in the next section.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print table of numbers&gt;&gt;=
public static void printTableOfNumbers() {
    String table = &quot;Table of the Java Numbers\n&quot; +
		 &quot;Primitive Type\tSize in Bits\tTypical Value\tMinimum Value\t\tMaximum Value\n&quot; +
		 &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;
	// byte
	table += &quot;byte\t\t&quot; + 8 + &quot;\t\t&quot; + (byte)5 + &quot;\t\t&quot; + Byte.MIN_VALUE + &quot;\t\t\t&quot; + Byte.MAX_VALUE + &quot;\n&quot;;
	// short
	table += &quot;short\t\t&quot; + 16 + &quot;\t\t&quot; + (short)1024 + &quot;\t\t&quot; + Short.MIN_VALUE + &quot;\t\t\t&quot; + Short.MAX_VALUE + &quot;\n&quot;;
	// int
	table += &quot;int\t\t&quot; + 32 + &quot;\t\t&quot; + 65536 + &quot;\t\t&quot; + Integer.MIN_VALUE + &quot;\t\t&quot; + Integer.MAX_VALUE + &quot;\n&quot;;
	// long
	table += &quot;long\t\t&quot; + 64 + &quot;\t\t&quot; + 1000000000L + &quot;\t&quot; + Long.MIN_VALUE + &quot;\t&quot; + Long.MAX_VALUE + &quot;\n&quot;;
	// float
	table += &quot;float\t\t&quot; + 32 + &quot;\t\t&quot; + 3.14215926 + &quot;\t&quot; + Float.MIN_VALUE + &quot;\t\t\t&quot; + Float.MAX_VALUE + &quot;\n&quot;;
	// double
	table += &quot;double\t\t&quot; + 64 + &quot;\t\t&quot; + 100e100 + &quot;\t\t&quot; + Double.MIN_VALUE + &quot;\t\t&quot; + Double.MAX_VALUE + &quot;\n&quot;;
	table +=
	     &quot;==============\t=============\t============\t=============\t\t=============\n&quot;;

	System.out.println(table);
}
&lt;/codeblock&gt;

We add this to the code for &lt;code&gt;PrintingObjects&lt;/code&gt; as shown here:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
printTableOfNumbers();
&lt;/codeblock&gt;

The result should be:

 Table of the Java Numbers
 Primitive Type  Size in Bits    Typical Value   Minimum Value        Maximum Value
 ==============  =============   ============    =============        =============
 byte            8               5               -128                 127
 short           16              1024            -32768               32767
 int             32              65536           -2147483648          2147483647
 long            64              1000000000      -9223372036854775808 9223372036854775807
 float           32              3.14215926      1.4E-45              3.4028235E38
 double          64              1.0E102         4.9E-324             1.7976931348623157E308
 ==============  =============   ============    =============        =============

=== Printing Booleans and Characters ===

The boolean primitive has only two values &lt;code&gt;true&lt;/code&gt; and &lt;code&gt;false&lt;/code&gt;. Let's use these
values to produce a truth table for the Exclusive-OR (XOR) operator which is implemented in Java as the &lt;code&gt;^&lt;/code&gt; operator.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;XOR table&gt;&gt;=
public static void truthTable() {
  String table =
          &quot;  A   \t   B   \t A XOR B\n&quot; +
          &quot;======\t=======\t========\n&quot; +
          false + &quot;\t&quot; + false + &quot;\t&quot; + (false ^ false) + &quot;\n&quot; +
          false + &quot;\t&quot; + true  + &quot;\t&quot; + (false ^ true ) + &quot;\n&quot; +
          true  + &quot;\t&quot; + false + &quot;\t&quot; + (true  ^ false) + &quot;\n&quot; +
          true  + &quot;\t&quot; + true  + &quot;\t&quot; + (true  ^ true ) + &quot;\n&quot; +
         &quot;======\t=======\t========\n&quot;;
  System.out.println(table);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
truthTable();
&lt;/codeblock&gt;

The result is:

   A   	   B   	 A XOR B
 ======	=======	========
 false	false	false
 false	true	true
 true	false	true
 true	true	false
 ======	=======	========

To illustrate the printing of character values we'll take a string &lt;code&gt;&quot;Now is the time for all good men to come to the aid of the party&quot;&lt;/code&gt;, convert it into an array of &lt;code&gt;char&lt;/code&gt;, perform a 5 character shift cypher on each character and then print the resulting cypher text.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple cypher&gt;&gt;=
public static String simpleCypher(String plaintext) {
   char [] letters = plaintext.toCharArray();
   String cypherText = &quot;&quot;;
   for (int i = 0; i &lt; plaintext.length(); i ++) {
     char letter = plaintext.charAt(i);
	 letter += 5;
	 cypherText += letter;
   }
   return cypherText;
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Printing objects&gt;&gt;=
System.out.println(simpleCypher(&quot;Now is the time for all good men to come to the aid of the party&quot;));
&lt;/codeblock&gt;

Here is the result:

  St|%nx%ymj%ynrj%ktw%fqq%ltti%rjs%yt%htrj%yt%ymj%fni%tk%ymj%ufwy~


=== Printing Strings ===

'''Complete me'''

A discussion of what happens when &lt;code&gt;String.toString&lt;/code&gt; is called.

=== Printing Metaclass information ===

'''Complete Me'''

What is printed when &lt;code&gt;Class.toString()&lt;/code&gt; is called and how &lt;code&gt;Object.toString()&lt;/code&gt; is able to call upon this meta class behaviour to print something for any object.

=== A Selection of further Examples from the API ===

'''Complete Me'''

A selection of examples to illustrate what is printed by other classes for example &lt;code&gt;Data&lt;/code&gt;, &lt;code&gt;List&lt;/code&gt;, &lt;code&gt;Map&lt;/code&gt;, &lt;code&gt;RegExp&lt;/code&gt;. This will help us to formulate a discussion of how to write our own &lt;code&gt;toString&lt;/code&gt; methods.

=== Program 2 ===

This program exercises all of the examples from the discussion of &quot;''More about'' &lt;code&gt;Object.toString{)&lt;/code&gt;.&quot;

'''Complete Me'''

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;PrintingObjects.java&gt;&gt;=
&lt;&lt;include a selection of classes from the API&gt;&gt;

public class PrintingObjects {
	public static void main (String[] args) {
	  &lt;&lt;Printing objects&gt;&gt;
	}

	&lt;&lt;print table of numbers&gt;&gt;
	&lt;&lt;XOR table&gt;&gt;
	&lt;&lt;simple cypher&gt;&gt;
}
&lt;/codeblock&gt;

== Converting Java Primitives to Strings ==

As discussed in the first part of this article, when called upon to print a primitive value, the Java compiler will insert code to wrap the
primitive in an instance of the primitive type's wrapper class. It will then call the wrapper class's &lt;code&gt;toString()&lt;/code&gt; method.
Thus, when compiled:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + l;
&lt;/codeblock&gt;
will actually produce code equivalent to:
&lt;codeblock language=&quot;java&quot;&gt;
long l = 1000000L;
String ls = &quot;&quot; + new Long(l).toString();
&lt;/codeblock&gt;

In this section, we explore this behaviour in more detail.
'''Complete Me'''

=== Define the test fixture ===

To demonstrate the behaviour of automatic string coercion, we'll first create a set of primitives:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Declare the primitives&gt;&gt;=
boolean flag = false;
char c = 'A';
byte b = (byte)127;
short s = (short)32767;
int i  = 10000000;
long l = 1000000000000L;
float f = 3.1415926F;
double d = 1.0e99;
&lt;/codeblock&gt;
Note you need to use a cast with the &lt;code&gt;byte&lt;/code&gt; and &lt;code&gt;short&lt;/code&gt; literals because the Java compiler will always convert a literal integer into an
&lt;code&gt;int&lt;/code&gt;. Similarly the postfixes &lt;code&gt;L&lt;/code&gt; and &lt;code&gt;F&lt;/code&gt; are needed because otherwise Java will compile an integer literal as an &lt;code&gt;int&lt;/code&gt; and a floating point literal as a &lt;code&gt;double&lt;/code&gt;.

To make the code of the test itself easier to understand, we create wrapper classes for each of these cases and add them to an array list.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Wrap the primitives and add to an array list&gt;&gt;=
ArrayList primitives = new ArrayList();
Boolean wflag = new Boolean(flag); primitives.add(wflag);
Character wc = new Character(c); primitives.add(wc);
Byte wb = new Byte(b); primitives.add(wb);
Short ws = new Short(s); primitives.add(ws);
Integer wi = new Integer(i); primitives.add(wi);
Long wl = new Long(l); primitives.add(wl);
Float wf = new Float(f); primitives.add(wf);
Double wd = new Double(d); primitives.add(wd);
&lt;/codeblock&gt;

=== Defining the test ===

For testing purposes, we want to take each element of the array list, convert the object to a string using &lt;code&gt;Object.toString()&lt;/code&gt;, and
compare the resulting string with the result of automatic &lt;code&gt;String&lt;/code&gt; coercion that results from &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Test primitive to string conversion&gt;&gt;=
for (int primitive = 0; primitive &lt; primitives.size(); primitive++) {
  Object wrapper = primitives.get(primitive);
  System.out.println(&quot;Testing toString for &quot; + wrapper.getClass());
  &lt;&lt;get result of toString&gt;&gt;
  &lt;&lt;get result of automatic string coercion&gt;&gt;
  &lt;&lt;compare results&gt;&gt;
}
&lt;/codeblock&gt;

All wrapper classes override the &lt;code&gt;toString()&lt;/code&gt;, so to get a printable string we simply call this method. There is no need to
force a cast, as the correct version of &lt;code&gt;toString&lt;/code&gt; method will be called at run time due to [http://en.wikipedia.org/wiki/Polymorphism_in_object-oriented_programming polymorphism].
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of toString&gt;&gt;=
String stringFromWrapper = wrapper.toString();
&lt;/codeblock&gt;

The proof that &lt;code&gt;wrapper.toString()&lt;/code&gt; is the same as the &lt;code&gt;&quot;&quot; + ''value''&lt;/code&gt; will be trickier because Java's static
type checking will not allow us to easily extract the value stored in the wrapper class. For now let us postulate that we can
create a static method &lt;code&gt;coerceWrappedPrimitiveValueToString(Object)&lt;/code&gt; that will take a wrapper object and return the value
of the wrapped primitive coerced to a string. With this method available we can write:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get result of automatic string coercion&gt;&gt;=
String coercedFromValueOfPrimitive = coerceWrappedPrimitiveValueToString(wrapper);
&lt;/codeblock&gt;
and the final test is now simply:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;compare results&gt;&gt;=
assert stringFromWrapper.equals(coercedFromValueOfPrimitive);
&lt;/codeblock&gt;

=== Validating the auto string coercion ===

We want to prove that the general statement &lt;code&gt;&quot;&quot; + ''primitive''&lt;/code&gt; is converted by the compiler to &lt;code&gt;new Wrapper(primitive).toString()&lt;/code&gt;.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;define a method to coerce a primitive to a string&gt;&gt;=
static String coerceWrappedPrimitiveValueToString(Object o) {
   &lt;&lt;process according to type of wrapper object&gt;&gt;
}
&lt;/codeblock&gt;

Unfortunately, Java's static type checking makes the coercion of the primitive value of a wrapper class much more difficult than the simple
polymorphic call to &lt;code&gt;wrapper.toString()&lt;/code&gt;. There is no equivalent polymorphic call &lt;code&gt;valueOf&lt;/code&gt;
that can return a primitive of undefined type. Instead, each wrapper class provides method with signature &lt;code&gt;''type'' ''type''Value()&lt;/code&gt;.
We will need to use ''run-time type identification'' (RTTI) to cast the object parameter to its wrapper class before we can extract the value
and coerce the value to a string.

We will need to identify the class of the wrapper object &lt;code&gt;o&lt;/code&gt; before we can assign the wrapped primitive value to a value of the correct type.
We will use a decision tree for this:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;process according to type of wrapper object&gt;&gt;=
if (o instanceof Boolean) {
  &lt;&lt;return value of Boolean coerced to String&gt;&gt;
}
else if (o instanceof Character) {
  &lt;&lt;return value of Character coerced to String&gt;&gt;
}
else if (o instanceof Byte) {
  &lt;&lt;return value of Byte coerced to String&gt;&gt;
}
else if (o instanceof Short) {
  &lt;&lt;return value of Short coerced to String&gt;&gt;
}
else if (o instanceof Integer) {
  &lt;&lt;return value of Integer coerced to String&gt;&gt;
}
else if (o instanceof Long) {
  &lt;&lt;return value of Long coerced to String&gt;&gt;
}
else if (o instanceof Float) {
  &lt;&lt;return value of Float coerced to String&gt;&gt;
}
else if (o instanceof Double) {
  &lt;&lt;return value of Double coerced to String&gt;&gt;
}
else {
  &lt;&lt;unexpected class: return default coercion&gt;&gt;
}
&lt;/codeblock&gt;

Having decided which wrapper class we are dealing with, we can get at the primitive type and coerce it to a string. Here's the
example for the &lt;code&gt;Long&lt;/code&gt; case. You'll note that we have to ''downcast'' the reference from &lt;code&gt;Object&lt;/code&gt; to
&lt;code&gt;Long&lt;/code&gt; before we can access the &lt;code&gt;longValue()&lt;/code&gt; method:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Long coerced to String&gt;&gt;=
long l = ((Long)o).longValue();
return &quot;&quot; + l;
&lt;/codeblock&gt;

The other types follow the same pattern:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Boolean coerced to String&gt;&gt;=
boolean b = ((Boolean)o).booleanValue();
return &quot;&quot; + b;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Character coerced to String&gt;&gt;=
char c = ((Character)o).charValue();
return &quot;&quot; + c;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Byte coerced to String&gt;&gt;=
byte aByte = ((Byte)o).byteValue();
return &quot;&quot; + aByte;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Short coerced to String&gt;&gt;=
short s = ((Short)o).shortValue();
return &quot;&quot; + s;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Integer coerced to String&gt;&gt;=
int i = ((Integer)o).intValue();
return &quot;&quot; + i;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Float coerced to String&gt;&gt;=
float f = ((Float)o).floatValue();
return &quot;&quot; + f;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;return value of Double coerced to String&gt;&gt;=
double d = ((Double)o).doubleValue();
return &quot;&quot; + d;
&lt;/codeblock&gt;

Finally, for the case where no match is found, we simply let &lt;code&gt;Object.toString()&lt;/code&gt; do its thing:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;unexpected class: return default coercion&gt;&gt;=
return &quot;&quot; + o;
&lt;/codeblock&gt;

=== Program 3 ===

The complete test class is:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ConvertPrimitivesToStrings.java&gt;&gt;=
import java.util.ArrayList;

public class ConvertPrimitivesToStrings {

  public static void main (String [] args) {
     System.out.println(&quot;Demonstrating that Java's built-in support for converting primitives\n&quot; +
        &quot;to Strings relies on the toString method&quot;);
     &lt;&lt;Declare the primitives&gt;&gt;

     &lt;&lt;Wrap the primitives and add to an array list&gt;&gt;

     &lt;&lt;Test primitive to string conversion&gt;&gt;
  }

  &lt;&lt;define a method to coerce a primitive to a string&gt;&gt;

}
&lt;/codeblock&gt;

== Using Automatic String Generation in your own Classes ==

=== The Default behaviour ===

'''Complete Me'''

Will discuss what happens when you don't override &lt;code&gt;Object.toString&lt;/code&gt; when you write your own classes...

=== Writing Your Own toString Method ===

... and the benefits you and your clients will get for free when you do.

=== Using Jakarta Commons ===

For more complex classes, it can become tedious to have to write consistently good consistent &lt;code&gt;toString&lt;/code&gt; methods. 
The [http://jakarta.apache.org/commons/ Apache Jakarta Commons] library comes to the rescue
here with the &lt;code&gt;org.apache.commons.lang.builder.ToStringBuilder()&lt;/code&gt;. We will illustrate the use of this in a custom
class of own own and demonstrate some of its other features, such as the use of ''reflection'' to completely automate the creation
of a &lt;code&gt;toString&lt;/code&gt; method, or even to interrogate foreign objects. This particular section may be a little too advanced for
this introductory article and it may benefit from presentation in a separate article.

'''Complete Me'''

== Discussion ==

'''Note: needs revision!''' Clearly you can call &lt;code&gt;toString()&lt;/code&gt; yourself whenever you need a printable version of an object or a primitive, but arguably the
compiler's default behaviour allows you to write clearer and cleaner code.

== References ==

Joshua Block, ''Effective Java'', Sun Microsystems Press, Addison Wesley, 2002.

Bruce Eckel, ''Thinking in Java'', 4th Edition, Prentice-Hall, 2006.

== See Also ==

* [[Convert Integer to String (Java)]]
* [[Conversion between numbers and strings]]

[[Category:Convert Object to String|Java]]
[[Category:Introductory examples|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Convert integer to English words (QBASIC)</title>
    <id>2817</id>
    <revision>
      <id>8181</id>
      <timestamp>2006-11-26T17:23:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Convert integer to English words (QBASIC)]] moved to [[Convert integer to words (QBASIC)]]: Okay, so it does other languages</comment>
      <text xml:space="preserve">#REDIRECT [[Convert integer to words (QBASIC)]]</text>
    </revision>
  </page>
  <page>
    <title>Convert integer to words (Java)</title>
    <id>2992</id>
    <revision>
      <id>8894</id>
      <timestamp>2007-02-08T18:51:57Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <comment>Started the article</comment>
      <text xml:space="preserve">{develop}
Here is the function for changing a number into words. It works for English and can be extended, by use of property bundles, for other languages.</text>
    </revision>
    <revision>
      <id>8895</id>
      <timestamp>2007-02-08T18:52:27Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}
Here is a function for changing a number into words. It works for English and can be extended, by use of property bundles, for other languages.</text>
    </revision>
    <revision>
      <id>8896</id>
      <timestamp>2007-02-08T18:55:08Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}
Here is a function for changing a number into words. It works for English and can be extended, by use of property bundles, for other languages.
[[Category:Programming language:Java]]
[[Category:Environment:Java Platform]]
[[Category:Convert Integer to String|Java]]</text>
    </revision>
    <revision>
      <id>8903</id>
      <timestamp>2007-02-08T19:08:21Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
Here is a function for changing a number into words. It works for English and can be extended, by use of property bundles, for other languages.
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Convert Integer to String|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Convert integer to words (QBASIC)</title>
    <id>2613</id>
    <revision>
      <id>7178</id>
      <timestamp>2006-08-09T06:39:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Add new code</comment>
      <text xml:space="preserve">Here is the function for changing a number into words.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLog10 = 0 THEN GOSUB Num2LangInit

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      dDigitGroup = aNumber - dDigitGroup * 10
      IF dDigitGroup &lt;&gt; 0 THEN dBuffer = dBuffer + &quot;-&quot; + Num2Lang((dDigitGroup), aLang)
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      dBuffer = Num2Lang(dDigitGroup, aLang) + dPowers(dRange)
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         ELSE
            dBuffer = dBuffer + &quot;,&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
   dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
   dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
   dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
   dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
   dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
   dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
   dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
   dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
   dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function

&lt;codeblock language=BASIC&gt;
&lt;&lt;num2lang.bas&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM J AS INTEGER
DIM dTest AS LONG

RANDOMIZE TIMER
CLS
FOR J = 1 TO 20
   dTest = INT(RND * 2 ^ 31 - 1)
   PRINT dTest; TAB(10); Num2Lang$(dTest, &quot;en-us&quot;)
   PRINT TAB(10); Num2Lang$(dTest, &quot;en-uk&quot;)
NEXT
SYSTEM
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7179</id>
      <timestamp>2006-08-09T06:42:38Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>tweak</comment>
      <text xml:space="preserve">Here is the function for changing a number into words.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLog10 = 0 THEN GOSUB Num2LangInit

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      dDigitGroup = aNumber - dDigitGroup * 10
      IF dDigitGroup &lt;&gt; 0 THEN dBuffer = dBuffer + &quot;-&quot; + Num2Lang((dDigitGroup), aLang)
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      dBuffer = Num2Lang(dDigitGroup, aLang) + dPowers(dRange)
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         ELSE
            dBuffer = dBuffer + &quot;,&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
   dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
   dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
   dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
   dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
   dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
   dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
   dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
   dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
   dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function

&lt;codeblock language=BASIC&gt;
&lt;&lt;num2lang.bas&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM J AS INTEGER
DIM dTest AS LONG

RANDOMIZE TIMER
CLS
FOR J = 1 TO 20
   dTest = INT(RND * 2 ^ 31 - 1)
   PRINT dTest; TAB(10); Num2Lang$(dTest, &quot;en-us&quot;)
   PRINT TAB(10); Num2Lang$(dTest, &quot;en-uk&quot;)
NEXT
SYSTEM

&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7180</id>
      <timestamp>2006-08-09T06:45:09Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>explain</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English and for US English. So far it doesn't work for other languages.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLog10 = 0 THEN GOSUB Num2LangInit

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      dDigitGroup = aNumber - dDigitGroup * 10
      IF dDigitGroup &lt;&gt; 0 THEN dBuffer = dBuffer + &quot;-&quot; + Num2Lang((dDigitGroup), aLang)
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      dBuffer = Num2Lang(dDigitGroup, aLang) + dPowers(dRange)
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         ELSE
            dBuffer = dBuffer + &quot;,&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
   dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
   dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
   dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
   dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
   dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
   dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
   dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
   dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
   dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function

&lt;codeblock language=BASIC&gt;
&lt;&lt;num2lang.bas&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM J AS INTEGER
DIM dTest AS LONG

RANDOMIZE TIMER
CLS
FOR J = 1 TO 20
   dTest = INT(RND * 2 ^ 31 - 1)
   PRINT dTest; TAB(10); Num2Lang$(dTest, &quot;en-us&quot;)
   PRINT TAB(10); Num2Lang$(dTest, &quot;en-uk&quot;)
NEXT
SYSTEM

&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7184</id>
      <timestamp>2006-08-10T03:20:11Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Add test scaffolding</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

&lt;codeblock language=BASIC&gt;
&lt;&lt;Definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;UnitTests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;UnitTest&gt;&gt;
&lt;&lt;Definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7185</id>
      <timestamp>2006-08-10T03:23:42Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>tweak</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7186</id>
      <timestamp>2006-08-10T03:25:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>tweak</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
  
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF

   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION

Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unittests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unittests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7198</id>
      <timestamp>2006-08-11T02:39:42Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>split it up a bit</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=
   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN

END FUNCTION
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7199</id>
      <timestamp>2006-08-11T02:50:44Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Add some explanation</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in alittle more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=
   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7200</id>
      <timestamp>2006-08-11T03:11:49Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>more reorg</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=
   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber
&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case.

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case.

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7201</id>
      <timestamp>2006-08-11T03:27:40Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>more explanation</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=
   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber
&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code.

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least inicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7202</id>
      <timestamp>2006-08-11T03:44:28Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>more explanation</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code The BASIC idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants and also by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add to much compication.

Also note the addition of .4 to the number when calculating the range. This shouldn't be necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least inicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7203</id>
      <timestamp>2006-08-11T03:52:09Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>more</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code The BASIC idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants and also by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add to much compication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least inicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7204</id>
      <timestamp>2006-08-11T03:58:12Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>carried away there !</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add to much compication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least inicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7205</id>
      <timestamp>2006-08-11T03:58:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;super&gt;31&lt;/super&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add to much compication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7206</id>
      <timestamp>2006-08-11T04:00:15Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>sigh</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each tme the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data on the first call to the function and then just used. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      SELECT CASE aLang
      CASE ELSE
         dDigitGroup = INT(aNumber / 10)
         dBuffer = dTens(dDigitGroup)
         IF dBuffer = &quot;&quot; THEN
            dDigitGroup = dDigitGroup - 1
            dBuffer = dTens(dDigitGroup)
         END IF
         dDigitGroup = aNumber - dDigitGroup * 10
         IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
            dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
         ELSEIF dDigitGroup &gt; 0 THEN
            dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
         END IF
      END SELECT
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add to much compication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify powers of ten vocabulary.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7207</id>
      <timestamp>2006-08-11T04:18:21Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Removed unnecessary SELECT construct and fixed typos</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang &lt;&gt; &quot;en-us&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7208</id>
      <timestamp>2006-08-11T04:25:12Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Automatic unit testing proves its worth yet again</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7209</id>
      <timestamp>2006-08-11T04:31:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>proviso</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7210</id>
      <timestamp>2006-08-11T04:48:29Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>justification for GOSUB use</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7220</id>
      <timestamp>2006-08-11T17:15:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>gosub again</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>7269</id>
      <timestamp>2006-08-13T20:03:34Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>[[Convert Integer to String (BASIC)]] moved to [[Convert Integer to String (QBASIC)]]: More specific dialect</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>8178</id>
      <timestamp>2006-11-26T17:23:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Convert Integer to String (QBASIC)]] moved to [[Convert integer to English words (QBASIC)]]: Better name - convert integer to string connotes 12 -&gt; &quot;12&quot;, not 12 -&gt; &quot;twelve&quot;</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>8180</id>
      <timestamp>2006-11-26T17:23:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Convert integer to English words (QBASIC)]] moved to [[Convert integer to words (QBASIC)]]: Okay, so it does other languages</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingts-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingts-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9842</id>
      <timestamp>2007-04-23T21:33:42Z</timestamp>
      <contributor>
        <ip>195.200.106.147</ip>
      </contributor>
      <comment>precisions about french and modified test cases</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.

Here are some precisions from a native french speaker : 

when &quot;cent&quot; (100) or &quot;vingt&quot; (20) is used in a plural form it gets a final 's' :

300 gives &quot;trois cents&quot;

80 gives &quot;quatre-vingts&quot;

BUT the 's' disappears if there are other numbers after that :

301 gives &quot;trois cent un&quot;

380 gives &quot;trois cent quatre vingts&quot;

384 gives &quot;trois cent quatre vingt quatre&quot;

I modified the test cases to reflect that : now they should fail !

here are links with samples and more explanations :
http://www.leconjugueur.com/frlesnombresecrits.php
http://www.miakinen.net/vrac/nombres

Also &quot;septante&quot;, &quot;octante&quot; and &quot;nonante&quot; DO exist in belgian french ( fr_be ) this is a frequent subject of discussion where belgian people argue that they are more logical than frenchs...
I guess you could support another &quot;language&quot; easily... maybe even two as I suspect the french speaking swiss to do the same.


The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.


Note: It would be great and easy to format the tests results according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol )

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt in&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9843</id>
      <timestamp>2007-04-24T03:27:14Z</timestamp>
      <contributor>
        <ip>68.147.195.158</ip>
      </contributor>
      <comment>Moved French speaker's helpful comments to discussion page</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated.


The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.


Note: It would be great and easy to format the tests results according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol )

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt in&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9847</id>
      <timestamp>2007-04-24T05:13:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.


Note: It would be great and easy to format the tests results according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol )

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt in&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9849</id>
      <timestamp>2007-04-24T05:22:06Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>French dialects</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG, dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dDigitGroup = INT(aNumber / 10)
      dBuffer = dTens(dDigitGroup)
      IF dBuffer = &quot;&quot; THEN
         dDigitGroup = dDigitGroup - 1
         dBuffer = dTens(dDigitGroup)
      END IF
      dDigitGroup = aNumber - dDigitGroup * 10
      IF aLang = &quot;fr&quot; AND dDigitGroup MOD 10 = 1 THEN
         dBuffer = dBuffer + &quot; et &quot; + Num2Lang(dDigitGroup, aLang)
      ELSEIF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot;-&quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dDigitGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dDigitGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dDigitGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dDigitGroup * 10 ^ dRange
      IF dDigitGroup &gt; 0 THEN
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot; and&quot;
         END IF
         dBuffer = dBuffer + &quot; &quot; + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE aLang
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cent&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliard&quot;
   CASE ELSE
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.


Note: It would be great and easy to format the tests results according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol )

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING

CLS
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE mStatus = &quot;&quot;
   READ mTest
   IF mTest = &quot;&quot; THEN
      mStatus = &quot;All tests Succeeded&quot;
   ELSE
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      PRINT LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;Last test failed (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
   END IF
LOOP
PRINT mStatus
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt in&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9912</id>
      <timestamp>2007-05-03T06:14:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>Updated code to handle French better</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG
   DIM dTensGroup AS LONG, dPowersGroup AS LONG
   DIM dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dTensGroup = INT(aNumber / 10)
      dBuffer = dTens(dTensGroup)
      IF dBuffer = &quot;&quot; THEN
         dTensGroup = dTensGroup - 1
         dBuffer = dTens(dTensGroup)
      END IF
      dDigitGroup = aNumber - dTensGroup * 10
      IF dDigitGroup &gt; 0 THEN
         IF LEFT$(aLang, 2) = &quot;fr&quot; AND RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
         IF LEFT$(aLang, 2) &lt;&gt; &quot;fr&quot; OR dDigitGroup MOD 10 &lt;&gt; 1 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSEIF aLang = &quot;fr&quot; AND dTensGroup = 8 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSE
            dBuffer = dBuffer + &quot; et &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dPowersGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dPowersGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dPowersGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dPowersGroup * 10 ^ dRange
     
      IF LEFT$(aLang, 2) = &quot;fr&quot; AND (dPowersGroup = 1 OR dDigitGroup &gt; 0) THEN
         IF RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
      END IF
      IF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot; &quot;
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot;and &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE LEFT$(aLang, 2)
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cents&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; millions&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliards&quot;
   CASE &quot;en&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   CASE ELSE
      dUnits(0) = &quot;0&quot;: dUnits(10) = &quot;0&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;1&quot;: dUnits(11) = &quot;1&quot;: dTens(1) = &quot;1&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;2&quot;: dUnits(12) = &quot;2&quot;: dTens(2) = &quot;2&quot;: dPowers(2) = &quot;&quot;
      dUnits(3) = &quot;3&quot;: dUnits(13) = &quot;3&quot;: dTens(3) = &quot;3&quot;: dPowers(3) = &quot;&quot;
      dUnits(4) = &quot;4&quot;: dUnits(14) = &quot;4&quot;: dTens(4) = &quot;4&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;5&quot;: dUnits(15) = &quot;5&quot;: dTens(5) = &quot;5&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;6&quot;: dUnits(16) = &quot;6&quot;: dTens(6) = &quot;6&quot;: dPowers(6) = &quot;&quot;
      dUnits(7) = &quot;7&quot;: dUnits(17) = &quot;7&quot;: dTens(7) = &quot;7&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;8&quot;: dUnits(18) = &quot;8&quot;: dTens(8) = &quot;8&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;9&quot;: dUnits(19) = &quot;9&quot;: dTens(9) = &quot;9&quot;: dPowers(9) = &quot;&quot;
   END SELECT
   SELECT CASE LEFT$(aLang, 5)
   CASE &quot;fr-be&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;octante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE &quot;fr-ch&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;huitante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE ELSE
      REM Do nothing
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

Note: the tests results are now formatted according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol)

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mTestCount AS INTEGER
DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING
DIM mDelay as SINGLE
DIM mTimer as SINGLE

mTestCount = 0
RESTORE TestCases
DO
   READ mTest
   IF mTest = &quot;&quot; THEN 
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
   END IF
LOOP

CLS
PRINT &quot;1..&quot; + LTRIM$(STR$(mTestCount))
mTestCount = 0
RESTORE TestCases
mStatus = &quot;&quot;
DO 
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      mStatus = &quot;ok&quot; + STR$(mTestCount)
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;not &quot; + mStatus
      END IF
      mStatus = mStatus + &quot; - &quot; + LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = mStatus + &quot; (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
      PRINT mStatus
      IF mExpected &lt;&gt; mGot THEN
         mDelay = 5
         mTimer = INT(TIMER)
         DO WHILE mDelay &gt; 0
            IF mTimer &lt;&gt; INT(TIMER) THEN
               mTimer = INT(TIMER)
               mDelay = mDelay - 1
            END IF
         LOOP
      END IF
   END IF
LOOP
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,70,&quot;soixante-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,70,&quot;septante&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,71,&quot;septante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,80,&quot;octante&quot;
   DATA &quot;*&quot;,&quot;fr-ch&quot;,80,&quot;huitante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt-un&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,81,&quot;octante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,82,&quot;quatre-vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,90,&quot;nonante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,900,&quot;neuf cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100000,&quot;cent mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200000,&quot;deux cents mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200025,&quot;deux cents mille vingt-cinq&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000100,&quot;un million cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000,&quot;deux millions&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2003201,&quot;deux million trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000000,&quot;deux milliards&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000003201,&quot;deux milliard trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9914</id>
      <timestamp>2007-05-03T06:42:36Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>fix test harness</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG
   DIM dTensGroup AS LONG, dPowersGroup AS LONG
   DIM dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds two minor complications. Firstly some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dTensGroup = INT(aNumber / 10)
      dBuffer = dTens(dTensGroup)
      IF dBuffer = &quot;&quot; THEN
         dTensGroup = dTensGroup - 1
         dBuffer = dTens(dTensGroup)
      END IF
      dDigitGroup = aNumber - dTensGroup * 10
      IF dDigitGroup &gt; 0 THEN
         IF LEFT$(aLang, 2) = &quot;fr&quot; AND RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
         IF LEFT$(aLang, 2) &lt;&gt; &quot;fr&quot; OR dDigitGroup MOD 10 &lt;&gt; 1 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSEIF aLang = &quot;fr&quot; AND dTensGroup = 8 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSE
            dBuffer = dBuffer + &quot; et &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. it's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 but luckily that doesn't add too much complication.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dPowersGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dPowersGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dPowersGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dPowersGroup * 10 ^ dRange
     
      IF LEFT$(aLang, 2) = &quot;fr&quot; AND (dPowersGroup = 1 OR dDigitGroup &gt; 0) THEN
         IF RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
      END IF
      IF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot; &quot;
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot;and &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE LEFT$(aLang, 2)
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cents&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; millions&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliards&quot;
   CASE &quot;en&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   CASE ELSE
      dUnits(0) = &quot;0&quot;: dUnits(10) = &quot;0&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;1&quot;: dUnits(11) = &quot;1&quot;: dTens(1) = &quot;1&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;2&quot;: dUnits(12) = &quot;2&quot;: dTens(2) = &quot;2&quot;: dPowers(2) = &quot;&quot;
      dUnits(3) = &quot;3&quot;: dUnits(13) = &quot;3&quot;: dTens(3) = &quot;3&quot;: dPowers(3) = &quot;&quot;
      dUnits(4) = &quot;4&quot;: dUnits(14) = &quot;4&quot;: dTens(4) = &quot;4&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;5&quot;: dUnits(15) = &quot;5&quot;: dTens(5) = &quot;5&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;6&quot;: dUnits(16) = &quot;6&quot;: dTens(6) = &quot;6&quot;: dPowers(6) = &quot;&quot;
      dUnits(7) = &quot;7&quot;: dUnits(17) = &quot;7&quot;: dTens(7) = &quot;7&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;8&quot;: dUnits(18) = &quot;8&quot;: dTens(8) = &quot;8&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;9&quot;: dUnits(19) = &quot;9&quot;: dTens(9) = &quot;9&quot;: dPowers(9) = &quot;&quot;
   END SELECT
   SELECT CASE LEFT$(aLang, 5)
   CASE &quot;fr-be&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;octante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE &quot;fr-ch&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;huitante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE ELSE
      REM Do nothing
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

Note: the tests results are now formatted according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol)

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mTestCount AS INTEGER
DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING
DIM mDelay AS SINGLE
DIM mTimer AS SINGLE

mTestCount = 0
RESTORE TestCases
DO
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      READ mLang, mNumber, mExpected
      mTestCount = mTestCount + 1
   END IF
LOOP

CLS
PRINT &quot;1..&quot; + LTRIM$(STR$(mTestCount))
mTestCount = 0
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE INKEY$ &lt;&gt; CHR$(27)
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      mStatus = &quot;ok&quot; + STR$(mTestCount)
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;not &quot; + mStatus
      END IF
      mStatus = mStatus + &quot; - &quot; + LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = mStatus + &quot; (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
      PRINT mStatus
      IF mExpected = mGot THEN
         mDelay = .5
      ELSE
         mDelay = 2.5
      END IF
      mTimer = INT(TIMER * 10)
      DO WHILE mDelay &gt; 0
         IF mTimer &lt;&gt; INT(TIMER * 10) THEN
            mTimer = INT(TIMER * 10)
            mDelay = mDelay - .1
         END IF
      LOOP
   END IF
LOOP
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,70,&quot;soixante-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,70,&quot;septante&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,71,&quot;septante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,80,&quot;octante&quot;
   DATA &quot;*&quot;,&quot;fr-ch&quot;,80,&quot;huitante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt-un&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,81,&quot;octante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,82,&quot;quatre-vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,90,&quot;nonante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,900,&quot;neuf cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100000,&quot;cent mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200000,&quot;deux cents mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200025,&quot;deux cents mille vingt-cinq&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000100,&quot;un million cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000,&quot;deux millions&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2003201,&quot;deux million trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000000,&quot;deux milliards&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000003201,&quot;deux milliard trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9922</id>
      <timestamp>2007-05-04T00:06:19Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>update the text to match last nights code update</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG
   DIM dTensGroup AS LONG, dPowersGroup AS LONG
   DIM dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds three minor complications. Firstly, some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly, &quot;quatre-vingts&quot; doesn't need an &quot;s&quot; at the end when followed by units and otherwise needs to be treated differently from the -ante&quot; words. Thirdly, umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section and its internal cases.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dTensGroup = INT(aNumber / 10)
      dBuffer = dTens(dTensGroup)
      IF dBuffer = &quot;&quot; THEN
         dTensGroup = dTensGroup - 1
         dBuffer = dTens(dTensGroup)
      END IF
      dDigitGroup = aNumber - dTensGroup * 10
      IF dDigitGroup &gt; 0 THEN
         IF LEFT$(aLang, 2) = &quot;fr&quot; AND RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
         IF LEFT$(aLang, 2) &lt;&gt; &quot;fr&quot; OR dDigitGroup MOD 10 &lt;&gt; 1 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSEIF aLang = &quot;fr&quot; AND dTensGroup = 8 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSE
            dBuffer = dBuffer + &quot; et &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. It's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 and has rules on when to use plurals for powers of ten and when not to.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dPowersGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dPowersGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dPowersGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dPowersGroup * 10 ^ dRange
     
      IF LEFT$(aLang, 2) = &quot;fr&quot; AND (dPowersGroup = 1 OR dDigitGroup &gt; 0) THEN
         IF RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
      END IF
      IF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot; &quot;
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot;and &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE LEFT$(aLang, 2)
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cents&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; millions&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliards&quot;
   CASE &quot;en&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   CASE ELSE
      dUnits(0) = &quot;0&quot;: dUnits(10) = &quot;0&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;1&quot;: dUnits(11) = &quot;1&quot;: dTens(1) = &quot;1&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;2&quot;: dUnits(12) = &quot;2&quot;: dTens(2) = &quot;2&quot;: dPowers(2) = &quot;&quot;
      dUnits(3) = &quot;3&quot;: dUnits(13) = &quot;3&quot;: dTens(3) = &quot;3&quot;: dPowers(3) = &quot;&quot;
      dUnits(4) = &quot;4&quot;: dUnits(14) = &quot;4&quot;: dTens(4) = &quot;4&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;5&quot;: dUnits(15) = &quot;5&quot;: dTens(5) = &quot;5&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;6&quot;: dUnits(16) = &quot;6&quot;: dTens(6) = &quot;6&quot;: dPowers(6) = &quot;&quot;
      dUnits(7) = &quot;7&quot;: dUnits(17) = &quot;7&quot;: dTens(7) = &quot;7&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;8&quot;: dUnits(18) = &quot;8&quot;: dTens(8) = &quot;8&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;9&quot;: dUnits(19) = &quot;9&quot;: dTens(9) = &quot;9&quot;: dPowers(9) = &quot;&quot;
   END SELECT
   SELECT CASE LEFT$(aLang, 5)
   CASE &quot;fr-be&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;octante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE &quot;fr-ch&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;huitante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE ELSE
      REM Do nothing
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

Note: the tests results are now formatted according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol).

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mTestCount AS INTEGER
DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING
DIM mDelay AS SINGLE
DIM mTimer AS SINGLE

mTestCount = 0
RESTORE TestCases
DO
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      READ mLang, mNumber, mExpected
      mTestCount = mTestCount + 1
   END IF
LOOP

CLS
PRINT &quot;1..&quot; + LTRIM$(STR$(mTestCount))
mTestCount = 0
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE INKEY$ &lt;&gt; CHR$(27)
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      mStatus = &quot;ok&quot; + STR$(mTestCount)
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;not &quot; + mStatus
      END IF
      mStatus = mStatus + &quot; - &quot; + LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = mStatus + &quot; (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
      PRINT mStatus
      IF mExpected = mGot THEN
         mDelay = .2
      ELSE
         mDelay = 2
      END IF
      mTimer = INT(TIMER * 10)
      DO WHILE mDelay &gt; 0
         IF mTimer &lt;&gt; INT(TIMER * 10) THEN
            mTimer = INT(TIMER * 10)
            mDelay = mDelay - .1
         END IF
      LOOP
   END IF
LOOP
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,70,&quot;soixante-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,70,&quot;septante&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,71,&quot;septante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,80,&quot;octante&quot;
   DATA &quot;*&quot;,&quot;fr-ch&quot;,80,&quot;huitante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt-un&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,81,&quot;octante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,82,&quot;quatre-vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,90,&quot;nonante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,900,&quot;neuf cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100000,&quot;cent mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200000,&quot;deux cents mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200025,&quot;deux cents mille vingt-cinq&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000100,&quot;un million cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000,&quot;deux millions&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2003201,&quot;deux million trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000000,&quot;deux milliards&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000003201,&quot;deux milliard trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>9923</id>
      <timestamp>2007-05-04T00:07:05Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>typo</comment>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG
   DIM dTensGroup AS LONG, dPowersGroup AS LONG
   DIM dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds three minor complications. Firstly, some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly, &quot;quatre-vingts&quot; doesn't need an &quot;s&quot; at the end when followed by units and otherwise needs to be treated differently from the &quot;-ante&quot; words. Thirdly, umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section and its internal cases.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dTensGroup = INT(aNumber / 10)
      dBuffer = dTens(dTensGroup)
      IF dBuffer = &quot;&quot; THEN
         dTensGroup = dTensGroup - 1
         dBuffer = dTens(dTensGroup)
      END IF
      dDigitGroup = aNumber - dTensGroup * 10
      IF dDigitGroup &gt; 0 THEN
         IF LEFT$(aLang, 2) = &quot;fr&quot; AND RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
         IF LEFT$(aLang, 2) &lt;&gt; &quot;fr&quot; OR dDigitGroup MOD 10 &lt;&gt; 1 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSEIF aLang = &quot;fr&quot; AND dTensGroup = 8 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSE
            dBuffer = dBuffer + &quot; et &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. It's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 and has rules on when to use plurals for powers of ten and when not to.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dPowersGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dPowersGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dPowersGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dPowersGroup * 10 ^ dRange
     
      IF LEFT$(aLang, 2) = &quot;fr&quot; AND (dPowersGroup = 1 OR dDigitGroup &gt; 0) THEN
         IF RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
      END IF
      IF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot; &quot;
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot;and &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE LEFT$(aLang, 2)
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cents&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; millions&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliards&quot;
   CASE &quot;en&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   CASE ELSE
      dUnits(0) = &quot;0&quot;: dUnits(10) = &quot;0&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;1&quot;: dUnits(11) = &quot;1&quot;: dTens(1) = &quot;1&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;2&quot;: dUnits(12) = &quot;2&quot;: dTens(2) = &quot;2&quot;: dPowers(2) = &quot;&quot;
      dUnits(3) = &quot;3&quot;: dUnits(13) = &quot;3&quot;: dTens(3) = &quot;3&quot;: dPowers(3) = &quot;&quot;
      dUnits(4) = &quot;4&quot;: dUnits(14) = &quot;4&quot;: dTens(4) = &quot;4&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;5&quot;: dUnits(15) = &quot;5&quot;: dTens(5) = &quot;5&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;6&quot;: dUnits(16) = &quot;6&quot;: dTens(6) = &quot;6&quot;: dPowers(6) = &quot;&quot;
      dUnits(7) = &quot;7&quot;: dUnits(17) = &quot;7&quot;: dTens(7) = &quot;7&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;8&quot;: dUnits(18) = &quot;8&quot;: dTens(8) = &quot;8&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;9&quot;: dUnits(19) = &quot;9&quot;: dTens(9) = &quot;9&quot;: dPowers(9) = &quot;&quot;
   END SELECT
   SELECT CASE LEFT$(aLang, 5)
   CASE &quot;fr-be&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;octante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE &quot;fr-ch&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;huitante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE ELSE
      REM Do nothing
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

Note: the tests results are now formatted according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol).

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mTestCount AS INTEGER
DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING
DIM mDelay AS SINGLE
DIM mTimer AS SINGLE

mTestCount = 0
RESTORE TestCases
DO
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      READ mLang, mNumber, mExpected
      mTestCount = mTestCount + 1
   END IF
LOOP

CLS
PRINT &quot;1..&quot; + LTRIM$(STR$(mTestCount))
mTestCount = 0
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE INKEY$ &lt;&gt; CHR$(27)
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      mStatus = &quot;ok&quot; + STR$(mTestCount)
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;not &quot; + mStatus
      END IF
      mStatus = mStatus + &quot; - &quot; + LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = mStatus + &quot; (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
      PRINT mStatus
      IF mExpected = mGot THEN
         mDelay = .2
      ELSE
         mDelay = 2
      END IF
      mTimer = INT(TIMER * 10)
      DO WHILE mDelay &gt; 0
         IF mTimer &lt;&gt; INT(TIMER * 10) THEN
            mTimer = INT(TIMER * 10)
            mDelay = mDelay - .1
         END IF
      LOOP
   END IF
LOOP
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,70,&quot;soixante-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,70,&quot;septante&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,71,&quot;septante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,80,&quot;octante&quot;
   DATA &quot;*&quot;,&quot;fr-ch&quot;,80,&quot;huitante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt-un&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,81,&quot;octante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,82,&quot;quatre-vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,90,&quot;nonante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,900,&quot;neuf cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100000,&quot;cent mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200000,&quot;deux cents mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200025,&quot;deux cents mille vingt-cinq&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000100,&quot;un million cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000,&quot;deux millions&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2003201,&quot;deux million trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000000,&quot;deux milliards&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000003201,&quot;deux milliard trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:BASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|BASIC]]</text>
    </revision>
    <revision>
      <id>10097</id>
      <timestamp>2007-05-16T00:30:31Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">Here is the function for changing a number into words. It works for English, for US English and for French. So far it doesn't work for other languages. Also please note that my French is pretty rusty, so I don't guarantee that the current algorithm produces valid French in all cases. The assistance of a fluent French speaker to add more test cases would be very much appreciated. Luckily such a person has added some test cases to the program and some helpful observations to the discussion page. The issues raised will be dealt with shortly.

The function is split into a &quot;run once&quot; initialisation portion followed by the part which calculates the actual words required to do the job. These portions will be discussed in a little more detail later in the article.
&lt;codeblock language=BASIC&gt;
&lt;&lt;definition&gt;&gt;=
FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)
&lt;&lt;variable declarations&gt;&gt;
&lt;&lt;initialisation call&gt;&gt;
&lt;&lt;function body&gt;&gt;
&lt;&lt;initialisation block&gt;&gt;
END FUNCTION
&lt;/codeblock&gt;

Two types of scope are used for the variables in this function. DIMensioned variables are automatically reinitialised to their default values whenever the function is called. STATIC variables retain their value between calls to the function. They are not strictly necessary in this function but their use makes the function faster by avoiding the need to set up the vocabulary arrays each time the function is called.  

&lt;codeblock language=BASIC&gt;
&lt;&lt;variable declarations&gt;&gt;=

   STATIC dLang AS STRING, dLog10 AS DOUBLE
   STATIC dUnits() AS STRING, dTens() AS STRING, dPowers() AS STRING

   DIM dBuffer AS STRING, dDigitGroup AS LONG
   DIM dTensGroup AS LONG, dPowersGroup AS LONG
   DIM dRange AS INTEGER
&lt;/codeblock&gt;

Note that QBASIC doesn't allow for the sizing of a static array at the time of its declaration. This has to be done later.

Basically the vocabulary arrays are loaded with data before use on the first call to the function and then just used on subsequent calls. The only case in which these arrays will need to be reloaded is when the language used is changed. 

Finally, if you have missgivings about the use of the GOSUB command in this piece of code please read on. Its use is discussed at a later point in this article.

&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation call&gt;&gt;=
   IF dLang &lt;&gt; aLang THEN
      GOSUB Num2LangInit
      dLang = aLang
   END IF
&lt;/codeblock&gt;

After the soup and salad we come to the meat of the function. In the two (and a half) languages covered so far we only really need to deal with three cases: zero to nineteen; twenty to ninety-nine; everything else. Since the specification for this task (the bottles of beer song) implies that we only need to deal with positive whole numbers and since I have arbitrarily decided that I only want to deal with 32-bit signed integers (the LONG type in BASIC) &quot;everything else&quot; implies any whole number between one hundred and 2&lt;sup&gt;31&lt;/sup&gt;-1. It would be trivial to handle negative numbers and not too much work to handle decimals but there's no need in this case. However with an eye to bugs or future expansion a fourth case has been added to handle numbers outside the range.

&lt;codeblock language=BASIC&gt;
&lt;&lt;function body&gt;&gt;=
   SELECT CASE aNumber

&lt;&lt;first case&gt;&gt;
&lt;&lt;second case&gt;&gt;
&lt;&lt;third case&gt;&gt;
&lt;&lt;other cases&gt;&gt;
   END SELECT

   Num2Lang = dBuffer

   EXIT FUNCTION
&lt;/codeblock&gt;

The first case contains a highly idiosyncratic set of numbers with little or no pattern and the easiest way to handle it is via the pre-initialised lookup table, dUnits.

&lt;codeblock language=BASIC&gt;
&lt;&lt;first case&gt;&gt;=
   CASE 0 TO 19
      dBuffer = dUnits(INT(aNumber))
&lt;/codeblock&gt;

The second case is pretty straightforward for English but handling French adds three minor complications. Firstly, some ten-words, &quot;septante&quot; for instance, don't exist in Parisian French, although they do in other dialects such as Belgian French. In those cases the base twenty system has to be used starting from the previous existing ten-word. Hence the first IF/ENDIF section in the following code. Secondly, &quot;quatre-vingts&quot; doesn't need an &quot;s&quot; at the end when followed by units and otherwise needs to be treated differently from the &quot;-ante&quot; words. Thirdly, umpty-one values have to be treated specially by adding the word &quot;et&quot; in between the tens and the units. Hence the second IF/ENDIF section and its internal cases.  


&lt;codeblock language=BASIC&gt;
&lt;&lt;second case&gt;&gt;=
   CASE 20 TO 99
      dTensGroup = INT(aNumber / 10)
      dBuffer = dTens(dTensGroup)
      IF dBuffer = &quot;&quot; THEN
         dTensGroup = dTensGroup - 1
         dBuffer = dTens(dTensGroup)
      END IF
      dDigitGroup = aNumber - dTensGroup * 10
      IF dDigitGroup &gt; 0 THEN
         IF LEFT$(aLang, 2) = &quot;fr&quot; AND RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
         IF LEFT$(aLang, 2) &lt;&gt; &quot;fr&quot; OR dDigitGroup MOD 10 &lt;&gt; 1 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSEIF aLang = &quot;fr&quot; AND dTensGroup = 8 THEN
            dBuffer = dBuffer + &quot;-&quot;
         ELSE
            dBuffer = dBuffer + &quot; et &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

The third case has the most complex code The basic idea is to identify which range the number falls into (thousands, millions, etc.) then use recursive calls to get the text for groups of three digits. That simple picture is clouded a little by the first range, the hundreds, which are treated a little differently in US English from other English variants. It's also complicated by French which uses the phrases &quot;cent&quot; and &quot;mille&quot; rather than &quot;un cent&quot; or &quot;un mille&quot; for 100 and 1,000 and has rules on when to use plurals for powers of ten and when not to.

Also note the addition of .4 to the number when calculating the range. This shouldn't have been necessary but a floating point approximation error leads to the wrong value being calculated for 100 if it isn't present. The calculation worked for all other values, even without the addition but them's the breaks. 

&lt;codeblock language=BASIC&gt;
&lt;&lt;third case&gt;&gt;=
   CASE 100 TO 2147483647
      dRange = INT(LOG(aNumber + .4) / dLog10)
      IF dRange &gt; 3 THEN dRange = INT(dRange / 3) * 3
      dPowersGroup = INT(aNumber / 10 ^ dRange)
      IF aLang = &quot;fr&quot; AND dPowersGroup = 1 AND dRange &lt; 5 THEN
         dBuffer = &quot;&quot;
      ELSE
         dBuffer = Num2Lang(dPowersGroup, aLang)
      END IF
      dBuffer = LTRIM$(dBuffer + dPowers(dRange))
      dDigitGroup = aNumber - dPowersGroup * 10 ^ dRange
     
      IF LEFT$(aLang, 2) = &quot;fr&quot; AND (dPowersGroup = 1 OR dDigitGroup &gt; 0) THEN
         IF RIGHT$(dBuffer, 1) = &quot;s&quot; THEN
            dBuffer = LEFT$(dBuffer, LEN(dBuffer) - 1)
         END IF
      END IF
      IF dDigitGroup &gt; 0 THEN
         dBuffer = dBuffer + &quot; &quot;
         IF dDigitGroup &lt; 100 AND aLang = &quot;en-uk&quot; THEN
            dBuffer = dBuffer + &quot;and &quot;
         END IF
         dBuffer = dBuffer + Num2Lang(dDigitGroup, aLang)
      END IF
&lt;/codeblock&gt;

Finally a default case was added during development to handle cases which hadn't been handled yet. If the code is extended to handle negative or floating point numbers at some time in the future this might come in handy again, so it has been left. At the moment it will catch negative numbers and produce a &quot;reasonable&quot; answer which will at least indicate that there is a problem in the input.

&lt;codeblock language=BASIC&gt;
&lt;&lt;other cases&gt;&gt;=
   CASE ELSE
      dBuffer = LTRIM$(STR$(aNumber))
&lt;/codeblock&gt;

Now we have the initialisation code for the function. It basically loads arrays with the vocabulary required for the current language. It also sets the LOG10 constant. This is required because QBASIC's built-in LOG functon deals in natural logarithms and we actually need base 10 logarithms to identify the right powers-of-ten word.

Just a word on the use of GOSUB and a label here. Many people recoil in horror from the GOSUB command nowadays with some vague fear that it is the GOTO command in disguise and that therefore its use is &quot;unstructured&quot;. In fact it has been removed altogether from the latest incarnation of BASIC, VB.NET and that is a pity. There is no doubt that GOSUB in the wrong hands can be misused badly. However it has at least one legitimate use and that use is the provision of structuring within a function or subroutine where the creation of extra functions or subroutines to carry out that structuring would be overkill. That is how it has been used here. While it could have been replaced altogether in this function, its use makes the code more readable than it would otherwise have been and thus its use is justified.
 
&lt;codeblock language=BASIC&gt;
&lt;&lt;initialisation block&gt;&gt;=
Num2LangInit:
   REDIM dUnits(19), dTens(9), dPowers(9)
   SELECT CASE LEFT$(aLang, 2)
   CASE &quot;fr&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;dix&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;un&quot;: dUnits(11) = &quot;onze&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;deux&quot;: dUnits(12) = &quot;douze&quot;: dTens(2) = &quot;vingt&quot;: dPowers(2) = &quot; cents&quot;
      dUnits(3) = &quot;trois&quot;: dUnits(13) = &quot;treize&quot;: dTens(3) = &quot;trente&quot;: dPowers(3) = &quot; mille&quot;
      dUnits(4) = &quot;quatre&quot;: dUnits(14) = &quot;quatorze&quot;: dTens(4) = &quot;quarante&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;cinq&quot;: dUnits(15) = &quot;quinze&quot;: dTens(5) = &quot;cinquante&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;seize&quot;: dTens(6) = &quot;soixante&quot;: dPowers(6) = &quot; millions&quot;
      dUnits(7) = &quot;sept&quot;: dUnits(17) = &quot;dix-sept&quot;: dTens(7) = &quot;&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;huit&quot;: dUnits(18) = &quot;dix-huit&quot;: dTens(8) = &quot;quatre-vingts&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;neuf&quot;: dUnits(19) = &quot;dix-neuf&quot;: dTens(9) = &quot;&quot;: dPowers(9) = &quot; milliards&quot;
   CASE &quot;en&quot;
      dUnits(0) = &quot;zero&quot;: dUnits(10) = &quot;ten&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;one&quot;: dUnits(11) = &quot;eleven&quot;: dTens(1) = &quot;&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;two&quot;: dUnits(12) = &quot;twelve&quot;: dTens(2) = &quot;twenty&quot;: dPowers(2) = &quot; hundred&quot;
      dUnits(3) = &quot;three&quot;: dUnits(13) = &quot;thirteen&quot;: dTens(3) = &quot;thirty&quot;: dPowers(3) = &quot; thousand&quot;
      dUnits(4) = &quot;four&quot;: dUnits(14) = &quot;fourteen&quot;: dTens(4) = &quot;forty&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;five&quot;: dUnits(15) = &quot;fifteen&quot;: dTens(5) = &quot;fifty&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;six&quot;: dUnits(16) = &quot;sixteen&quot;: dTens(6) = &quot;sixty&quot;: dPowers(6) = &quot; million&quot;
      dUnits(7) = &quot;seven&quot;: dUnits(17) = &quot;seventeen&quot;: dTens(7) = &quot;seventy&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;eight&quot;: dUnits(18) = &quot;eighteen&quot;: dTens(8) = &quot;eighty&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;nine&quot;: dUnits(19) = &quot;nineteen&quot;: dTens(9) = &quot;ninety&quot;: dPowers(9) = &quot; billion&quot;
   CASE ELSE
      dUnits(0) = &quot;0&quot;: dUnits(10) = &quot;0&quot;: dTens(0) = &quot;&quot;: dPowers(0) = &quot;&quot;
      dUnits(1) = &quot;1&quot;: dUnits(11) = &quot;1&quot;: dTens(1) = &quot;1&quot;: dPowers(1) = &quot;&quot;
      dUnits(2) = &quot;2&quot;: dUnits(12) = &quot;2&quot;: dTens(2) = &quot;2&quot;: dPowers(2) = &quot;&quot;
      dUnits(3) = &quot;3&quot;: dUnits(13) = &quot;3&quot;: dTens(3) = &quot;3&quot;: dPowers(3) = &quot;&quot;
      dUnits(4) = &quot;4&quot;: dUnits(14) = &quot;4&quot;: dTens(4) = &quot;4&quot;: dPowers(4) = &quot;&quot;
      dUnits(5) = &quot;5&quot;: dUnits(15) = &quot;5&quot;: dTens(5) = &quot;5&quot;: dPowers(5) = &quot;&quot;
      dUnits(6) = &quot;6&quot;: dUnits(16) = &quot;6&quot;: dTens(6) = &quot;6&quot;: dPowers(6) = &quot;&quot;
      dUnits(7) = &quot;7&quot;: dUnits(17) = &quot;7&quot;: dTens(7) = &quot;7&quot;: dPowers(7) = &quot;&quot;
      dUnits(8) = &quot;8&quot;: dUnits(18) = &quot;8&quot;: dTens(8) = &quot;8&quot;: dPowers(8) = &quot;&quot;
      dUnits(9) = &quot;9&quot;: dUnits(19) = &quot;9&quot;: dTens(9) = &quot;9&quot;: dPowers(9) = &quot;&quot;
   END SELECT
   SELECT CASE LEFT$(aLang, 5)
   CASE &quot;fr-be&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;octante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE &quot;fr-ch&quot;
      dTens(7) = &quot;septante&quot;
      dTens(8) = &quot;huitante&quot;
      dTens(9) = &quot;nonante&quot;
   CASE ELSE
      REM Do nothing
   END SELECT
   dLog10 = LOG(10)
   RETURN
&lt;/codeblock&gt;

The next piece of the file is a scaffold which you can use to test the Num2Lang function. When there are so many ways that things can go wrong, it's important to automate the testing process so that the same tests are run every time.

The floating point approximation error discussed above demonstrates the need for comprehensive testing. There was no logical error in the code before the &quot;+ .4&quot; was added to it. Nevertheless the function did not return the correct result when the input value was 100, so the cause had to be identified and a workaround created. Comprehensive unit testing will find this sort of error where logic and code writing skills will not.

Note: the tests results are now formatted according to the TAP format (see http://en.wikipedia.org/wiki/Test_Anything_Protocol).

&lt;codeblock language=BASIC&gt;
&lt;&lt;unit tests&gt;&gt;=
DECLARE FUNCTION Num2Lang$ (aNumber AS LONG, aLang AS STRING)

DIM mTestCount AS INTEGER
DIM mStatus AS STRING
DIM mTest AS STRING
DIM mLang AS STRING
DIM mNumber AS LONG
DIM mExpected AS STRING
DIM mGot AS STRING
DIM mDelay AS SINGLE
DIM mTimer AS SINGLE

mTestCount = 0
RESTORE TestCases
DO
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      READ mLang, mNumber, mExpected
      mTestCount = mTestCount + 1
   END IF
LOOP

CLS
PRINT &quot;1..&quot; + LTRIM$(STR$(mTestCount))
mTestCount = 0
RESTORE TestCases
mStatus = &quot;&quot;
DO WHILE INKEY$ &lt;&gt; CHR$(27)
   READ mTest
   IF mTest = &quot;&quot; THEN
      EXIT DO
   ELSE
      mTestCount = mTestCount + 1
      READ mLang, mNumber, mExpected
      mGot = Num2Lang$(mNumber, mLang)
      mStatus = &quot;ok&quot; + STR$(mTestCount)
      IF mExpected &lt;&gt; mGot THEN
         mStatus = &quot;not &quot; + mStatus
      END IF
      mStatus = mStatus + &quot; - &quot; + LEFT$(mLang + &quot;: &quot; + LTRIM$(STR$(mNumber)) + SPACE$(15), 15) + &quot;'&quot; + mGot + &quot;'&quot;
      IF mExpected &lt;&gt; mGot THEN
         mStatus = mStatus + &quot; (Expected '&quot; + mExpected + &quot;')&quot;
      END IF
      PRINT mStatus
      IF mExpected = mGot THEN
         mDelay = .2
      ELSE
         mDelay = 2
      END IF
      mTimer = INT(TIMER * 10)
      DO WHILE mDelay &gt; 0
         IF mTimer &lt;&gt; INT(TIMER * 10) THEN
            mTimer = INT(TIMER * 10)
            mDelay = mDelay - .1
         END IF
      LOOP
   END IF
LOOP
SYSTEM

TestCases:
   DATA &quot;*&quot;,&quot;en-uk&quot;,0,&quot;zero&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1,&quot;one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,9,&quot;nine&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,10,&quot;ten&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,11,&quot;eleven&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,19,&quot;nineteen&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,20,&quot;twenty&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,21,&quot;twenty-one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,100,&quot;one hundred&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,101,&quot;one hundred and one&quot;
   DATA &quot;*&quot;,&quot;en-us&quot;,101,&quot;one hundred one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1000,&quot;one thousand&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1001,&quot;one thousand and one&quot;
   DATA &quot;*&quot;,&quot;en-uk&quot;,1958,&quot;one thousand nine hundred and fifty-eight&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,10,&quot;dix&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,11,&quot;onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,21,&quot;vingt et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,22,&quot;vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,29,&quot;vingt-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,60,&quot;soixante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,61,&quot;soixante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,62,&quot;soixante-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,70,&quot;soixante-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,70,&quot;septante&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,71,&quot;septante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,71,&quot;soixante et onze&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,79,&quot;soixante-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,80,&quot;quatre-vingts&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,80,&quot;octante&quot;
   DATA &quot;*&quot;,&quot;fr-ch&quot;,80,&quot;huitante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,81,&quot;quatre-vingt-un&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,81,&quot;octante et un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,82,&quot;quatre-vingt-deux&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,90,&quot;quatre-vingt-dix&quot;
   DATA &quot;*&quot;,&quot;fr-be&quot;,90,&quot;nonante&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,99,&quot;quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100,&quot;cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,101,&quot;cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,900,&quot;neuf cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,999,&quot;neuf cent quatre-vingt-dix-neuf&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000,&quot;mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1100,&quot;mille cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,100000,&quot;cent mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200000,&quot;deux cents mille&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,200025,&quot;deux cents mille vingt-cinq&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000000,&quot;un million&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,1000100,&quot;un million cent&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000,&quot;deux millions&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2003201,&quot;deux million trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000000000,&quot;deux milliards&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,2000003201,&quot;deux milliard trois mille deux cent un&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,300,&quot;trois cents&quot;
   DATA &quot;*&quot;,&quot;fr&quot;,301,&quot;trois cent un&quot;
   DATA &quot;&quot;
&lt;/codeblock&gt;

&lt;codeblock language=BASIC&gt;
&lt;&lt;NUM2LANG.BAS&gt;&gt;=
&lt;&lt;unit tests&gt;&gt;
&lt;&lt;definition&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:QBASIC]]
[[Category:Environment:DOS]]
[[Category:Convert Integer to String|QBASIC]]</text>
    </revision>
  </page>
  <page>
    <title>Convert number to words (Java)</title>
    <id>2991</id>
    <revision>
      <id>8893</id>
      <timestamp>2007-02-08T18:48:44Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <text xml:space="preserve">{{develop}}</text>
    </revision>
  </page>
  <page>
    <title>Cooley-Tukey FFT algorithm (C)</title>
    <id>2763</id>
    <revision>
      <id>8009</id>
      <timestamp>2006-11-14T14:35:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial version, untested, no optimizations yet</comment>
      <text xml:space="preserve">{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (size == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{todo|Discuss optimizations}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8010</id>
      <timestamp>2006-11-14T14:37:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Caps</comment>
      <text xml:space="preserve">{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (size == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8011</id>
      <timestamp>2006-11-14T14:39:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>{{develop}}, Files, Test driver empty sections</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (size == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

{{TODO}}

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8012</id>
      <timestamp>2006-11-14T14:51:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Basic files</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (size == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
#include &quot;fft.h&quot;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8013</id>
      <timestamp>2006-11-14T14:55:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix compiler errors</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (size == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8014</id>
      <timestamp>2006-11-14T14:56:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Compiler error</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8015</id>
      <timestamp>2006-11-14T15:22:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>#defines</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8016</id>
      <timestamp>2006-11-14T15:54:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Move around headers a bit</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Radix-2 decimation in time ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

Unfortunately, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall. The approach of ''radix-2 decimation in time'' is to separate the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8017</id>
      <timestamp>2006-11-14T17:23:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add DFT_naive</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of sine and cosine requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive(complex* x, int N);
&lt;&lt;Simple FFT&gt;&gt;=
complex* DFT_naive(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

This works well for small inputs and does not place any requirements on ''N''. At the expense of additional space, we could avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''. 

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8019</id>
      <timestamp>2006-11-15T01:41:42Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Complex arithmetic */ Magnitude</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive(complex* x, int N);
&lt;&lt;Simple FFT&gt;&gt;=
complex* DFT_naive(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

This works well for small inputs and does not place any requirements on ''N''. At the expense of additional space, we could avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''. 

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8020</id>
      <timestamp>2006-11-15T01:48:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Naïve evaluation of definition */ Add a second naive version</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Simple FFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;, computing only the ''N'' ''N''th roots of unity and then using integer remainder to determine which one we want:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Simple FFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8021</id>
      <timestamp>2006-11-15T01:53:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix chunk labels, discuss motivation</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;, computing only the ''N'' ''N''th roots of unity and then using integer remainder to determine which one we want:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8022</id>
      <timestamp>2006-11-15T01:54:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move up memory management headers and PI</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;, computing only the ''N'' ''N''th roots of unity and then using integer remainder to determine which one we want:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8023</id>
      <timestamp>2006-11-15T02:03:59Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Naïve evaluation of definition */ More explanation</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);
    
    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12381</id>
      <timestamp>2008-01-30T17:23:47Z</timestamp>
      <contributor>
        <ip>206.165.101.124</ip>
      </contributor>
      <comment>added free(d) and free(e).</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

{{TODO|Discuss optimizations}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12462</id>
      <timestamp>2008-02-01T09:01:22Z</timestamp>
      <contributor>
        <username>Tim Band</username>
        <id>1631</id>
      </contributor>
      <comment>Added optimizations (removing memory allocations and pre-calculating twiddle factors)</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
	return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
	FFT_buffer(x, N, 1, out, scratch);
	free(scratch);
	return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
    	twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
	free(twiddles);
	free(scratch);
	return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

{{TODO}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12463</id>
      <timestamp>2008-02-01T09:03:20Z</timestamp>
      <contributor>
        <username>Tim Band</username>
        <id>1631</id>
      </contributor>
      <minor/>
      <comment>Added language tags</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
	return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
	FFT_buffer(x, N, 1, out, scratch);
	free(scratch);
	return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
    	twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
	free(twiddles);
	free(scratch);
	return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

{{TODO}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12464</id>
      <timestamp>2008-02-01T09:06:35Z</timestamp>
      <contributor>
        <username>Tim Band</username>
        <id>1631</id>
      </contributor>
      <minor/>
      <comment>fixed tab-alignment</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
		complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
    	twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

{{TODO}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12471</id>
      <timestamp>2008-02-01T10:32:53Z</timestamp>
      <contributor>
        <ip>86.11.3.194</ip>
      </contributor>
      <comment>oops! corrected the fact that I was calculating twice as many twiddle factors as necessary</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N/2);
    int k;
    for (k = 0; k != N/2; ++k) {
    	twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

{{TODO}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12472</id>
      <timestamp>2008-02-01T11:20:16Z</timestamp>
      <contributor>
        <ip>86.11.3.194</ip>
      </contributor>
      <comment>It suits my next optimization better if I swap where I put D and E. So much for no surprizes.</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* E) {
    complex * D = E + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N/2);
    int k;
    for (k = 0; k != N/2; ++k) {
    	twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

{{TODO}}

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12477</id>
      <timestamp>2008-02-01T15:03:58Z</timestamp>
      <contributor>
        <ip>86.11.3.194</ip>
      </contributor>
      <comment>Added function-call overhead removal optimizations</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* E) {
    complex * D = E + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N/2);
    int k;
    for (k = 0; k != N/2; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: removing recursion ==

This is a decidedly nontrivial optimization, for not a lot of speed increase. However, it does lend itself well to futher optimization.

To remove recursion we must be able to perform all the parts of each iteration in one pass. Here is a table of how we will arrange the results for each iteration for a DFT of length 8:

{|
|-
|initial
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[4][0] || X[5][0] || X[6][0] || X[7][0]
|-
|re-interpretation
| E[0][0] || E[1][0] || E[2][0] || E[3][0] || D[0][0] || D[1][0] || D[2][0] || D[3][0]
|-
|calculation of next Xs
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[0][1] || X[1][1] || X[2][1] || X[3][1]
|-
|re-interpretation
| E[0][0] || E[1][0] || D[0][0] || D[1][0] || E[0][1] || E[1][1] || D[0][1] || D[1][1]
|-
|calculation of next Xs
| X[0][0] || X[0][1] || X[1][0] || X[1][1] || X[0][2] || X[0][3] || X[1][2] || X[1][3]
|-
|re-interpretation
| E[0][0] || D[0][0] || E[0][1] || D[0][1] || E[0][2] || D[0][2] || E[0][3] || D[0][3]
|-
|final calculation of Xs
| X[0][0] || X[0][1] || X[0][2] || X[0][3] || X[0][4] || X[0][5] || X[0][6] || X[0][7]
|}

where &lt;code&gt;X[n]&lt;/code&gt; represents what would have been the output from one call of &lt;code&gt;FFT_simple&lt;/code&gt; and &lt;code&gt;E[n]&lt;/code&gt; and &lt;code&gt;D[n]&lt;/code&gt; represent the intermediate values used by that same call.

{{TODO|explain this better!}}

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E, * D;
    complex* Xp, * Xstart;

    if (N == 1) {
        /* N == 1 is now a special case, not the end of the recursion! */
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        for(k = 0; k != n; k++) {
            for (m = 0; m != skip; ++m) {
                D = E + skip;
                *D = complex_mult(twiddles[k * skip], *D);
                *Xp = complex_add(*E, *D);
                Xp[N/2] = complex_sub(*E, *D);
                ++Xp;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

Note that in the arrangement above, the same twiddle factor is being invoked repeatedly in the inner loop. This suggests further optimizations, which, when combined with inlining of the complex arithmetic, produces a worthwhile speed improvement:

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E;
    complex* Xp, * Xp2, * Xstart;

    if (N == 1) {
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        Xp2 = Xstart + N/2;
        for(k = 0; k != n; k++) {
        	double tim = twiddles[k * skip].im;
        	double tre = twiddles[k * skip].re;
            for (m = 0; m != skip; ++m) {
            	complex* D = E + skip;
            	/* twiddle *D to get dre and dim */
            	double dre = D-&gt;re * tre - D-&gt;im * tim;
            	double dim = D-&gt;re * tim + D-&gt;im * tre;
                Xp-&gt;re = E-&gt;re + dre;
                Xp-&gt;im = E-&gt;im + dim;
                Xp2-&gt;re = E-&gt;re - dre;
                Xp2-&gt;im = E-&gt;im - dim;
                ++Xp;
                ++Xp2;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15457</id>
      <timestamp>2008-11-17T07:02:04Z</timestamp>
      <contributor>
        <ip>192.25.240.225</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] += complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* E) {
    complex * D = E + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N/2);
    int k;
    for (k = 0; k != N/2; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: removing recursion ==

This is a decidedly nontrivial optimization, for not a lot of speed increase. However, it does lend itself well to futher optimization.

To remove recursion we must be able to perform all the parts of each iteration in one pass. Here is a table of how we will arrange the results for each iteration for a DFT of length 8:

{|
|-
|initial
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[4][0] || X[5][0] || X[6][0] || X[7][0]
|-
|re-interpretation
| E[0][0] || E[1][0] || E[2][0] || E[3][0] || D[0][0] || D[1][0] || D[2][0] || D[3][0]
|-
|calculation of next Xs
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[0][1] || X[1][1] || X[2][1] || X[3][1]
|-
|re-interpretation
| E[0][0] || E[1][0] || D[0][0] || D[1][0] || E[0][1] || E[1][1] || D[0][1] || D[1][1]
|-
|calculation of next Xs
| X[0][0] || X[0][1] || X[1][0] || X[1][1] || X[0][2] || X[0][3] || X[1][2] || X[1][3]
|-
|re-interpretation
| E[0][0] || D[0][0] || E[0][1] || D[0][1] || E[0][2] || D[0][2] || E[0][3] || D[0][3]
|-
|final calculation of Xs
| X[0][0] || X[0][1] || X[0][2] || X[0][3] || X[0][4] || X[0][5] || X[0][6] || X[0][7]
|}

where &lt;code&gt;X[n]&lt;/code&gt; represents what would have been the output from one call of &lt;code&gt;FFT_simple&lt;/code&gt; and &lt;code&gt;E[n]&lt;/code&gt; and &lt;code&gt;D[n]&lt;/code&gt; represent the intermediate values used by that same call.

{{TODO|explain this better!}}

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E, * D;
    complex* Xp, * Xstart;

    if (N == 1) {
        /* N == 1 is now a special case, not the end of the recursion! */
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        for(k = 0; k != n; k++) {
            for (m = 0; m != skip; ++m) {
                D = E + skip;
                *D = complex_mult(twiddles[k * skip], *D);
                *Xp = complex_add(*E, *D);
                Xp[N/2] = complex_sub(*E, *D);
                ++Xp;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

Note that in the arrangement above, the same twiddle factor is being invoked repeatedly in the inner loop. This suggests further optimizations, which, when combined with inlining of the complex arithmetic, produces a worthwhile speed improvement:

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E;
    complex* Xp, * Xp2, * Xstart;

    if (N == 1) {
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        Xp2 = Xstart + N/2;
        for(k = 0; k != n; k++) {
        	double tim = twiddles[k * skip].im;
        	double tre = twiddles[k * skip].re;
            for (m = 0; m != skip; ++m) {
            	complex* D = E + skip;
            	/* twiddle *D to get dre and dim */
            	double dre = D-&gt;re * tre - D-&gt;im * tim;
            	double dim = D-&gt;re * tim + D-&gt;im * tre;
                Xp-&gt;re = E-&gt;re + dre;
                Xp-&gt;im = E-&gt;im + dim;
                Xp2-&gt;re = E-&gt;re - dre;
                Xp2-&gt;im = E-&gt;im - dim;
                ++Xp;
                ++Xp2;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15458</id>
      <timestamp>2008-11-17T11:08:18Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

{{Category:Cooley-Tukey FFT algorithm}}

Here we describe a C implementation of Cooley-Tukey. We begin with a straightforward implementation and then describe various performance improvements. Like most practical implementations, we will concentrate on the case where the vector length is a power of 2.

== Complex arithmetic ==

Although the newest version of C, C99, has library support for complex number datatypes and arithmetic, it is not widely supported. We write simple implementations of a few basic operations we need here, with little explanation; for a more detailed discussion, see [[:Category:Complex numbers]].

&lt;codeblock language=c&gt;
&lt;&lt;complex number datatype&gt;&gt;=
typedef struct complex_t {
    double re;
    double im;
} complex;

&lt;&lt;complex number prototypes&gt;&gt;=
complex complex_from_polar(double r, double theta_radians);
double  complex_magnitude(complex c);
complex complex_add(complex left, complex right);
complex complex_sub(complex left, complex right);
complex complex_mult(complex left, complex right);

&lt;&lt;complex number function definitions&gt;&gt;=
complex complex_from_polar(double r, double theta_radians) {
    complex result;
    result.re = r * cos(theta_radians);
    result.im = r * sin(theta_radians);
    return result;
}

double complex_magnitude(complex c) {
    return sqrt(c.re*c.re + c.im*c.im);
}

complex complex_add(complex left, complex right) {
    complex result;
    result.re = left.re + right.re;
    result.im = left.im + right.im;
    return result;
}

complex complex_sub(complex left, complex right) {
    complex result;
    result.re = left.re - right.re;
    result.im = left.im - right.im;
    return result;
}

complex complex_mult(complex left, complex right) {
    complex result;
    result.re = left.re*right.re - left.im*right.im;
    result.im = left.re*right.im + left.im*right.re;
    return result;
}
&lt;/codeblock&gt;

The use of &lt;code&gt;sin()&lt;/code&gt;, &lt;code&gt;cos()&lt;/code&gt;, and &lt;code&gt;sqrt()&lt;/code&gt; requires the header math.h:

&lt;codeblock language=c&gt;
&lt;&lt;complex number headers&gt;&gt;=
#include &lt;math.h&gt;
&lt;/codeblock&gt;

== Naïve evaluation of definition ==

First we discuss the simplest possible DFT solution in order to address some of the issues in a simpler setting. Suppose that our input vector is '''x''' and our output vector is '''X'''. Then the discrete Fourier transform is defined by the formula:

:For each &lt;math&gt;0 \le k &lt; N&lt;/math&gt;, &lt;math&gt; X_k =  \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;

The quantity &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt; is most easily described in terms of its polar complex coordinates: it is on the unit circle (distance ''r''=1 from the origin) and forms an angle &amp;theta; of &lt;math&gt;-\frac{2\pi}{N} nk&lt;/math&gt; radians with the positive real axis. This enables us to evaluate the definition as follows:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_1(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_1(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], complex_from_polar(1, -2*PI*n*k/N)));
        }
    }
    return X;
}
&lt;/codeblock&gt;

We require headers for memory management and need to define &lt;code&gt;PI&lt;/code&gt;:

&lt;codeblock language=c&gt;
&lt;&lt;FFT headers&gt;&gt;=
#include &lt;stdlib.h&gt;

&lt;&lt;FFT constants&gt;&gt;=
#define PI  3.1415926535897932
&lt;/codeblock&gt;

This works well for very small inputs and does not place any requirements on ''N''. At the expense of additional space, we can avoid repeatedly recomputing the factors &lt;math&gt;e^{-\frac{2\pi i}{N} nk}&lt;/math&gt;. Instead, we compute only the ''N'' values &lt;math&gt;e^{-\frac{2\pi i}{N} k}&lt;/math&gt; for &lt;math&gt;0 \leq k &lt; N&lt;/math&gt; and use the fact that &lt;math&gt;e^{2\pi i k} = 1&lt;/math&gt; to reduce to one of these:

:&lt;math&gt;e^{-\frac{2\pi i}{N} nk} = e^{-\frac{2\pi i}{N} K}&lt;/math&gt; where &lt;math&gt;K \equiv nk\pmod N&lt;/math&gt; and &lt;math&gt;0 \leq K &lt; N&lt;/math&gt;.

In code:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* DFT_naive_2(complex* x, int N);
&lt;&lt;Naive DFT&gt;&gt;=
complex* DFT_naive_2(complex* x, int N) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* Nth_root = (complex*) malloc(sizeof(struct complex_t) * N);
    int k, n;
    for(k=0; k&lt;N; k++) {
        Nth_root[k] = complex_from_polar(1, -2*PI*k/N);
    }
    for(k=0; k&lt;N; k++) {
        X[k].re = X[k].im = 0.0;
        for(n=0; n&lt;N; n++) {
            X[k] = complex_add(X[k], complex_mult(x[n], Nth_root[(n*k) % N]));
        }
    }
    free(Nth_root);
    return X;
}
&lt;/codeblock&gt;

This considerably speeds the algorithm in practice. Unfortunately, even with this change, directly evaluating this sum for each ''k'' requires &lt;math&gt;O(N^2)&lt;/math&gt; time overall, which is prohibitive for large ''N''.

== Radix-2 decimation in time ==

The ''radix-2 decimation in time'' algorithm uses a divide-and-conquer approach to improve efficiency. It begins by separating the input vector '''x''' into two smaller vectors '''d''' and '''e''', with '''d''' containing the odd-numbered elements of the original vector and '''e''' containing the even-numbered elements. For example:

:'''x''' = (1, 2, 3, 4, 5, 6)
:'''d''' = (2, 4, 6)
:'''e''' = (1, 3, 5)

(Keep in mind that the indexing starts at zero). We then recursively compute the FFTs of '''d''' and '''e''', call them '''D''' and '''E'''. We use them to construct '''X''' according to the following formula, which can be shown directly from the definition:

:&lt;math&gt; \begin{matrix}
X_k       &amp; = &amp; E_k +  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2 \\
X_{k+N/2} &amp; = &amp; E_k -  e^{-\frac{2\pi i}{N}k} D_k &amp; \mbox{ } 0 \le k &lt; N/2
\end{matrix}
&lt;/math&gt;

Thus, all we need to do to compute '''X''' is to compute '''D''', '''E''', and the ''N''/2 complex roots of unity specified by &lt;math&gt;e^{-\frac{2\pi i}{N}k}&lt;/math&gt; for &lt;math&gt;0 \le k &lt; N/2&lt;/math&gt; (called ''twiddle factors''), then do some basic arithmetic. The additional work after computing '''D''' and '''E''' is linear, so the analysis is just like that of mergesort, requiring &lt;math&gt;O(N \log N)&lt;/math&gt; worst-case time. Following is a straightforward implementation based on recursion using the above formulas:

&lt;codeblock language=c&gt;
&lt;&lt;FFT prototypes&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */);
&lt;&lt;Simple FFT&gt;&gt;=
complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * d, * e, * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    e = (complex*) malloc(sizeof(struct complex_t) * N/2);
    d = (complex*) malloc(sizeof(struct complex_t) * N/2);
    for(k = 0; k &lt; N/2; k++) {
        e[k] = x[2*k];
        d[k] = x[2*k + 1];
    }

    E = FFT_simple(e, N/2);
    D = FFT_simple(d, N/2);

    free(e);
    free(d);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}
&lt;/codeblock&gt;

Although this works, is simple, and has good asymptotic performance, in practice the large number of allocations above degrade speed and triple memory use, which is particularly harmful on large inputs. Additionally, many of the &lt;code&gt;complex_from_polar()&lt;/code&gt; calls are redundant, since only ''N''th roots of unity are used anywhere in the recursion tree. Finally, this implementation has considerable function call overhead and would ideally be replaced by a simpler algorithm on small subvectors.

== Optimization: removing memory allocations 1 ==

One obvious optimization is to remove the allocations for ''e'' and ''d'', seeing as these are simple re-arrangements of some elements of ''x''. The algorithms above assume that the input is a contiguous array, but if we relax this assumption so that it will accept inputs of the form &lt;code&gt;x[0], x[skip], x[skip*2], x[skip*3]...&lt;/code&gt; then ''e'' and ''d'' are simply subarrays of ''x'' with different values of ''skip'':

&lt;codeblock language=c&gt;
complex* FFT_skip(complex* x, int N /* must be a power of 2 */, int skip) {
    complex* X = (complex*) malloc(sizeof(struct complex_t) * N);
    complex * D, * E;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return X;
    }

    E = FFT_skip(x, N/2, skip*2);
    D = FFT_skip(x + skip, N/2, skip*2);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }

    free(D);
    free(E);
    return X;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    return FFT_skip(x, N, 1);
}
&lt;/codeblock&gt;

== Optimization: removing memory allocations 2 ==

A second optimization is to remove the allocation of ''X'' at the beginning of each iteration. It can be seen that ''X'' is not required until ''e'' and ''d'' (now subarrays of ''x'') are finished with. So we could use a scratch buffer to hold ''E'' and ''D'' before calculating ''X'', using ''X'' as the scratch buffer when calculating ''E'' and ''D'':

&lt;codeblock language=c&gt;
void FFT_buffer(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* E) {
    complex * D = E + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_buffer(x, N/2, skip*2, E, X);
    FFT_buffer(x + skip, N/2, skip*2, D, X);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(complex_from_polar(1, -2.0*PI*k/N), D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    FFT_buffer(x, N, 1, out, scratch);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: pre-calculating twiddle factors ==

It can be seen that the same twiddle factors are being re-calculated constantly. Firstly, the calculation of ''E'' and the calculation of ''D'' require exactly the same twiddle factors. Secondly, the calculation of ''E'' and ''D'' require the even-numbered twiddle factors that the calculation of ''X'' requires. Therefore we can use a constant array of twiddle factors with a skip, just like we did for ''x''. Luckily, the skip for this array of twiddle factors is the same as the skip for ''x'', so we do not need to pass around an extra value for it.

Note that although the code below allocates memory and calculates the twiddle factors once per call, in practice these would likely be re-usable over many calls.

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, int N /* must be a power of 2 */, int skip,
        complex* X, complex* D, complex* twiddles) {
    complex * E = D + N/2;
    int k;

    if (N == 1) {
        X[0] = x[0];
        return;
    }

    /* for now we can use X as a scratch buffer */
    FFT_calculate(x, N/2, skip*2, E, X, twiddles);
    FFT_calculate(x + skip, N/2, skip*2, D, X, twiddles);

    for(k = 0; k &lt; N/2; k++) {
        /* Multiply entries of D by the twiddle factors e^(-2*pi*i/N * k) */
        D[k] = complex_mult(twiddles[k*skip], D[k]);
    }

    for(k = 0; k &lt; N/2; k++) {
        X[k]       = complex_add(E[k], D[k]);
        X[k + N/2] = complex_sub(E[k], D[k]);
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N/2);
    int k;
    for (k = 0; k != N/2; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, 1, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: removing recursion ==

This is a decidedly nontrivial optimization, for not a lot of speed increase. However, it does lend itself well to futher optimization.

To remove recursion we must be able to perform all the parts of each iteration in one pass. Here is a table of how we will arrange the results for each iteration for a DFT of length 8:

{|
|-
|initial
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[4][0] || X[5][0] || X[6][0] || X[7][0]
|-
|re-interpretation
| E[0][0] || E[1][0] || E[2][0] || E[3][0] || D[0][0] || D[1][0] || D[2][0] || D[3][0]
|-
|calculation of next Xs
| X[0][0] || X[1][0] || X[2][0] || X[3][0] || X[0][1] || X[1][1] || X[2][1] || X[3][1]
|-
|re-interpretation
| E[0][0] || E[1][0] || D[0][0] || D[1][0] || E[0][1] || E[1][1] || D[0][1] || D[1][1]
|-
|calculation of next Xs
| X[0][0] || X[0][1] || X[1][0] || X[1][1] || X[0][2] || X[0][3] || X[1][2] || X[1][3]
|-
|re-interpretation
| E[0][0] || D[0][0] || E[0][1] || D[0][1] || E[0][2] || D[0][2] || E[0][3] || D[0][3]
|-
|final calculation of Xs
| X[0][0] || X[0][1] || X[0][2] || X[0][3] || X[0][4] || X[0][5] || X[0][6] || X[0][7]
|}

where &lt;code&gt;X[n]&lt;/code&gt; represents what would have been the output from one call of &lt;code&gt;FFT_simple&lt;/code&gt; and &lt;code&gt;E[n]&lt;/code&gt; and &lt;code&gt;D[n]&lt;/code&gt; represent the intermediate values used by that same call.

{{TODO|explain this better!}}

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E, * D;
    complex* Xp, * Xstart;

    if (N == 1) {
        /* N == 1 is now a special case, not the end of the recursion! */
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        for(k = 0; k != n; k++) {
            for (m = 0; m != skip; ++m) {
                D = E + skip;
                *D = complex_mult(twiddles[k * skip], *D);
                *Xp = complex_add(*E, *D);
                Xp[N/2] = complex_sub(*E, *D);
                ++Xp;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Optimization: reducing function-call overhead ==

Note that in the arrangement above, the same twiddle factor is being invoked repeatedly in the inner loop. This suggests further optimizations, which, when combined with inlining of the complex arithmetic, produces a worthwhile speed improvement:

&lt;codeblock language=c&gt;
void FFT_calculate(complex* x, long N /* must be a power of 2 */,
        complex* X, complex* scratch, complex* twiddles) {
    int k, m, n;
    int skip;
    bool evenIteration = N &amp; 0x55555555;
    complex* E;
    complex* Xp, * Xp2, * Xstart;

    if (N == 1) {
    	X[0] = x[0];
    	return;
    }

    E = x;

    for (n = 1; n &lt; N; n *= 2) {
        Xstart = evenIteration? scratch : X;
        skip = N/(2 * n);
        /* each of D and E is of length n, and each element of each D and E is
        separated by 2*skip. The Es begin at E[0] to E[skip - 1] and the Ds
        begin at E[skip] to E[2*skip - 1] */
        Xp = Xstart;
        Xp2 = Xstart + N/2;
        for(k = 0; k != n; k++) {
        	double tim = twiddles[k * skip].im;
        	double tre = twiddles[k * skip].re;
            for (m = 0; m != skip; ++m) {
            	complex* D = E + skip;
            	/* twiddle *D to get dre and dim */
            	double dre = D-&gt;re * tre - D-&gt;im * tim;
            	double dim = D-&gt;re * tim + D-&gt;im * tre;
                Xp-&gt;re = E-&gt;re + dre;
                Xp-&gt;im = E-&gt;im + dim;
                Xp2-&gt;re = E-&gt;re - dre;
                Xp2-&gt;im = E-&gt;im - dim;
                ++Xp;
                ++Xp2;
                ++E;
            }
            E += skip;
        }
        E = Xstart;
        evenIteration = !evenIteration;
    }
}

complex* FFT_get_twiddle_factors(int N) {
    complex* twiddles = (complex*) malloc(sizeof(struct complex_t) * N);
    int k;
    for (k = 0; k != N; ++k) {
        twiddles[k] = complex_from_polar(1.0, -2.0*PI*k/N);
    }
    return twiddles;
}

complex* FFT_simple(complex* x, int N /* must be a power of 2 */) {
    complex* out = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* scratch = (complex*) malloc(sizeof(struct complex_t) * N);
    complex* twiddles = FFT_get_twiddle_factors(N);
    FFT_calculate(x, N, out, scratch, twiddles);
    free(twiddles);
    free(scratch);
    return out;
}
&lt;/codeblock&gt;

== Files ==

We create a few separate modules: one for our basic complex number support, one for the FFT implementations, and one for the test driver and &lt;code&gt;main()&lt;/code&gt;, described in the next section. We include the complex number header in the FFT header for the &lt;code&gt;complex&lt;/code&gt; type.

&lt;codeblock language=c&gt;
&lt;&lt;complex_simple.h&gt;&gt;=
#ifndef _COMPLEX_SIMPLE_H_
#define _COMPLEX_SIMPLE_H_

&lt;&lt;complex number datatype&gt;&gt;
&lt;&lt;complex number prototypes&gt;&gt;

#endif /* #ifndef _COMPLEX_SIMPLE_H_ */

&lt;&lt;complex_simple.c&gt;&gt;=
#include &quot;complex_simple.h&quot;
&lt;&lt;complex number headers&gt;&gt;

&lt;&lt;complex number function definitions&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=c&gt;
&lt;&lt;fft.h&gt;&gt;=
#ifndef _FFT_H_
#define _FFT_H_

#include &quot;complex_simple.h&quot;

&lt;&lt;FFT prototypes&gt;&gt;

#endif /* #ifndef _FFT_H_ */

&lt;&lt;fft.c&gt;&gt;=
#include &quot;fft.h&quot;
&lt;&lt;FFT headers&gt;&gt;

&lt;&lt;FFT constants&gt;&gt;

&lt;&lt;Naive DFT&gt;&gt;

&lt;&lt;Simple FFT&gt;&gt;

&lt;/codeblock&gt;

== Test driver ==

{{TODO}}

[[Category:Cooley-Tukey FFT algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Cosine table (C)</title>
    <id>3142</id>
    <revision>
      <id>10256</id>
      <timestamp>2007-05-18T12:06:35Z</timestamp>
      <contributor>
        <username>Mtopolov</username>
        <id>532</id>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=C&gt;
int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>10257</id>
      <timestamp>2007-05-18T12:07:08Z</timestamp>
      <contributor>
        <username>Mtopolov</username>
        <id>532</id>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;
int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>10258</id>
      <timestamp>2007-05-18T12:10:17Z</timestamp>
      <contributor>
        <username>Mtopolov</username>
        <id>532</id>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;=
int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>10259</id>
      <timestamp>2007-05-18T12:11:41Z</timestamp>
      <contributor>
        <username>Mtopolov</username>
        <id>532</id>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;=
#ifndef FIX_COSINES_TAB_H
#define FIX_COSINES_TAB_H

int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
#endif //FIX_COSINES_TAB_H
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>10268</id>
      <timestamp>2007-05-19T05:01:36Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>{{codedump}}</comment>
      <text xml:space="preserve">{{codedump}}
&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;=
#ifndef FIX_COSINES_TAB_H
#define FIX_COSINES_TAB_H

int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
#endif //FIX_COSINES_TAB_H
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>10269</id>
      <timestamp>2007-05-19T05:02:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>cat</comment>
      <text xml:space="preserve">{{codedump}}
&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;=
#ifndef FIX_COSINES_TAB_H
#define FIX_COSINES_TAB_H

int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
#endif //FIX_COSINES_TAB_H
&lt;/codeblock&gt;

[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>10270</id>
      <timestamp>2007-05-19T05:02:55Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>[[Cosines tables - full 8 bit circle (0-255)]] moved to [[Cosine table (C)]]: LP style</comment>
      <text xml:space="preserve">{{codedump}}
&lt;codeblock language=C&gt;
&lt;&lt;fcostab.h&gt;&gt;=
#ifndef FIX_COSINES_TAB_H
#define FIX_COSINES_TAB_H

int fCosTab[512] =
{
   65536L,  65531L,  65516L,  65492L,  65457L,  65413L,  65358L,  65294L,
   65220L,  65137L,  65043L,  64940L,  64827L,  64704L,  64571L,  64429L,
   64277L,  64115L,  63944L,  63763L,  63572L,  63372L,  63162L,  62943L,
   62714L,  62476L,  62228L,  61971L,  61705L,  61429L,  61145L,  60851L,
   60547L,  60235L,  59914L,  59583L,  59244L,  58896L,  58538L,  58172L,
   57798L,  57414L,  57022L,  56621L,  56212L,  55794L,  55368L,  54934L,
   54491L,  54040L,  53581L,  53114L,  52639L,  52156L,  51665L,  51166L,
   50660L,  50146L,  49624L,  49095L,  48559L,  48015L,  47464L,  46906L,
   46341L,  45769L,  45190L,  44604L,  44011L,  43412L,  42806L,  42194L,
   41576L,  40951L,  40320L,  39683L,  39040L,  38391L,  37736L,  37076L,
   36410L,  35738L,  35062L,  34380L,  33692L,  33000L,  32303L,  31600L,
   30893L,  30182L,  29466L,  28745L,  28020L,  27291L,  26558L,  25821L,
   25080L,  24335L,  23586L,  22834L,  22078L,  21320L,  20557L,  19792L,
   19024L,  18253L,  17479L,  16703L,  15924L,  15143L,  14359L,  13573L,
   12785L,  11996L,  11204L,  10411L,  9616L,   8820L,   8022L,   7224L,
   6424L,   5623L,   4821L,   4019L,   3216L,   2412L,   1608L,   804L,
   0L,      -804L,   -1608L,  -2412L,  -3216L,  -4019L,  -4821L,  -5623L,
   -6424L,  -7224L,  -8022L,  -8820L,  -9616L,  -10411L, -11204L, -11996L,
   -12785L, -13573L, -14359L, -15143L, -15924L, -16703L, -17479L, -18253L,
   -19024L, -19792L, -20557L, -21320L, -22078L, -22834L, -23586L, -24335L,
   -25080L, -25821L, -26558L, -27291L, -28020L, -28745L, -29466L, -30182L,
   -30893L, -31600L, -32303L, -33000L, -33692L, -34380L, -35062L, -35738L,
   -36410L, -37076L, -37736L, -38391L, -39040L, -39683L, -40320L, -40951L,
   -41576L, -42194L, -42806L, -43412L, -44011L, -44604L, -45190L, -45769L,
   -46341L, -46906L, -47464L, -48015L, -48559L, -49095L, -49624L, -50146L,
   -50660L, -51166L, -51665L, -52156L, -52639L, -53114L, -53581L, -54040L,
   -54491L, -54934L, -55368L, -55794L, -56212L, -56621L, -57022L, -57414L,
   -57798L, -58172L, -58538L, -58896L, -59244L, -59583L, -59914L, -60235L,
   -60547L, -60851L, -61145L, -61429L, -61705L, -61971L, -62228L, -62476L,
   -62714L, -62943L, -63162L, -63372L, -63572L, -63763L, -63944L, -64115L,
   -64277L, -64429L, -64571L, -64704L, -64827L, -64940L, -65043L, -65137L,
   -65220L, -65294L, -65358L, -65413L, -65457L, -65492L, -65516L, -65531L,
   -65536L, -65531L, -65516L, -65492L, -65457L, -65413L, -65358L, -65294L,
   -65220L, -65137L, -65043L, -64940L, -64827L, -64704L, -64571L, -64429L,
   -64277L, -64115L, -63944L, -63763L, -63572L, -63372L, -63162L, -62943L,
   -62714L, -62476L, -62228L, -61971L, -61705L, -61429L, -61145L, -60851L,
   -60547L, -60235L, -59914L, -59583L, -59244L, -58896L, -58538L, -58172L,
   -57798L, -57414L, -57022L, -56621L, -56212L, -55794L, -55368L, -54934L,
   -54491L, -54040L, -53581L, -53114L, -52639L, -52156L, -51665L, -51166L,
   -50660L, -50146L, -49624L, -49095L, -48559L, -48015L, -47464L, -46906L,
   -46341L, -45769L, -45190L, -44604L, -44011L, -43412L, -42806L, -42194L,
   -41576L, -40951L, -40320L, -39683L, -39040L, -38391L, -37736L, -37076L,
   -36410L, -35738L, -35062L, -34380L, -33692L, -33000L, -32303L, -31600L,
   -30893L, -30182L, -29466L, -28745L, -28020L, -27291L, -26558L, -25821L,
   -25080L, -24335L, -23586L, -22834L, -22078L, -21320L, -20557L, -19792L,
   -19024L, -18253L, -17479L, -16703L, -15924L, -15143L, -14359L, -13573L,
   -12785L, -11996L, -11204L, -10411L, -9616L,  -8820L,  -8022L,  -7224L,
   -6424L,  -5623L,  -4821L,  -4019L,  -3216L,  -2412L,  -1608L,  -804L,
   0L,      804L,    1608L,   2412L,   3216L,   4019L,   4821L,   5623L,
   6424L,   7224L,   8022L,   8820L,   9616L,   10411L,  11204L,  11996L,
   12785L,  13573L,  14359L,  15143L,  15924L,  16703L,  17479L,  18253L,
   19024L,  19792L,  20557L,  21320L,  22078L,  22834L,  23586L,  24335L,
   25080L,  25821L,  26558L,  27291L,  28020L,  28745L,  29466L,  30182L,
   30893L,  31600L,  32303L,  33000L,  33692L,  34380L,  35062L,  35738L,
   36410L,  37076L,  37736L,  38391L,  39040L,  39683L,  40320L,  40951L,
   41576L,  42194L,  42806L,  43412L,  44011L,  44604L,  45190L,  45769L,
   46341L,  46906L,  47464L,  48015L,  48559L,  49095L,  49624L,  50146L,
   50660L,  51166L,  51665L,  52156L,  52639L,  53114L,  53581L,  54040L,
   54491L,  54934L,  55368L,  55794L,  56212L,  56621L,  57022L,  57414L,
   57798L,  58172L,  58538L,  58896L,  59244L,  59583L,  59914L,  60235L,
   60547L,  60851L,  61145L,  61429L,  61705L,  61971L,  62228L,  62476L,
   62714L,  62943L,  63162L,  63372L,  63572L,  63763L,  63944L,  64115L,
   64277L,  64429L,  64571L,  64704L,  64827L,  64940L,  65043L,  65137L,
   65220L,  65294L,  65358L,  65413L,  65457L,  65492L,  65516L,  65531L
};
#endif //FIX_COSINES_TAB_H
&lt;/codeblock&gt;

[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Cosines tables - full 8 bit circle (0-255)</title>
    <id>3144</id>
    <revision>
      <id>10271</id>
      <timestamp>2007-05-19T05:02:55Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>[[Cosines tables - full 8 bit circle (0-255)]] moved to [[Cosine table (C)]]: LP style</comment>
      <text xml:space="preserve">#REDIRECT [[Cosine table (C)]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (C Sharp)</title>
    <id>2818</id>
    <revision>
      <id>8182</id>
      <timestamp>2006-11-26T17:32:26Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial implementation based on C version</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/// &lt;summary&gt;Sorts array a where each element is between 0 and numValues-1.&lt;/summary&gt;
void CountingSort(int[] a, int numValues) {
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for(int i=0; i &lt; a.Length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i=0; i &lt; numValues; i++) {
    for (int j=0; j &lt; counts[i]; j++) {
        a[outputPos] = i;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

&lt;!-- TODO: Test main --&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8183</id>
      <timestamp>2006-11-26T17:49:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Test main</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/// &lt;summary&gt;Sorts array a where each element is between 0 and numValues-1.&lt;/summary&gt;
void CountingSort(int[] a, int numValues) {
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for(int i=0; i &lt; a.Length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i=0; i &lt; numValues; i++) {
    for (int j=0; j &lt; counts[i]; j++) {
        a[outputPos] = i;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

We test the implementation by generating a list of integers falling in a given range, sorting it, and verifying that the results match those of the .NET Framework's &lt;a href=&quot;http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlrfsystemarrayclasssorttopic.asp&quot;&gt;&lt;code&gt;Array.Sort()&lt;/code&gt;&lt;/a&gt; method. The list size and range are specified on the command line.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort.cs&gt;&gt;=
using System;
using System.IO;

public class CountingSort {
    &lt;&lt;CountingSort method&gt;&gt;

    pubic static void Main(string[] args) {
        int listSize = int.Parse(args[0]);
        int numValues = int.Parse(args[1]);

        // Generate list of random values
        int[] a = new int[listSize];
        Random r = new Random();
        for(int i=0; i &lt; a.Length; i++) {
            a[i] = r.Next(numValues);
        }

        // Copy list to new array
        int[] a2 = new int[listSize];
        Array.Copy(a, a2, listSize);

        // Sort the two arrays
        CountingSort(a);
        Array.Sort(a2);

        // Compare the two arrays
        for (int i=0; i &lt; listSize; i++) {
            if (a[i] != a2[i]) {
                Console.WriteLine(&quot;Error: Results do not match.&quot;);
                return;
            }
        }
        Console.WriteLine(&quot;Sort successful&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8184</id>
      <timestamp>2006-11-26T17:54:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>A few fixes</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/// &lt;summary&gt;Sorts array a where each element is between 0 and numValues-1.&lt;/summary&gt;
static void Sort(int[] a, int numValues) {
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for(int i=0; i &lt; a.Length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i=0; i &lt; numValues; i++) {
    for (int j=0; j &lt; counts[i]; j++) {
        a[outputPos] = i;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

We test the implementation by generating a list of integers falling in a given range, sorting it, and verifying that the results match those of the .NET Framework's &lt;a href=&quot;http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlrfsystemarrayclasssorttopic.asp&quot;&gt;&lt;code&gt;Array.Sort()&lt;/code&gt;&lt;/a&gt; method. The list size and range are specified on the command line.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort.cs&gt;&gt;=
using System;
using System.IO;

public class CountingSort {
    &lt;&lt;CountingSort method&gt;&gt;

    public static void Main(string[] args) {
        int listSize = int.Parse(args[0]);
        int numValues = int.Parse(args[1]);

        // Generate list of random values
        int[] a = new int[listSize];
        Random r = new Random();
        for(int i=0; i &lt; a.Length; i++) {
            a[i] = r.Next(numValues);
        }

        // Copy list to new array
        int[] a2 = new int[listSize];
        Array.Copy(a, a2, listSize);

        // Sort the two arrays
        CountingSort(a);
        Array.Sort(a2);

        // Compare the two arrays
        for (int i=0; i &lt; listSize; i++) {
            if (a[i] != a2[i]) {
                Console.WriteLine(&quot;Error: Results do not match.&quot;);
                return;
            }
        }
        Console.WriteLine(&quot;Sort successful&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8185</id>
      <timestamp>2006-11-26T17:57:08Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Oops, one last fix</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/// &lt;summary&gt;Sorts array a where each element is between 0 and numValues-1.&lt;/summary&gt;
static void Sort(int[] a, int numValues) {
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for(int i=0; i &lt; a.Length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i=0; i &lt; numValues; i++) {
    for (int j=0; j &lt; counts[i]; j++) {
        a[outputPos] = i;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

We test the implementation by generating a list of integers falling in a given range, sorting it, and verifying that the results match those of the .NET Framework's &lt;a href=&quot;http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlrfsystemarrayclasssorttopic.asp&quot;&gt;&lt;code&gt;Array.Sort()&lt;/code&gt;&lt;/a&gt; method. The list size and range are specified on the command line.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort.cs&gt;&gt;=
using System;
using System.IO;

public class CountingSort {
    &lt;&lt;CountingSort method&gt;&gt;

    public static void Main(string[] args) {
        int listSize = int.Parse(args[0]);
        int numValues = int.Parse(args[1]);

        // Generate list of random values
        int[] a = new int[listSize];
        Random r = new Random();
        for(int i=0; i &lt; a.Length; i++) {
            a[i] = r.Next(numValues);
        }

        // Copy list to new array
        int[] a2 = new int[listSize];
        Array.Copy(a, a2, listSize);

        // Sort the two arrays
        Sort(a, numValues);
        Array.Sort(a2);

        // Compare the two arrays
        for (int i=0; i &lt; listSize; i++) {
            if (a[i] != a2[i]) {
                Console.WriteLine(&quot;Error: Results do not match.&quot;);
                return;
            }
        }
        Console.WriteLine(&quot;Sort successful&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8186</id>
      <timestamp>2006-11-26T22:36:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>fix link</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/// &lt;summary&gt;Sorts array a where each element is between 0 and numValues-1.&lt;/summary&gt;
static void Sort(int[] a, int numValues) {
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for(int i=0; i &lt; a.Length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i=0; i &lt; numValues; i++) {
    for (int j=0; j &lt; counts[i]; j++) {
        a[outputPos] = i;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

We test the implementation by generating a list of integers falling in a given range, sorting it, and verifying that the results match those of the .NET Framework's [http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlrfsystemarrayclasssorttopic.asp &lt;code&gt;Array.Sort()&lt;/code&gt;] method. The list size and range are specified on the command line.

&lt;codeblock language=&quot;c#&quot;&gt;
&lt;&lt;CountingSort.cs&gt;&gt;=
using System;
using System.IO;

public class CountingSort {
    &lt;&lt;CountingSort method&gt;&gt;

    public static void Main(string[] args) {
        int listSize = int.Parse(args[0]);
        int numValues = int.Parse(args[1]);

        // Generate list of random values
        int[] a = new int[listSize];
        Random r = new Random();
        for(int i=0; i &lt; a.Length; i++) {
            a[i] = r.Next(numValues);
        }

        // Copy list to new array
        int[] a2 = new int[listSize];
        Array.Copy(a, a2, listSize);

        // Sort the two arrays
        Sort(a, numValues);
        Array.Sort(a2);

        // Compare the two arrays
        for (int i=0; i &lt; listSize; i++) {
            if (a[i] != a2[i]) {
                Console.WriteLine(&quot;Error: Results do not match.&quot;);
                return;
            }
        }
        Console.WriteLine(&quot;Sort successful&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:C Sharp]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (C)</title>
    <id>1522</id>
    <revision>
      <id>2032</id>
      <timestamp>2006-03-04T03:39:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Write initial article with sort implementation, no test main yet</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort.c&gt;&gt;=
#include &lt;stdio.h&gt;   /* printf */
#include &lt;stdlib.h&gt;  /* exit */

/* Sorts a[0..length-1] where each element is between 0 and num_values-1. */
void counting_sort(int a[], unsigned int length, int num_values) {
    &lt;&lt;counting_sort variable declarations&gt;&gt;
    int* counts = malloc(sizeof(int) * num_values);
    if (counts == NULL) {
        printf(&quot;Out of memory\n&quot;);
        exit(-1);
    }
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int i;
&lt;&lt;count occurrences&gt;&gt;=
for(i=0; i&lt;length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of a[i] as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int j, output_pos;
&lt;&lt;generate result&gt;&gt;=
output_pos = 0;
for (i=0; i&lt;num_values; i++) {
    for (j=0; j&lt;counts[i]; j++) {
        a[output_pos] = i;
        output_pos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=c&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

&lt;!-- TODO: Test main --&gt;

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>3305</id>
      <timestamp>2006-03-14T08:28:06Z</timestamp>
      <contributor>
        <ip>62.92.39.137</ip>
      </contributor>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort.c&gt;&gt;=
#include &lt;stdio.h&gt;   /* printf */
#include &lt;stdlib.h&gt;  /* exit */

/* Sorts a[0..length-1] where each element is between 0 and num_values-1. */
void counting_sort(int a[], unsigned int length, int num_values) {
    &lt;&lt;counting_sort variable declarations&gt;&gt;
    int* counts = malloc(sizeof(int) * num_values);
    if (counts == NULL)
    {
        printf(&quot;Out of memory\n&quot;);
        exit(-1);
    }
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int i;
&lt;&lt;count occurrences&gt;&gt;=
for(i=0; i&lt;length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of a[i] as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int j, output_pos;
&lt;&lt;generate result&gt;&gt;=
output_pos = 0;
for (i=0; i&lt;num_values; i++) {
    for (j=0; j&lt;counts[i]; j++) {
        a[output_pos] = i;
        output_pos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=c&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

&lt;!-- TODO: Test main --&gt;

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>3306</id>
      <timestamp>2006-03-14T09:18:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Revert: just changing one of the braces just makes it inconsistent</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort.c&gt;&gt;=
#include &lt;stdio.h&gt;   /* printf */
#include &lt;stdlib.h&gt;  /* exit */

/* Sorts a[0..length-1] where each element is between 0 and num_values-1. */
void counting_sort(int a[], unsigned int length, int num_values) {
    &lt;&lt;counting_sort variable declarations&gt;&gt;
    int* counts = malloc(sizeof(int) * num_values);
    if (counts == NULL) {
        printf(&quot;Out of memory\n&quot;);
        exit(-1);
    }
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int i;
&lt;&lt;count occurrences&gt;&gt;=
for(i=0; i&lt;length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of a[i] as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int j, output_pos;
&lt;&lt;generate result&gt;&gt;=
output_pos = 0;
for (i=0; i&lt;num_values; i++) {
    for (j=0; j&lt;counts[i]; j++) {
        a[output_pos] = i;
        output_pos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=c&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

&lt;!-- TODO: Test main --&gt;

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4214</id>
      <timestamp>2006-04-21T18:56:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Memory leak</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort.c&gt;&gt;=
#include &lt;stdio.h&gt;   /* printf */
#include &lt;stdlib.h&gt;  /* exit */

/* Sorts a[0..length-1] where each element is between 0 and num_values-1. */
void counting_sort(int a[], unsigned int length, int num_values) {
    &lt;&lt;counting_sort variable declarations&gt;&gt;
    int* counts = malloc(sizeof(int) * num_values);
    if (counts == NULL) {
        printf(&quot;Out of memory\n&quot;);
        exit(-1);
    }
    &lt;&lt;perform sort&gt;&gt;
    free(counts);
}
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int i;
&lt;&lt;count occurrences&gt;&gt;=
for(i=0; i&lt;length; i++) {
    counts[a[i]]++;
}
&lt;/codeblock&gt;

Note the use of a[i] as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=c&gt;
&lt;&lt;counting_sort variable declarations&gt;&gt;=
unsigned int j, output_pos;
&lt;&lt;generate result&gt;&gt;=
output_pos = 0;
for (i=0; i&lt;num_values; i++) {
    for (j=0; j&lt;counts[i]; j++) {
        a[output_pos] = i;
        output_pos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=c&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

&lt;!-- TODO: Test main --&gt;

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (Haskell)</title>
    <id>3542</id>
    <revision>
      <id>14364</id>
      <timestamp>2008-08-20T05:00:03Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>maybe?</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space. (Although the implementation here is very inefficient. I'm not even sure if it qualifies as a counting sort.)

We begin by declaring a function that takes as arguments the list to be sorted, and the domain (in sort order) that we are sorting by as another list. Note that we require that the type that we are sorting be able to be compared for equality, as we will need that to &quot;count&quot; later. This is reflected in the type of the function:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting sort&gt;&gt;=
csort :: (Eq a) =&gt; [a] -&gt; [a] -&gt; [a]
csort seq dom = &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. First, I use the List Monad to iterate through all the elements of the domain, in order:
&lt;codeblock language=haskell&gt;
&lt;&lt;generate result&gt;&gt;=
do x &lt;- dom
   &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Then, I ''count'' the number of times that element occurs in the sequence.  In this case, I simply find those occurrences and extract them with &quot;filter&quot;. Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.
&lt;codeblock language=haskell&gt;
&lt;&lt;count occurences&gt;&gt;=
filter (x ==) seq
&lt;/codeblock&gt;

The occurrences for each element of the domain will now be grouped together, sorted by the order of the elements in the domain.

Finally we package things up with a few tests:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting_sort.hs&gt;&gt;=
&lt;&lt;counting sort&gt;&gt;

main :: IO ()
main = do print &quot;counting sort of 3.1415926535897931&quot;
          print $ csort &quot;3.1415926535897931&quot; &quot;0123456789&quot;
          print &quot;counting sort of 2.71828182846&quot;
          print $ csort &quot;2.71828182846&quot; &quot;0123456789&quot;
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

[[Category:Programming language:Haskell]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>14365</id>
      <timestamp>2008-08-20T05:01:49Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space. (Although the implementation here is very inefficient. I'm not even sure if it qualifies as a counting sort.)

We begin by declaring a function that takes as arguments the list to be sorted, and the domain (in sort order) that we are sorting by as another list. Note that we require that the type that we are sorting be able to be compared for equality, as we will need that to &quot;count&quot; later. This is reflected in the type of the function:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting sort&gt;&gt;=
csort :: (Eq a) =&gt; [a] -&gt; [a] -&gt; [a]
csort seq dom =
  &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. First, I use the List Monad to iterate through all the elements of the domain, in order:
&lt;codeblock language=haskell&gt;
&lt;&lt;generate result&gt;&gt;=
do x &lt;- dom
   &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Then, I ''count'' the number of times that element occurs in the sequence.  In this case, I simply find those occurrences and extract them with &quot;filter&quot;. Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.
&lt;codeblock language=haskell&gt;
&lt;&lt;count occurences&gt;&gt;=
filter (x ==) seq
&lt;/codeblock&gt;

The occurrences for each element of the domain will now be grouped together, sorted by the order of the elements in the domain.

Finally we package things up with a few tests:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting_sort.hs&gt;&gt;=
&lt;&lt;counting sort&gt;&gt;

main :: IO ()
main = do putStrLn &quot;counting sort of 3.1415926535897931&quot;
          putStrLn $ csort &quot;3.1415926535897931&quot; &quot;0123456789&quot;
          putStrLn &quot;counting sort of 2.71828182846&quot;
          putStrLn $ csort &quot;2.71828182846&quot; &quot;0123456789&quot;
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
&quot;counting sort of 3.1415926535897931&quot;
&quot;11123334555678999&quot;
&quot;counting sort of 2.71828182846&quot;
&quot;112224678888&quot;
&lt;/pre&gt;

[[Category:Programming language:Haskell]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>14366</id>
      <timestamp>2008-08-20T05:02:17Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space. (Although the implementation here is very inefficient. I'm not even sure if it qualifies as a counting sort.)

We begin by declaring a function that takes as arguments the list to be sorted, and the domain (in sort order) that we are sorting by as another list. Note that we require that the type that we are sorting be able to be compared for equality, as we will need that to &quot;count&quot; later. This is reflected in the type of the function:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting sort&gt;&gt;=
csort :: (Eq a) =&gt; [a] -&gt; [a] -&gt; [a]
csort seq dom =
  &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. First, I use the List Monad to iterate through all the elements of the domain, in order:
&lt;codeblock language=haskell&gt;
&lt;&lt;generate result&gt;&gt;=
do x &lt;- dom
   &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Then, I ''count'' the number of times that element occurs in the sequence.  In this case, I simply find those occurrences and extract them with &quot;filter&quot;. Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.
&lt;codeblock language=haskell&gt;
&lt;&lt;count occurences&gt;&gt;=
filter (x ==) seq
&lt;/codeblock&gt;

The occurrences for each element of the domain will now be grouped together, sorted by the order of the elements in the domain.

Finally we package things up with a few tests:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting_sort.hs&gt;&gt;=
&lt;&lt;counting sort&gt;&gt;

main :: IO ()
main = do putStrLn &quot;counting sort of 3.1415926535897931&quot;
          putStrLn $ csort &quot;3.1415926535897931&quot; &quot;0123456789&quot;
          putStrLn &quot;counting sort of 2.71828182846&quot;
          putStrLn $ csort &quot;2.71828182846&quot; &quot;0123456789&quot;
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
11123334555678999
counting sort of 2.71828182846
112224678888
&lt;/pre&gt;

[[Category:Programming language:Haskell]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>14805</id>
      <timestamp>2008-10-01T13:50:55Z</timestamp>
      <contributor>
        <ip>80.220.102.30</ip>
      </contributor>
      <comment>your example iterates through the list much more than twice</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space. (Although the implementation here is very inefficient. I'm not even sure if it qualifies as a counting sort.)

We begin by declaring a function that takes as arguments the list to be sorted, and the domain (in sort order) that we are sorting by as another list. Note that we require that the type that we are sorting be able to be compared for equality, as we will need that to &quot;count&quot; later. This is reflected in the type of the function:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting sort&gt;&gt;=
csort :: (Eq a) =&gt; [a] -&gt; [a] -&gt; [a]
csort seq dom =
  &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. First, I use the List Monad to iterate through all the elements of the domain, in order:
&lt;codeblock language=haskell&gt;
&lt;&lt;generate result&gt;&gt;=
do x &lt;- dom
   &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Then, I ''count'' the number of times that element occurs in the sequence.  In this case, I simply find those occurrences and extract them with &quot;filter&quot;. Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.
&lt;codeblock language=haskell&gt;
&lt;&lt;count occurences&gt;&gt;=
filter (x ==) seq
&lt;/codeblock&gt;

The occurrences for each element of the domain will now be grouped together, sorted by the order of the elements in the domain.

Finally we package things up with a few tests:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting_sort.hs&gt;&gt;=
&lt;&lt;counting sort&gt;&gt;

main :: IO ()
main = do putStrLn &quot;counting sort of 3.1415926535897931&quot;
          putStrLn $ csort &quot;3.1415926535897931&quot; &quot;0123456789&quot;
          putStrLn &quot;counting sort of 2.71828182846&quot;
          putStrLn $ csort &quot;2.71828182846&quot; &quot;0123456789&quot;
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
11123334555678999
counting sort of 2.71828182846
112224678888
&lt;/pre&gt;


For an implementation that runs through the list just twice see [[http://kks.cabal.fi/laskentalajittelu ]] 

[[Category:Programming language:Haskell]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>14832</id>
      <timestamp>2008-10-04T08:58:39Z</timestamp>
      <contributor>
        <ip>130.231.48.68</ip>
      </contributor>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space. (Although the implementation here is very inefficient. I'm not even sure if it qualifies as a counting sort.)

We begin by declaring a function that takes as arguments the list to be sorted, and the domain (in sort order) that we are sorting by as another list. Note that we require that the type that we are sorting be able to be compared for equality, as we will need that to &quot;count&quot; later. This is reflected in the type of the function:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting sort&gt;&gt;=
csort :: (Eq a) =&gt; [a] -&gt; [a] -&gt; [a]
csort seq dom =
  &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. First, I use the List Monad to iterate through all the elements of the domain, in order:
&lt;codeblock language=haskell&gt;
&lt;&lt;generate result&gt;&gt;=
do x &lt;- dom
   &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Then, I ''count'' the number of times that element occurs in the sequence.  In this case, I simply find those occurrences and extract them with &quot;filter&quot;. Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.
&lt;codeblock language=haskell&gt;
&lt;&lt;count occurences&gt;&gt;=
filter (x ==) seq
&lt;/codeblock&gt;

The occurrences for each element of the domain will now be grouped together, sorted by the order of the elements in the domain.

Finally we package things up with a few tests:
&lt;codeblock language=haskell&gt;
&lt;&lt;counting_sort.hs&gt;&gt;=
&lt;&lt;counting sort&gt;&gt;

main :: IO ()
main = do putStrLn &quot;counting sort of 3.1415926535897931&quot;
          putStrLn $ csort &quot;3.1415926535897931&quot; &quot;0123456789&quot;
          putStrLn &quot;counting sort of 2.71828182846&quot;
          putStrLn $ csort &quot;2.71828182846&quot; &quot;0123456789&quot;
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
11123334555678999
counting sort of 2.71828182846
112224678888
&lt;/pre&gt;


For an implementation that runs through the list just twice see [[http://kks.cabal.fi/laskentalajittelu/CountingSortHaskell ]] 

[[Category:Programming language:Haskell]]
[[Category:Counting sort]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (Java)</title>
    <id>3273</id>
    <revision>
      <id>11981</id>
      <timestamp>2008-01-09T07:54:30Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll assume the elements take on integer values, but the same ideas apply to any type. We begin by declaring an array that will hold a counter for each possible value that an element can take on:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CountingSort method&gt;&gt;=
/** Sorts array a where each element is between 0 and numValues-1. */
public static void sort(int[] a) {
    &lt;&lt;find range&gt;&gt;
    int[] counts = new int[numValues];
    &lt;&lt;perform sort&gt;&gt;
}
&lt;/codeblock&gt;

To find the range of numbers, we traverse the array to find the minimum and maximum. If you already know the range, then you can skip this step and pass it into the function directly.
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;find range&gt;&gt;=
if (a.length == 0)
  return;

int max = a[0], min = a[0];
for (int i = 1; i &lt; a.length; i++) {
    if (a[i] &gt; max)
        max = a[i];
    else if (a[i] &lt; min)
        min = a[i];
}
int numValues = max - min + 1;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we iterate through the list, counting the number of times we observe each element by incrementing the array value corresponding to each element:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;count occurrences&gt;&gt;=
for (int i = 0; i &lt; a.length; i++) {
    counts[a[i]-min]++;
}
&lt;/codeblock&gt;

Note the use of &lt;code&gt;a[i]&lt;/code&gt; as an array index. This is what makes counting sort not a comparison sort. In the second phase, ''generate result'', we iterate through the counts array, outputting the counted number of elements for each value:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate result&gt;&gt;=
int outputPos = 0;
for (int i = 0; i &lt; numValues; i++) {
    for (int j = 0; j &lt; counts[i]; j++) {
        a[outputPos] = i+min;
        outputPos++;
    }
}
&lt;/codeblock&gt;

Although this is a doubly-nested loop, the way in which we set the counters guarantees that the inner loop is executed only a linear (''O''(''n'')) number of times. Putting together these two phases, the sort is now complete:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;perform sort&gt;&gt;=
&lt;&lt;count occurrences&gt;&gt;
&lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

We test the implementation by generating a list of integers falling in a given range, sorting it, and verifying that the results match those of Java's [http://java.sun.com/javase/6/docs/api/java/util/Arrays.html#sort(int[]) &lt;code&gt;Arrays.sort()&lt;/code&gt;] method. The list size and range are specified on the command line.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;CountingSort.java&gt;&gt;=
import java.util.Arrays;
import java.util.Random;

public class CountingSort {
    &lt;&lt;CountingSort method&gt;&gt;

    public static void main(String[] args) {
        int listSize = Integer.parseInt(args[0]);
        int numValues = Integer.parseInt(args[1]);

        // Generate list of random values
        int[] a = new int[listSize];
        Random r = new Random();
        for (int i = 0; i &lt; a.length; i++) {
            a[i] = r.nextInt(numValues);
        }

        // Copy list to new array
        int[] a2 = new int[listSize];
        System.arraycopy(a, 0, a2, 0, listSize);

        // Sort the two arrays
        sort(a);
        Arrays.sort(a2);

        // Compare the two arrays
        for (int i = 0; i &lt; listSize; i++) {
            if (a[i] != a2[i]) {
                System.out.println(&quot;Error: Results do not match.&quot;);
                return;
            }
        }
        System.out.println(&quot;Sort successful&quot;);
    }
}
&lt;/codeblock&gt;

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Counting sort|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (Python, functional)</title>
    <id>2887</id>
    <revision>
      <id>8454</id>
      <timestamp>2007-01-03T18:15:34Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=sum(equal.outer(seq, dom)))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\alpha \backslash + / \omega \circ . = \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8455</id>
      <timestamp>2007-01-03T18:17:22Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>try to fix codeblocks</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom)))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\alpha \backslash + / \omega \circ . = \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8456</id>
      <timestamp>2007-01-03T18:20:05Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>try to fix codeblocks</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom))))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\alpha \backslash + / \omega \circ . = \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8457</id>
      <timestamp>2007-01-03T18:20:50Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>try to fix codeblocks</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom)))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\alpha \backslash + / \omega \circ . = \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8458</id>
      <timestamp>2007-01-03T18:23:10Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>rebalance parens</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\alpha \backslash + / \omega \circ . = \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8481</id>
      <timestamp>2007-01-04T08:55:56Z</timestamp>
      <contributor>
        <ip>127.0.0.1</ip>
      </contributor>
      <comment>correct APL</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom))
&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\left ( + / \omega \circ . = \alpha \right ) / \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>8499</id>
      <timestamp>2007-01-07T21:43:57Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>neaten code</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(equal.outer(seq, dom))&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from Numeric import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(&quot;3.1415926535897931&quot;, &quot;0123456789&quot;)
        print &quot;counting sort of 2.71828182846&quot;
        print csort(&quot;2.71828182846&quot;, &quot;0123456789&quot;)
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\left ( + / \omega \circ . = \alpha \right ) / \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>16038</id>
      <timestamp>2009-01-25T22:12:26Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>port to numpy</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

''NB. Due to an apparent numpy bug with &lt;code&gt;equal.outer&lt;/code&gt; we currently use &lt;code&gt;newaxis&lt;/code&gt; by hand to perform this operation''

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(seq[:,newaxis] == dom[newaxis,:], 0)&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from numpy import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        a=lambda str: fromstring(str,dtype=&quot;S1&quot;)
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(a(&quot;3.1415926535897931&quot;), a(&quot;0123456789&quot;))
        print &quot;counting sort of 2.71828182846&quot;
        print csort(a(&quot;2.71828182846&quot;), a(&quot;0123456789&quot;))
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
[1 1 1 2 3 3 3 4 5 5 5 6 7 8 9 9 9]
counting sort of 2.71828182846
[1 1 2 2 2 4 6 7 8 8 8 8]
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\left ( + / \omega \circ . = \alpha \right ) / \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>16039</id>
      <timestamp>2009-01-25T22:14:18Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>expected output</comment>
      <text xml:space="preserve">Counting sort is a very simple sort that is efficient for lists that take on only a small number of values. A linear-time algorithm based on array indexing, it trades time for space.

For the purposes of this article, we'll use character elements that are restricted to integer digits, but the same ideas apply to any type. We begin by declaring a function that takes as arguments the sequence to be sorted, and the domain (in sort order) that we are sorting by.

&lt;codeblock language=python&gt;
&lt;&lt;counting sort&gt;&gt;=
lambda seq, dom: &lt;&lt;generate result&gt;&gt;
&lt;/codeblock&gt;

Next, we perform the sort. There are two phases to counting sort. In the first phase, ''count occurrences'', we count the number of times each element of the domain occurs in the sequence.  Note that we are comparing the elements of the sequence with the elements of the domain, not with each other &amp;mdash; this is what makes counting sort not a comparison sort.

''NB. Due to an apparent numpy bug with &lt;code&gt;equal.outer&lt;/code&gt; we currently use &lt;code&gt;newaxis&lt;/code&gt; by hand to perform this operation''

&lt;codeblock language=python&gt;
&lt;&lt;count occurences&gt;&gt;=
sum(seq[:,newaxis] == dom[newaxis,:], 0)&lt;/codeblock&gt;

In the second phase, ''generate result'', we use &lt;code&gt;repeat&lt;/code&gt; to repeat each element of the domain as many times as we counted it in the original sequence.

&lt;codeblock language=python&gt;
&lt;&lt;generate result&gt;&gt;=
repeat(dom, &lt;&lt;count occurences&gt;&gt;)
&lt;/codeblock&gt;

Finally we package things up with a few tests:

&lt;codeblock language=python&gt;
&lt;&lt;counting_sort.py&gt;&gt;=
from numpy import *

csort=&lt;&lt;counting sort&gt;&gt;

if __name__ == &quot;__main__&quot;:
        a=lambda str: fromstring(str,dtype=&quot;S1&quot;)
        print &quot;counting sort of 3.1415926535897931&quot;
        print csort(a(&quot;3.1415926535897931&quot;), a(&quot;0123456789&quot;))
        print &quot;counting sort of 2.71828182846&quot;
        print csort(a(&quot;2.71828182846&quot;), a(&quot;0123456789&quot;))
&lt;/codeblock&gt;

that we expect to produce the following output:

&lt;pre&gt;
counting sort of 3.1415926535897931
['1' '1' '1' '2' '3' '3' '3' '4' '5' '5' '5' '6' '7' '8' '9' '9' '9']
counting sort of 2.71828182846
['1' '1' '2' '2' '2' '4' '6' '7' '8' '8' '8' '8']
&lt;/pre&gt;

----

''this definition of counting sort may appear terse, but it is actually an expansion of the APL equivalent, in which the definition of csort would be something along the lines of &lt;math&gt;\left ( + / \omega \circ . = \alpha \right ) / \alpha&lt;/math&gt;''

[[Category:Programming language:Python]]
[[Category:Counting sort]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (Scala)</title>
    <id>1887</id>
    <revision>
      <id>4106</id>
      <timestamp>2006-04-12T15:13:56Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    assume( end &lt;= array.length) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 
        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {
        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {'count'(item) = count([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))
        count( i) = count( i) + count( i -1)
        
      /* {'count'(item) = count([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {
        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 
        array(i) = scratch( i)
    }
  }
&lt;codeblock/&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;codeblock/&gt;

Execution

&lt;pre&gt;
test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>4107</id>
      <timestamp>2006-04-12T15:18:18Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    assume( end &lt;= array.length) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {'count'(item) = count([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {'count'(item) = count([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4108</id>
      <timestamp>2006-04-12T15:32:22Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>naming in state comments</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    assume( end &lt;= array.length) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {count(item) = 'count elements'([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(item) = 'count elements'([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4109</id>
      <timestamp>2006-04-12T15:37:08Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>execution line was incomplete</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    assume( end &lt;= array.length) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {count(item) = 'count elements'([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(item) = 'count elements'([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4110</id>
      <timestamp>2006-04-12T16:02:57Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>precondition now complete</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {
    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; List.fromArray( array.subArray(0, end)).forall( (x: Int) =&gt; min &lt;= x &amp;&amp; x &lt;= max)) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {count(item) = 'count elements'([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(item) = 'count elements'([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4111</id>
      <timestamp>2006-04-12T16:10:10Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>== in state comments</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; List.fromArray( array.subArray(0, end))
                        .forall( (x: Int) =&gt; min &lt;= x &amp;&amp; x &lt;= max)) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count values
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        count( item) = count( item) +1 ;
      }

      /* {count(item) == 'count elements'([ x | (array(x) - min) == item])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(item) == 'count elements'([ x | (array(x) - min) &lt;= item])} */   

      // reposition array values in scratch
      // each item value at count( item) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val item = array(i) - min ;
        
        scratch( count( item) -1) = array(i) ;
        count( item) = count( item) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4114</id>
      <timestamp>2006-04-13T12:13:10Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>var name 'item' to 'normValue' and suppressed precond inferred type</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; List.fromArray( array.subArray(0, end))
                        .forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count normalized Values
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        count( normValue) = count( normValue) +1 ;
      }

      /* {count(normValue) == 'count elements'([ x | (array(x) - min) == normValue])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(normValue) == 'count elements'([ x | (array(x) - min) &lt;= normValue])} */ 
      
      // now count(normValue) has the topmost ordered position for normValue  

      // reposition array values in scratch
      // each value at count( normValue) position and backwards
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4115</id>
      <timestamp>2006-04-13T13:09:06Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>comment on repeated values</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; List.fromArray( array.subArray(0, end))
                        .forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count normalized Values
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        count( normValue) = count( normValue) +1 ;
      }

      /* {count(normValue) == 'count elements'([ x | (array(x) - min) == normValue])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(normValue) == 'count elements'([ x | (array(x) - min) &lt;= normValue])} */ 
      
      // now count(normValue) has the topmost ordered position for normValue  

      // reposition array values in scratch
      // each value at count( normValue) position 
      // decrementing count( normValue) for next position of repeated values
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSort.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSort extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSort

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4468</id>
      <timestamp>2006-05-07T13:52:14Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>avoided list conv. on precond.</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=scala&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; array.subArray(0, end).forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 
       
      // init counters 
      for (val i &lt;- Iterator.range( 0, sortRange)) 

        count( i) = 0 ;
      
      // count normalized Values
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        count( normValue) = count( normValue) +1 ;
      }

      /* {count(normValue) == 'count elements'([ x | (array(x) - min) == normValue])} */   
      
      // accumulate counters
      for (val i &lt;- Iterator.range( 1, sortRange))

        count( i) = count( i) + count( i -1)

        
      /* {count(normValue) == 'count elements'([ x | (array(x) - min) &lt;= normValue])} */ 
      
      // now count(normValue) has the topmost ordered position for normValue  

      // reposition array values in scratch
      // each value at count( normValue) position 
      // decrementing count( normValue) for next position of repeated values
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = array(i) - min ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) 

        array(i) = scratch( i)
    }
  }
&lt;/codeblock&gt;

Testing

&lt;codeblock language=scala&gt;
&lt;&lt;CountingSortTest.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSortTest extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

Execution:
&lt;pre&gt;
scala test.CountingSortTest

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>4524</id>
      <timestamp>2006-05-10T00:30:03Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>split code for better reading, defined function normalized</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; array.subArray(0, end).forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 

      def normalized( i: Int) = array( i) - min 
       
      &lt;&lt;count_values_and_accumulate&gt;&gt;
      
      // now count(normValue) has the topmost ordered position for normValue  

      // reposition array values in scratch
      // each value at count( normValue) position 
      // decrementing count( normValue) for next position of repeated values
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = normalized( i) ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) { 

        array(i) = scratch( i)
      }
    }
  }
&lt;/codeblock&gt;

Count normalized values and accumulate counters, so each accumulated counter will hold the topmost ordered position for the value it indexes.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;count_values_and_accumulate&gt;&gt;=

// init counters 
for (val i &lt;- Iterator.range( 0, sortRange)) count( i) = 0 ;
      
// count normalized Values
for (val i &lt;- Iterator.range( 0, end)) {

  val normValue = normalized( i) ;
  count( normValue) = count( normValue) +1 ;
}
      
// accumulate counters
for (val i &lt;- Iterator.range( 1, sortRange)) {

  count( i) = count( i) + count( i -1)
}

/* {count(normValue) == 'count elements x where (normalized( x) &lt;= normValue')} */ 

&lt;/codeblock&gt;



== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;CountingSortTest.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSortTest extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.CountingSortTest

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>5798</id>
      <timestamp>2006-06-03T09:54:22Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>better comments</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; array.subArray(0, end).forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 

      def normalized( i: Int) = array( i) - min 
       
      &lt;&lt;count_values_and_accumulate&gt;&gt;
      
      // now count(normValue) == topmost (if repeated values) of order( normValue)  

      // reposition array values in scratch
      // each value at count( normValue) position 
      // decrementing count( normValue) for next position of repeated values
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = normalized( i) ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) { 

        array(i) = scratch( i)
      }
    }
  }
&lt;/codeblock&gt;

Count normalized values and accumulate counters, so each accumulated counter will hold the topmost ordered position for the value it indexes.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;count_values_and_accumulate&gt;&gt;=

// init counters 
for (val i &lt;- Iterator.range( 0, sortRange)){

  count( i) = 0 ;
}
      
// count normalized array values
for (val i &lt;- Iterator.range( 0, end)) {

  val normValue = normalized( i) ;
  count( normValue) = count( normValue) +1 ;
}
      
// accumulate counters
for (val i &lt;- Iterator.range( 1, sortRange)) {

  count( i) = count( i) + count( i -1)
}

/** 
* count(normValue) will hold the number of elements 
* with normalized value less than or equal to normValue, 
* so the topmost (for repeated values) order position
*
* {count(normValue) == 'count elements x where (normalized( x) &lt;= normValue')} 
*/ 

&lt;/codeblock&gt;



== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;CountingSortTest.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSortTest extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.CountingSortTest

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
    <revision>
      <id>5801</id>
      <timestamp>2006-06-03T10:15:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Counting sort (Scala, simple)]] moved to [[Counting sort (Scala)]]: Keep it at a shorter title unless/until a need for differentiation arises</comment>
      <text xml:space="preserve">Here is a simple Counting sort in Scala:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;counting_sort&gt;&gt;=
  
  // scaladoc (javadoc like) documentation 
  
  /**
  * 
  * @param array : array to sort
  * @param end   : number of elements to sort
  * @param max   : upper bound for array values
  * @param min   : lower bound for array values
  */

  def cSort( array: Array[Int], end: Int, max: Int, min: Int): Unit = {

    // precondition
    assume( end &lt;= array.length 
            &amp;&amp; array.subArray(0, end).forall( x =&gt; (min &lt;= x &amp;&amp; x &lt;= max))) ;
    
    if ( end &lt; 2) {}  // nothing to sort

    else if (end == 2) {
      if (array( 0) &gt; array(1)) {

        // swap values
        val temp = array(0) ;
        array(0) = array(1) ;
        array(1) = temp ;
      }
    }
    else  {
      
      val sortRange = max - min +1 
      val count = new Array[Int]( sortRange)  
      val scratch = new Array[Int]( end) 

      def normalized( i: Int) = array( i) - min 
       
      &lt;&lt;count_values_and_accumulate&gt;&gt;
      
      // now count(normValue) == topmost (if repeated values) of order( normValue)  

      // reposition array values in scratch
      // each value at count( normValue) position 
      // decrementing count( normValue) for next position of repeated values
      
      for (val i &lt;- Iterator.range( 0, end)) {

        val normValue = normalized( i) ;
        
        scratch( count( normValue) -1) = array(i) ;
        count( normValue) = count( normValue) -1 ;
      }
      
      // copy scratch ordered values back into array
      for (val i &lt;- Iterator.range( 0, end)) { 

        array(i) = scratch( i)
      }
    }
  }
&lt;/codeblock&gt;

Count normalized values and accumulate counters, so each accumulated counter will hold the topmost ordered position for the value it indexes.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;count_values_and_accumulate&gt;&gt;=

// init counters 
for (val i &lt;- Iterator.range( 0, sortRange)){

  count( i) = 0 ;
}
      
// count normalized array values
for (val i &lt;- Iterator.range( 0, end)) {

  val normValue = normalized( i) ;
  count( normValue) = count( normValue) +1 ;
}
      
// accumulate counters
for (val i &lt;- Iterator.range( 1, sortRange)) {

  count( i) = count( i) + count( i -1)
}

/** 
* count(normValue) will hold the number of elements 
* with normalized value less than or equal to normValue, 
* so the topmost (for repeated values) order position
*
* {count(normValue) == 'count elements x where (normalized( x) &lt;= normValue')} 
*/ 

&lt;/codeblock&gt;



== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;CountingSortTest.scala&gt;&gt;=
package test;

import scala.testing.UnitTest ;

object CountingSortTest extends Application {

  &lt;&lt;counting_sort&gt;&gt;
  
  def test = {
    val sample1 = Array( 5, 3, 7, 10, 2, 7, 3)
    val expected1 = Array( 2, 3, 3, 5, 7, 7, 10)
    
    val min = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.min( x,y)} ;
    val max = List.fromArray( sample1) reduceLeft { (x: Int, y: Int) =&gt; Math.max( x,y)} ;
    val actual1 = { 
                    cSort( sample1, sample1.length, max, min) ;
                    sample1 
                   }
    UnitTest.assertSameElements(  actual1, expected1)
  }

  test
}


&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.CountingSortTest

passed ok
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Counting sort]]</text>
    </revision>
  </page>
  <page>
    <title>Counting sort (Scala, simple)</title>
    <id>2261</id>
    <revision>
      <id>5802</id>
      <timestamp>2006-06-03T10:15:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Counting sort (Scala, simple)]] moved to [[Counting sort (Scala)]]: Keep it at a shorter title unless/until a need for differentiation arises</comment>
      <text xml:space="preserve">#REDIRECT [[Counting sort (Scala)]]</text>
    </revision>
  </page>
  <page>
    <title>Cubic spline (Python)</title>
    <id>2743</id>
    <revision>
      <id>7885</id>
      <timestamp>2006-10-29T10:52:30Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial code dump</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; t-1 &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2 \\
B_1 &amp; = &amp; 3(1-t)(t)^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming Language:Python]]</text>
    </revision>
    <revision>
      <id>7886</id>
      <timestamp>2006-10-30T08:24:48Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* cubic spline interpolator */ codeblock was fine, math had typo</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; t-1 &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming Language:Python]]</text>
    </revision>
    <revision>
      <id>7887</id>
      <timestamp>2006-10-30T08:35:01Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* cubic spline interpolator */ +exposition</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; 1-t &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the factors of three?  When we perform a linear interpolation, we use a linear combination of &lt;math&gt;t&lt;/math&gt; and &lt;math&gt;1-t&lt;/math&gt; as weights.  The square of that generates 4 weights, and the cube 8, but multiplication is commutative, so given &lt;math&gt; ttt + tt(1-t) + t(1-t)t + ... + (1-t)(1-t)t + (1-t)(1-t)(1-t) &lt;/math&gt; we can cut the work in half by grouping like terms.

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

''Question: which symmetry axes of the cube produce the 1-3-3-1 pattern?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming Language:Python]]</text>
    </revision>
    <revision>
      <id>8074</id>
      <timestamp>2006-11-16T21:53:13Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>fix cat name</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; 1-t &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the factors of three?  When we perform a linear interpolation, we use a linear combination of &lt;math&gt;t&lt;/math&gt; and &lt;math&gt;1-t&lt;/math&gt; as weights.  The square of that generates 4 weights, and the cube 8, but multiplication is commutative, so given &lt;math&gt; ttt + tt(1-t) + t(1-t)t + ... + (1-t)(1-t)t + (1-t)(1-t)(1-t) &lt;/math&gt; we can cut the work in half by grouping like terms.

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

''Question: which symmetry axes of the cube produce the 1-3-3-1 pattern?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>8538</id>
      <timestamp>2007-01-13T20:22:49Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* wrapping up */ +cat</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; 1-t &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the factors of three?  When we perform a linear interpolation, we use a linear combination of &lt;math&gt;t&lt;/math&gt; and &lt;math&gt;1-t&lt;/math&gt; as weights.  The square of that generates 4 weights, and the cube 8, but multiplication is commutative, so given &lt;math&gt; ttt + tt(1-t) + t(1-t)t + ... + (1-t)(1-t)t + (1-t)(1-t)(1-t) &lt;/math&gt; we can cut the work in half by grouping like terms.

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

''Question: which symmetry axes of the cube produce the 1-3-3-1 pattern?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming language:Python]]
[[Category:Numerical interpolation]]</text>
    </revision>
    <revision>
      <id>8539</id>
      <timestamp>2007-01-13T20:25:06Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* wrapping up */ +cat</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from Numeric import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; 1-t &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the factors of three?  When we perform a linear interpolation, we use a linear combination of &lt;math&gt;t&lt;/math&gt; and &lt;math&gt;1-t&lt;/math&gt; as weights.  The square of that generates 4 weights, and the cube 8, but multiplication is commutative, so given &lt;math&gt; ttt + tt(1-t) + t(1-t)t + ... + (1-t)(1-t)t + (1-t)(1-t)(1-t) &lt;/math&gt; we can cut the work in half by grouping like terms.

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

''Question: which symmetry axes of the cube produce the 1-3-3-1 pattern?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming language:Python]]
[[Category:Numerical interpolation]]
[[Category:Typesetting]]</text>
    </revision>
    <revision>
      <id>16028</id>
      <timestamp>2009-01-24T22:15:51Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>update to numpy</comment>
      <text xml:space="preserve">== cubic spline interpolator ==

Spline interpolation is repetitive math, not symbolic computation, so we will use the &lt;code&gt;Numeric Python&lt;/code&gt; package.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
from numpy import *
&lt;/codeblock&gt;

We precalculate a set of cubic [http://en.wikipedia.org/wiki/Bernstein_polynomial Bernstein bases],
starting with a linear base.  
Instead of a continuous &lt;math&gt; t &lt;/math&gt;,
we'll &lt;b&gt;s&lt;/b&gt;tep from 0 to 256 (inclusive!) by 1/256
to generate a discrete table useful over the range &lt;math&gt; [0,1] &lt;/math&gt;.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
s = arange(257)/256.0
&lt;/codeblock&gt;

We need &lt;math&gt; 1-t &lt;/math&gt; as well, but that is simple:
it is the mirror image of &lt;math&gt; t &lt;/math&gt;.
Rather than recalulate, we take &lt;b&gt;z&lt;/b&gt; to be that same as &lt;b&gt;s&lt;/b&gt;, only read backwards.  (with a stride of -1)

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
z = s[::-1]
&lt;/codeblock&gt;

Now we build up each cubic basis as a function of our existing linear terms.&lt;br&gt;
&lt;math&gt;
\begin{matrix}
B_3 &amp; = &amp; (1-t)^3 \\
B_2 &amp; = &amp; 3(1-t)^2t \\
B_1 &amp; = &amp; 3(1-t)t^2 \\
B_0 &amp; = &amp; t^3
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;lookup table&gt;&gt;=
b = transpose(array((z*z*z,
                   3*z*z*s, 
                   3*z*s*s,
                     s*s*s)))
&lt;/codeblock&gt;

Why the factors of three?  When we perform a linear interpolation, we use a linear combination of &lt;math&gt;t&lt;/math&gt; and &lt;math&gt;1-t&lt;/math&gt; as weights.  The square of that generates 4 weights, and the cube 8, but multiplication is commutative, so given &lt;math&gt; ttt + tt(1-t) + t(1-t)t + ... + (1-t)(1-t)t + (1-t)(1-t)(1-t) &lt;/math&gt; we can cut the work in half by grouping like terms.

Why the transposition?  So that cubic spline evaluation simplifies to the dot product &lt;math&gt; B_3(t)c_0 + B_2(t)c_1 + B_1(t)c_2 + B_0(t)c_3 &lt;/math&gt; 

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;definition&gt;&gt;=
def cubicspline(c,t): return dot(b[t],c)
&lt;/codeblock&gt;

''Exercise: what changes are necessary to interpolate several sets of control points in parallel?''

''Question: which symmetry axes of the cube produce the 1-3-3-1 pattern?''

== wrapping up ==

Finally, we test the output by generating a little Postscript,

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;cubicspline.py&gt;&gt;=
&lt;&lt;lookup table&gt;&gt;
&lt;&lt;definition&gt;&gt;
if __name__ == &quot;__main__&quot;:
        cs = reshape(array([
        533,179, 533,179, 483,0, 483,0,
        483,0, 483,0, 28,0, 28,0,
        28,0,28,0, 28,24, 28,24,
        28,24, 28,24, 81,24, 81,24,
        81,24, 109,24, 117,53, 117,76,
        117,76, 117,76, 117,600, 117,600,
        117,600, 117,618, 99,637, 81,637,
        81,637, 81,637, 28,637, 28,637,
        28,637, 28,637, 28,661, 28,661,
        28,661, 28,661, 259,661, 259,661,
        259,661, 259,661, 259,637, 259,637,
        259,637, 259,637, 206,637, 206,637,
        206,637, 187,637, 172,618, 172,600,
        172,600, 172,600, 172,73, 172,73,
        172,73, 172,50, 184,23, 210,23,
        210,23, 210,23, 330,23, 330,23,
        330,23, 416,23, 495,99, 518,179,
        518,179, 518,179, 533,179, 533,179,
        ]),(-1,4,2))

        print &quot;%!&quot;
        print &quot;20 200 translate&quot;
        print &quot;.8 .8 scale&quot;
        print &quot;%d %d moveto&quot; % tuple(cs[0][0])

        for (x,y) in [cubicspline(c,16*t) for c in cs for t in arange(17)]:
                print x,y,&quot;lineto&quot;

        print &quot;stroke showpage&quot;
&lt;/codeblock&gt;
which, when run, yields the following output:

[[Image:Cubic_spline_sample_output.png]]

[[Category:Programming language:Python]]
[[Category:Numerical interpolation]]
[[Category:Typesetting]]</text>
    </revision>
  </page>
  <page>
    <title>Cuckoo Hashing</title>
    <id>3997</id>
    <revision>
      <id>17051</id>
      <timestamp>2011-02-10T12:24:19Z</timestamp>
      <contributor>
        <username>Bogwonch</username>
        <id>2211</id>
      </contributor>
      <comment>Cuckoo Hashing</comment>
      <text xml:space="preserve">= Cuckoo Hashing =

Cuckoo hashing is a great way of making a hash table without resorting to chaining to resolve collisions. The basic idea is to use two or more hash functions for every key. This means that for every thing in the table there are two or more places in the table it could be.

Given here is a simple implementation of Cuckoo hashing using the Haskell programming language.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
module Main where
import Data.Array
import Data.List
import System.Random
&lt;/codeblock&gt;
== Types, Eggs and Tables ==

Every thing in our hash table will store a value and a list of hash-functions used to place it in the table. For simplicity we're only going to insert whole numbers into the hash table. We'll call these things eggs.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type Value        = Int
type Index        = Int
type HashFunction = (Value -&gt; Index)
type Egg          = (Value, [HashFunction])
&lt;/codeblock&gt;
The Cuckoo hashtable will store a lot of these eggs. We'll use an array to make the table and we'll say that every location may (or may not) contain an egg.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type CuckooTable = Array Index (Maybe Egg)
&lt;/codeblock&gt;
To make our empty table we make a big array which contains Nothing.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
createCuckooTable :: Int -&gt; CuckooTable
createCuckooTable i = listArray (1, i) $ repeat Nothing
&lt;/codeblock&gt;
To make an egg we take a value and a list of hash functions. We repeat the hash functions in an endless cycle so we know the order to use them in.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
createEgg :: Value -&gt; [HashFunction] -&gt; Egg 
createEgg v hs = (v, cycle hs)
&lt;/codeblock&gt;
== Adding Eggs ==

When we insert an egg into our table we'll take the first hash function from the list inside the egg, and use it to find the place the egg belongs.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
value :: Egg -&gt; Value
value = fst

hashEgg :: Egg -&gt; (Index, Egg)
hashEgg egg@(v, h:hs) = (h v, (v,hs))
&lt;/codeblock&gt;
If the place the egg should go is empty then we'll place the egg there. If it isn't empty then we'll kick-out the egg currently in its place and place the new-egg there instead. We'll try and place the kicked-out egg using its next hash function and repeat this until either we find an empty slot, or we reach a limit on the number of kick-outs we allow ourselves to do.

If we go over the number of kick-outs we are allowed we will have an error.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type Error = String

addEgg :: CuckooTable -&gt; Egg -&gt; Either Error CuckooTable
addEgg = addEgg' kickOutsAllowed
&lt;/codeblock&gt;
We will make the kick-outs allowed a fixed number to make it simpler.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
  where
    kickOutsAllowed = 20
&lt;/codeblock&gt;
&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=

addEgg' :: Int -&gt; CuckooTable -&gt; Egg -&gt; Either Error CuckooTable
addEgg' 0 _ _              = Left &amp;quot;We have kicked-out too many eggs&amp;quot;
addEgg' kickouts table egg = let (index, egg') = hashEgg egg
                                 place         = table ! index
                              in case place of
&lt;/codeblock&gt;
In the case the place is empty we'll just put the egg there.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                Nothing       -&gt; Right $ table // [(index, Just egg')]
&lt;/codeblock&gt;
If there is another egg there and it has the same value as the egg we are trying to insert we can ignore it.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                Just otherEgg -&gt; if value egg == value otherEgg 
                                                 then Right table
&lt;/codeblock&gt;
If it isn't the same egg then we kick-out the other egg, and put our new egg in its place. We can try and add the other egg again, if our kickout limit isn't too low.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                                 else 
                                                   let table' = table // [(index, Just egg')]
                                                   in addEgg' (kickouts-1) table' otherEgg
&lt;/codeblock&gt;
== Testing the Table ==

To show how well the Cuckoo hashtable works we will try add random numbers to the table and how many eggs we can add before we get hit our kick-out limit.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
testTilFailure :: [Egg] -&gt; CuckooTable -&gt; Integer -&gt; Integer
testTilFailure (e:es) t n = 
  case (addEgg t e) of
    Left  err -&gt; n
    Right t'  -&gt; testTilFailure es t' (1+n)

testCuckooTable :: (RandomGen g) =&gt; [HashFunction] -&gt; g -&gt; Integer
testCuckooTable hashes gen =
  let eggs = map (flip createEgg $ hashes) $ randoms gen
  in testTilFailure eggs (createCuckooTable tableSize) 0
&lt;/codeblock&gt;
To test the table we'll use a size of 8243: a prime number. We'll also make three hash functions for the testing.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
tableSize = 8243

hash1 :: HashFunction
hash1 x = 1+ ((58193 + 1258207*y + 2808193*y^2)`mod` 308383) `mod` tableSize
  where y = abs x

hash2 :: HashFunction
hash2 x = 1+ ((711929 + 1810057*y + 9767*y^2)  `mod` 608459) `mod` tableSize
  where y = abs x

hash3 :: HashFunction
hash3 x = 1+ ((459257 + 808481*y + 2958259*y^2)`mod` 1358333) `mod` tableSize
  where y = abs x
&lt;/codeblock&gt;
We can run our tests like this. We'll repeat them a million times and take the average so we get good data.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
testNumber = 1000000

average :: [Integer] -&gt; Integer
average ns = sum `div` length
  where
    sum    = foldl1' (+) ns
    length = foldl' (\n _ -&gt; 1+n) 0 ns 

main :: IO()
main = do
  gen &amp;lt;- newStdGen
  let test = replicate testNumber $ testCuckooTable [hash1,hash2,hash3] gen

  print $ average test
&lt;/codeblock&gt;
== Results ==

* Using three hash functions: 6076 insertions.
* Using two hash functions: 3993 insertions.
* Using one hash function: 95 insertions.</text>
    </revision>
    <revision>
      <id>17052</id>
      <timestamp>2011-02-10T12:28:43Z</timestamp>
      <contributor>
        <username>Bogwonch</username>
        <id>2211</id>
      </contributor>
      <minor/>
      <comment>Fixed quotes</comment>
      <text xml:space="preserve">= Cuckoo Hashing =

Cuckoo hashing is a great way of making a hash table without resorting to chaining to resolve collisions. The basic idea is to use two or more hash functions for every key. This means that for every thing in the table there are two or more places in the table it could be.

Given here is a simple implementation of Cuckoo hashing using the Haskell programming language.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
module Main where
import Data.Array
import Data.List
import System.Random
&lt;/codeblock&gt;
== Types, Eggs and Tables ==

Every thing in our hash table will store a value and a list of hash-functions used to place it in the table. For simplicity we're only going to insert whole numbers into the hash table. We'll call these things eggs.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type Value        = Int
type Index        = Int
type HashFunction = (Value -&gt; Index)
type Egg          = (Value, [HashFunction])
&lt;/codeblock&gt;
The Cuckoo hashtable will store a lot of these eggs. We'll use an array to make the table and we'll say that every location may (or may not) contain an egg.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type CuckooTable = Array Index (Maybe Egg)
&lt;/codeblock&gt;
To make our empty table we make a big array which contains Nothing.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
createCuckooTable :: Int -&gt; CuckooTable
createCuckooTable i = listArray (1, i) $ repeat Nothing
&lt;/codeblock&gt;
To make an egg we take a value and a list of hash functions. We repeat the hash functions in an endless cycle so we know the order to use them in.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
createEgg :: Value -&gt; [HashFunction] -&gt; Egg 
createEgg v hs = (v, cycle hs)
&lt;/codeblock&gt;
== Adding Eggs ==

When we insert an egg into our table we'll take the first hash function from the list inside the egg, and use it to find the place the egg belongs.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
value :: Egg -&gt; Value
value = fst

hashEgg :: Egg -&gt; (Index, Egg)
hashEgg egg@(v, h:hs) = (h v, (v,hs))
&lt;/codeblock&gt;
If the place the egg should go is empty then we'll place the egg there. If it isn't empty then we'll kick-out the egg currently in its place and place the new-egg there instead. We'll try and place the kicked-out egg using its next hash function and repeat this until either we find an empty slot, or we reach a limit on the number of kick-outs we allow ourselves to do.

If we go over the number of kick-outs we are allowed we will have an error.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
type Error = String

addEgg :: CuckooTable -&gt; Egg -&gt; Either Error CuckooTable
addEgg = addEgg' kickOutsAllowed
&lt;/codeblock&gt;
We will make the kick-outs allowed a fixed number to make it simpler.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
  where
    kickOutsAllowed = 20
&lt;/codeblock&gt;
&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=

addEgg' :: Int -&gt; CuckooTable -&gt; Egg -&gt; Either Error CuckooTable
addEgg' 0 _ _              = Left &quot;We have kicked-out too many eggs&quot;
addEgg' kickouts table egg = let (index, egg') = hashEgg egg
                                 place         = table ! index
                              in case place of
&lt;/codeblock&gt;
In the case the place is empty we'll just put the egg there.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                Nothing       -&gt; Right $ table // [(index, Just egg')]
&lt;/codeblock&gt;
If there is another egg there and it has the same value as the egg we are trying to insert we can ignore it.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                Just otherEgg -&gt; if value egg == value otherEgg 
                                                 then Right table
&lt;/codeblock&gt;
If it isn't the same egg then we kick-out the other egg, and put our new egg in its place. We can try and add the other egg again, if our kickout limit isn't too low.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
                                                 else 
                                                   let table' = table // [(index, Just egg')]
                                                   in addEgg' (kickouts-1) table' otherEgg
&lt;/codeblock&gt;
== Testing the Table ==

To show how well the Cuckoo hashtable works we will try add random numbers to the table and how many eggs we can add before we get hit our kick-out limit.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
testTilFailure :: [Egg] -&gt; CuckooTable -&gt; Integer -&gt; Integer
testTilFailure (e:es) t n = 
  case (addEgg t e) of
    Left  err -&gt; n
    Right t'  -&gt; testTilFailure es t' (1+n)

testCuckooTable :: (RandomGen g) =&gt; [HashFunction] -&gt; g -&gt; Integer
testCuckooTable hashes gen =
  let eggs = map (flip createEgg $ hashes) $ randoms gen
  in testTilFailure eggs (createCuckooTable tableSize) 0
&lt;/codeblock&gt;
To test the table we'll use a size of 8243: a prime number. We'll also make three hash functions for the testing.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
tableSize = 8243

hash1 :: HashFunction
hash1 x = 1+ ((58193 + 1258207*y + 2808193*y^2)`mod` 308383) `mod` tableSize
  where y = abs x

hash2 :: HashFunction
hash2 x = 1+ ((711929 + 1810057*y + 9767*y^2)  `mod` 608459) `mod` tableSize
  where y = abs x

hash3 :: HashFunction
hash3 x = 1+ ((459257 + 808481*y + 2958259*y^2)`mod` 1358333) `mod` tableSize
  where y = abs x
&lt;/codeblock&gt;
We can run our tests like this. We'll repeat them a million times and take the average so we get good data.

&lt;codeblock language=haskell&gt;
&lt;&lt;CuckooHashing&gt;&gt;=
testNumber = 1000000

average :: [Integer] -&gt; Integer
average ns = sum `div` length
  where
    sum    = foldl1' (+) ns
    length = foldl' (\n _ -&gt; 1+n) 0 ns 

main :: IO()
main = do
  gen &lt;- newStdGen
  let test = replicate testNumber $ testCuckooTable [hash1,hash2,hash3] gen

  print $ average test
&lt;/codeblock&gt;
== Results ==

* Using three hash functions: 6076 insertions.
* Using two hash functions: 3993 insertions.
* Using one hash function: 95 insertions.</text>
    </revision>
  </page>
  <page>
    <title>Data Acquisition (Matlab)</title>
    <id>3802</id>
    <revision>
      <id>5376</id>
      <timestamp>2006-05-30T08:03:25Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuteurs
* Thomson Financial DataStream

Matlab have a built-in access (through toolboxes) for:
* Bloomberg
* Thomson Financial DataStream
* yahoo finance


[[Category:Programming language:Matlab]]</text>
    </revision>
    <revision>
      <id>5377</id>
      <timestamp>2006-05-30T08:05:30Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Financial Data Access */</comment>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuteurs
* Thomson Financial DataStream

Matlab have a built-in access (through toolboxes) for:
* [[Matlab Bloomberg data access|Bloomberg]]
* [[Matlab Thomson Financial DataStream data access|Thomson Financial DataStream]]
* [Matlab yahoo finance data access|yahoo finance]]


[[Category:Programming language:Matlab]]</text>
    </revision>
    <revision>
      <id>5378</id>
      <timestamp>2006-05-30T08:05:44Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <comment>/* Financial Data Access */</comment>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuteurs
* Thomson Financial DataStream

Matlab have a built-in access (through toolboxes) for:
* [[Matlab Bloomberg data access|Bloomberg]]
* [[Matlab Thomson Financial DataStream data access|Thomson Financial DataStream]]
* [[Matlab yahoo finance data access|yahoo finance]]


[[Category:Programming language:Matlab]]</text>
    </revision>
    <revision>
      <id>6446</id>
      <timestamp>2006-06-22T07:42:56Z</timestamp>
      <contributor>
        <ip>145.253.242.35</ip>
      </contributor>
      <comment>/* Financial Data Access */</comment>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuters
* Thomson Financial DataStream

Matlab have a built-in access (through toolboxes) for:
* [[Matlab Bloomberg data access|Bloomberg]]
* [[Matlab Thomson Financial DataStream data access|Thomson Financial DataStream]]
* [[Matlab yahoo finance data access|yahoo finance]]


[[Category:Programming language:Matlab]]</text>
    </revision>
    <revision>
      <id>7446</id>
      <timestamp>2006-08-21T16:48:57Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Category:Programming language:MATLAB]]</comment>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuters
* Thomson Financial DataStream

Matlab have a built-in access (through toolboxes) for:
* [[Matlab Bloomberg data access|Bloomberg]]
* [[Matlab Thomson Financial DataStream data access|Thomson Financial DataStream]]
* [[Matlab yahoo finance data access|yahoo finance]]


[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>7477</id>
      <timestamp>2006-08-26T02:47:58Z</timestamp>
      <contributor>
        <ip>141.158.5.202</ip>
      </contributor>
      <comment>/* Financial Data Access */</comment>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuters
* Thomson Financial DataStream

MATLAB has a built-in access (through toolboxes) for:
* [[MATLAB Bloomberg data access|Bloomberg]]
* [[MATLAB Thomson Financial DataStream data access|Thomson Financial DataStream]]
* [[MATLAB yahoo finance data access|yahoo finance]]


[[Category:Programming language:MATLAB]]</text>
    </revision>
    <revision>
      <id>7873</id>
      <timestamp>2006-10-27T15:46:20Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">Matlab allows to access to a lot of external data.

==Financial Data Access==

The main financial data providers are:
* Bloomberg
* Reuters
* Thomson Financial DataStream

MATLAB has a built-in access (through toolboxes) for:
* [[MATLAB Bloomberg data access|Bloomberg]]
* [[Thomson Financial DataStream data access (Matlab)|Thomson Financial DataStream]]
* [[MATLAB yahoo finance data access|yahoo finance]]


[[Category:Programming language:MATLAB]]</text>
    </revision>
  </page>
  <page>
    <title>Depth-first search (C Plus Plus)</title>
    <id>1903</id>
    <revision>
      <id>4191</id>
      <timestamp>2006-04-20T02:53:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Preliminary implementation, a bit of explanation, much to do</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack). Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=c&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex&lt;T&gt;
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; successors;
    bool visited;

public:
    vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
    T get_data() const { return data; }

    typedef std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
    successor_list_iterator successors_begin() const
        { return successors.begin(); }
    successor_list_iterator successors_end() const
        { return successors.end(); }

    bool is_visited() const { return visited; }
    void set_visited(const bool visited) { this-&gt;visited = visited; }
};
&lt;/codeblock&gt;

''TODO: add more explanation''

&lt;codeblock language=c&gt;
template &lt;typename T&gt;
bool depth_first_search(const vertex&lt;T&gt;&amp; start,
                        unary_function&lt; bool, vertex&lt;T&gt; &gt; is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    if (is_goal(start))
    {
        result.push_back(&amp;start);
        return true;
    }
    vertex&lt;T&gt;::successor_list_iterator iter = start.successors_begin();
    while (iter != start.successors_end())
    {
        result.push_back(&amp;start);
        if (depth_first_search(*iter, is_goal, result))
        {
            return true;
        }
        result.pop_back();
    }
    return false;
}
&lt;/codeblock&gt;

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4205</id>
      <timestamp>2006-04-20T23:11:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Expand explanation/rearrange implementation a bit</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack). Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex&lt;T&gt;
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search. The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
template &lt;typename T&gt;
bool depth_first_search(const vertex&lt;T&gt;&amp; start,
                        unary_function&lt; bool, vertex&lt;T&gt; &gt; is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(*iter, is_goal, result))
    {
        return true;
    }
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
if (std::find(result.begin(), result.end(), &amp;start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4212</id>
      <timestamp>2006-04-21T18:43:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Expand some more with sample code and some fixes</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex&lt;T&gt;
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T&gt;
bool depth_first_search(const vertex&lt;T&gt;&amp; start,
                        unary_function&lt; bool, vertex&lt;T&gt; &gt; is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(*iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(edges[i].target);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_value() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_value() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4213</id>
      <timestamp>2006-04-21T18:52:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Improvements and tradeoffs</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex&lt;T&gt;
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T&gt;
bool depth_first_search(const vertex&lt;T&gt;&amp; start,
                        unary_function&lt; bool, vertex&lt;T&gt; &gt; is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(*iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(edges[i].target);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_value() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_value() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a hash table. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantages that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4241</id>
      <timestamp>2006-04-22T02:00:20Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Compiler error fixes</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(const vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a hash table. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantages that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4242</id>
      <timestamp>2006-04-22T02:01:05Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Kill a const that's complicating things</comment>
      <text xml:space="preserve">{{develop}}

Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a hash table. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantages that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4261</id>
      <timestamp>2006-04-24T09:18:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Remove develop tag (it works); add output</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a hash table. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantages that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>4262</id>
      <timestamp>2006-04-24T09:19:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Improvements and tradeoffs */ Tweak</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==

This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a &lt;code&gt;std::set&lt;/code&gt;. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>6018</id>
      <timestamp>2006-06-08T08:11:00Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Sample code */ Add sample image of a Petersen graph</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a &lt;code&gt;std::set&lt;/code&gt;. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>6824</id>
      <timestamp>2006-07-11T12:47:31Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Depth-first search (C Plus Plus)]] moved to [[Depth-first search (C Plus Plus) on Wheels]]</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a &lt;code&gt;std::set&lt;/code&gt;. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>6984</id>
      <timestamp>2006-07-11T14:29:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Depth-first search (C Plus Plus) on Wheels]] moved to [[Depth-first search (C Plus Plus)]]: revert</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a &lt;code&gt;std::set&lt;/code&gt;. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>15777</id>
      <timestamp>2009-01-04T17:00:43Z</timestamp>
      <contributor>
        <ip>221.224.108.82</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

http://www.message_zelractr.com/</text>
    </revision>
    <revision>
      <id>15778</id>
      <timestamp>2009-01-04T17:49:14Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.224.108.82|221.224.108.82]] ([[User_talk:221.224.108.82|221.224.108.82]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like C++ because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, templating over the node data type and creating a &lt;code&gt;std::list&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;type definition headers&gt;&gt;=
#include &lt;list&gt;

&lt;&lt;vertex class&gt;&gt;=
template &lt;typename T&gt;
class vertex
{
private:
    T data;
    std::list&lt;vertex&lt;T&gt;*&gt; _successors;

public:
    &lt;&lt;vertex public methods&gt;&gt;
};
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
vertex&lt;T&gt;(const T data) { this-&gt;data = data; }
T get_data() const { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
typedef typename std::list&lt;vertex&lt;T&gt;*&gt;::const_iterator successor_list_iterator;
std::list&lt;vertex&lt;T&gt;*&gt;&amp; successors() { return _successors; }
&lt;/codeblock&gt;

We also include a typedef to briefen long iterator type names. Now we're prepared to write our depth-first search.

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result list, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
template &lt;typename T, typename GoalFunction&gt;
bool depth_first_search(vertex&lt;T&gt;&amp; start,
                        GoalFunction is_goal,
                        std::list&lt; vertex&lt;T&gt;* &gt;&amp; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push_back(&amp;start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop_back();
    return false; 
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
typename vertex&lt;T&gt;::successor_list_iterator iter = start.successors().begin();
while (iter != start.successors().end())
{
    if (depth_first_search(**iter, is_goal, result))
    {
        return true;
    }
    iter++;
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (is_goal(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (std::find(result.begin(), result.end(), &amp;start) != result.end())
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;&amp;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;sample header files&gt;&gt;=
#include &lt;vector&gt;
&lt;&lt;sample using statements&gt;&gt;=
using namespace std;
&lt;&lt;generate Petersen graph&gt;&gt;=
vector&lt; vertex&lt;int&gt; &gt; PetersenGraph()
{
    vector&lt; vertex&lt;int&gt; &gt; v;
    for(int i=0; i&lt;10; i++)
    {
        v.push_back(vertex&lt;int&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
struct { int source; int target; } edges[] =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (unsigned int i=0; i&lt;sizeof(edges)/sizeof(edges[0]); i++)
{
    v[edges[i].source].successors().push_back(&amp;v[edges[i].target]);
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dfs_sample.cpp&gt;&gt;=
#include &lt;iostream&gt;
&lt;&lt;sample header files&gt;&gt;
&lt;&lt;type definition headers&gt;&gt;

&lt;&lt;sample using statements&gt;&gt;

&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

bool is_goal(vertex&lt;int&gt; v)
{
    return v.get_data() == 7;
}

int main(void)
{
    vector&lt; vertex&lt;int&gt; &gt; v = PetersenGraph();
    list&lt; vertex&lt;int&gt;* &gt; path;
    if (depth_first_search(v[0], is_goal, path))
    {
        cout &lt;&lt; &quot;Found path: &quot;;
        list&lt; vertex&lt;int&gt;* &gt;::iterator iter = path.begin();
        while (iter != path.end())
        {
            cout &lt;&lt; (*iter)-&gt;get_data() &lt;&lt; &quot; &quot;;
            iter++;
        }
        cout &lt;&lt; endl;
    }
    else
    {
        cout &lt;&lt; &quot;No path found&quot; &lt;&lt; endl;
    }
    return 0;
}

&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far, such as a &lt;code&gt;std::set&lt;/code&gt;. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
  </page>
  <page>
    <title>Depth-first search (Java)</title>
    <id>3272</id>
    <revision>
      <id>11976</id>
      <timestamp>2008-01-09T06:11:58Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>copied from c++ section</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Java because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, genericizing over the node data type and creating a &lt;code&gt;List&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Stack;

&lt;&lt;vertex class&gt;&gt;=
public class Vertex&lt;T&gt;
{
    private final T data;
    private final List&lt;Vertex&lt;T&gt;&gt; _successors = new ArrayList&lt;Vertex&lt;T&gt;&gt;();

    &lt;&lt;vertex public methods&gt;&gt;

    &lt;&lt;depth first search&gt;&gt;

    &lt;&lt;generate Petersen graph&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
Vertex(T data) { this.data = data; }
T getData() { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
List&lt;Vertex&lt;T&gt;&gt; successors() { return _successors; }
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
public static boolean &lt;T&gt; depthFirstSearch(Vertex&lt;T&gt; start,
                                           GoalFunction&lt;T&gt; isGoal,
                                           Stack&lt;Vertex&lt;T&gt;&gt; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push(start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop();
    return false; 
}
&lt;/codeblock&gt;

We provide a functor interface for the goal predicate:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;goal functor interface&gt;&gt;=
interface GoalFunction&lt;T&gt;
{
    boolean evaluate(Vertex&lt;T&gt; o);
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for (Vertex&lt;T&gt; v : start.successors()) {
    if (depthFirstSearch(v, isGoal, result))
    {
        return true;
    }
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (isGoal.evaluate(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (result.contains(start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
public static List&lt;Vertex&lt;Integer&gt;&gt; petersenGraph()
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = new ArrayList&lt;Vertex&lt;Integer&gt;&gt;();
    for (int i = 0; i &lt; 10; i++)
    {
        v.add(new Vertex&lt;Integer&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
int[][] edges =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int[] e : edges)
{
    v.get(e[0]).successors().add(v.get(e[1]));
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = petersenGraph();
    Stack&lt;Vertex&lt;Integer&gt;&gt; path = new Stack&lt;Vertex&lt;Integer&gt;&gt;();
    if (depthFirstSearch(v.get(0), new GoalFunction&lt;Integer&gt;() {
        public boolean evaluate(Vertex&lt;Integer&gt; v)
        {
            return v.getData() == 7;
        }
    }, path))
    {
        System.out.print(&quot;Found path: &quot;);
        for (Vertex&lt;Integer&gt; u : path)
        {
            System.out.print(u.getData() + &quot; &quot;);
        }
        System.out.println();
    }
    else
    {
        System.out.println(&quot;No path found&quot;);
    }
}

&lt;&lt;dfs_sample.cpp&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;goal functor interface&gt;&gt;

&lt;&lt;vertex class&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11977</id>
      <timestamp>2008-01-09T06:12:38Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Java because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, genericizing over the node data type and creating a &lt;code&gt;List&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Stack;

&lt;&lt;vertex class&gt;&gt;=
public class Vertex&lt;T&gt;
{
    private final T data;
    private final List&lt;Vertex&lt;T&gt;&gt; _successors = new ArrayList&lt;Vertex&lt;T&gt;&gt;();

    &lt;&lt;vertex public methods&gt;&gt;

    &lt;&lt;depth first search&gt;&gt;

    &lt;&lt;generate Petersen graph&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
Vertex(T data) { this.data = data; }
T getData() { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
List&lt;Vertex&lt;T&gt;&gt; successors() { return _successors; }
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
public static boolean &lt;T&gt; depthFirstSearch(Vertex&lt;T&gt; start,
                                           GoalFunction&lt;T&gt; isGoal,
                                           Stack&lt;Vertex&lt;T&gt;&gt; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push(start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop();
    return false; 
}
&lt;/codeblock&gt;

We provide a functor interface for the goal predicate:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;goal functor interface&gt;&gt;=
interface GoalFunction&lt;T&gt;
{
    boolean evaluate(Vertex&lt;T&gt; o);
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for (Vertex&lt;T&gt; v : start.successors()) {
    if (depthFirstSearch(v, isGoal, result))
    {
        return true;
    }
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (isGoal.evaluate(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (result.contains(start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
public static List&lt;Vertex&lt;Integer&gt;&gt; petersenGraph()
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = new ArrayList&lt;Vertex&lt;Integer&gt;&gt;();
    for (int i = 0; i &lt; 10; i++)
    {
        v.add(new Vertex&lt;Integer&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
int[][] edges =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int[] e : edges)
{
    v.get(e[0]).successors().add(v.get(e[1]));
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = petersenGraph();
    Stack&lt;Vertex&lt;Integer&gt;&gt; path = new Stack&lt;Vertex&lt;Integer&gt;&gt;();
    if (depthFirstSearch(v.get(0), new GoalFunction&lt;Integer&gt;() {
        public boolean evaluate(Vertex&lt;Integer&gt; v)
        {
            return v.getData() == 7;
        }
    }, path))
    {
        System.out.print(&quot;Found path: &quot;);
        for (Vertex&lt;Integer&gt; u : path)
        {
            System.out.print(u.getData() + &quot; &quot;);
        }
        System.out.println();
    }
    else
    {
        System.out.println(&quot;No path found&quot;);
    }
}

&lt;&lt;Vertex.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;goal functor interface&gt;&gt;

&lt;&lt;vertex class&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11978</id>
      <timestamp>2008-01-09T06:13:44Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Java because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, genericizing over the node data type and creating a &lt;code&gt;List&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Stack;

&lt;&lt;vertex class&gt;&gt;=
public class Vertex&lt;T&gt;
{
    private final T data;
    private final List&lt;Vertex&lt;T&gt;&gt; _successors = new ArrayList&lt;Vertex&lt;T&gt;&gt;();

    &lt;&lt;vertex public methods&gt;&gt;

    &lt;&lt;depth first search&gt;&gt;

    &lt;&lt;generate Petersen graph&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
Vertex(T data) { this.data = data; }
T getData() { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
List&lt;Vertex&lt;T&gt;&gt; successors() { return _successors; }
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
public static &lt;T&gt; boolean depthFirstSearch(Vertex&lt;T&gt; start,
                                           GoalFunction&lt;T&gt; isGoal,
                                           Stack&lt;Vertex&lt;T&gt;&gt; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push(start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop();
    return false; 
}
&lt;/codeblock&gt;

We provide a functor interface for the goal predicate:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;goal functor interface&gt;&gt;=
interface GoalFunction&lt;T&gt;
{
    boolean evaluate(Vertex&lt;T&gt; o);
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for (Vertex&lt;T&gt; v : start.successors()) {
    if (depthFirstSearch(v, isGoal, result))
    {
        return true;
    }
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (isGoal.evaluate(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (result.contains(start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
public static List&lt;Vertex&lt;Integer&gt;&gt; petersenGraph()
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = new ArrayList&lt;Vertex&lt;Integer&gt;&gt;();
    for (int i = 0; i &lt; 10; i++)
    {
        v.add(new Vertex&lt;Integer&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
int[][] edges =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int[] e : edges)
{
    v.get(e[0]).successors().add(v.get(e[1]));
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = petersenGraph();
    Stack&lt;Vertex&lt;Integer&gt;&gt; path = new Stack&lt;Vertex&lt;Integer&gt;&gt;();
    if (depthFirstSearch(v.get(0), new GoalFunction&lt;Integer&gt;() {
        public boolean evaluate(Vertex&lt;Integer&gt; v)
        {
            return v.getData() == 7;
        }
    }, path))
    {
        System.out.print(&quot;Found path: &quot;);
        for (Vertex&lt;Integer&gt; u : path)
        {
            System.out.print(u.getData() + &quot; &quot;);
        }
        System.out.println();
    }
    else
    {
        System.out.println(&quot;No path found&quot;);
    }
}

&lt;&lt;Vertex.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;goal functor interface&gt;&gt;

&lt;&lt;vertex class&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search]]
[[Category:Environment:Portable]]
[[Category:Programming language:C Plus Plus]]</text>
    </revision>
    <revision>
      <id>11979</id>
      <timestamp>2008-01-09T06:17:50Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Java because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, genericizing over the node data type and creating a &lt;code&gt;List&lt;/code&gt; of successor vertices:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Stack;

&lt;&lt;vertex class&gt;&gt;=
public class Vertex&lt;T&gt;
{
    private final T data;
    private final List&lt;Vertex&lt;T&gt;&gt; _successors = new ArrayList&lt;Vertex&lt;T&gt;&gt;();

    &lt;&lt;vertex public methods&gt;&gt;

    &lt;&lt;depth first search&gt;&gt;

    &lt;&lt;generate Petersen graph&gt;&gt;

    &lt;&lt;main method&gt;&gt;
}
&lt;/codeblock&gt;

Each vertex is initialized with its vertex data or label, which we provide an accessor for:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
Vertex(T data) { this.data = data; }
T getData() { return data; }
&lt;/codeblock&gt;

For this simple example, we provide direct access to the successors list, although this violates encapsulation:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;vertex public methods&gt;&gt;=
List&lt;Vertex&lt;T&gt;&gt; successors() { return _successors; }
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
public static &lt;T&gt; boolean depthFirstSearch(Vertex&lt;T&gt; start,
                                           GoalFunction&lt;T&gt; isGoal,
                                           Stack&lt;Vertex&lt;T&gt;&gt; result)
{
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.push(start);

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    // No path was found
    result.pop();
    return false; 
}
&lt;/codeblock&gt;

We provide a functor interface for the goal predicate:
&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;goal functor interface&gt;&gt;=
interface GoalFunction&lt;T&gt;
{
    boolean evaluate(Vertex&lt;T&gt; o);
}
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return true:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for (Vertex&lt;T&gt; v : start.successors()) {
    if (depthFirstSearch(v, isGoal, result))
    {
        return true;
    }
}
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return true immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if (isGoal.evaluate(start))
{
    return true;
}
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return false immediately if we've followed a cycle:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if (result.contains(start))
{
    return false;
}
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
public static List&lt;Vertex&lt;Integer&gt;&gt; petersenGraph()
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = new ArrayList&lt;Vertex&lt;Integer&gt;&gt;();
    for (int i = 0; i &lt; 10; i++)
    {
        v.add(new Vertex&lt;Integer&gt;(i));
    }
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v;
}
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
int[][] edges =
    {{0,1}, {1,0}, {1,2}, {2,1}, {2,3}, {3,2}, {3,4}, {4,3}, {4,0}, {0,4},
     {5,6}, {6,5}, {6,7}, {7,6}, {7,8}, {8,7}, {8,9}, {9,8}, {9,5}, {5,9},
     {5,0}, {0,5}, {6,2}, {2,6}, {7,4}, {4,7}, {8,1}, {1,8}, {9,3}, {3,9}};
for (int[] e : edges)
{
    v.get(e[0]).successors().add(v.get(e[1]));
}
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;main method&gt;&gt;=
public static void main(String[] args)
{
    List&lt;Vertex&lt;Integer&gt;&gt; v = petersenGraph();
    Stack&lt;Vertex&lt;Integer&gt;&gt; path = new Stack&lt;Vertex&lt;Integer&gt;&gt;();
    if (depthFirstSearch(v.get(0), new GoalFunction&lt;Integer&gt;() {
        public boolean evaluate(Vertex&lt;Integer&gt; v)
        {
            return v.getData() == 7;
        }
    }, path))
    {
        System.out.print(&quot;Found path: &quot;);
        for (Vertex&lt;Integer&gt; u : path)
        {
            System.out.print(u.getData() + &quot; &quot;);
        }
        System.out.println();
    }
    else
    {
        System.out.println(&quot;No path found&quot;);
    }
}

&lt;&lt;Vertex.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;goal functor interface&gt;&gt;

&lt;&lt;vertex class&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Java]]
[[Category:Environment:Portable]]
[[Category:Programming language:Java]]</text>
    </revision>
  </page>
  <page>
    <title>Depth-first search (Python)</title>
    <id>3537</id>
    <revision>
      <id>14293</id>
      <timestamp>2008-08-15T20:06:21Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>from java</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []

    def __str__(self):
        return `data`
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop(0)
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges =
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ = &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, path
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>14294</id>
      <timestamp>2008-08-15T20:07:01Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Sample code */</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []

    def __str__(self):
        return `data`
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop(0)
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges = \
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ = &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, path
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>14295</id>
      <timestamp>2008-08-15T20:07:18Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Sample code */</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []

    def __str__(self):
        return `data`
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop(0)
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges = \
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, path
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>14296</id>
      <timestamp>2008-08-15T20:09:33Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop(0)
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges = \
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, [u.data for u in path]
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: 0 1 2 3 4 7
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>14297</id>
      <timestamp>2008-08-15T20:09:56Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop(0)
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges = \
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, [u.data for u in path]
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: [0, 1, 2, 3, 4, 7]
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>15001</id>
      <timestamp>2008-10-13T23:58:03Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Depth first search */</comment>
      <text xml:space="preserve">Depth-first search is simple to implement in a procedural language like Python because it always expands the node most recently seen, making it ideal to implement with a stack (such as the procedural call stack).

== Graph representation ==

Since we'll need to traverse through all the children of each node we visit, we choose an adjacency-list representation for the graph, creating a list of successor vertices. Each vertex is initialized with its vertex data or label.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;vertex class&gt;&gt;=
class Vertex:
    def __init__(self, data):
        self.data = data
        self.successors = []
&lt;/codeblock&gt;

== Depth first search ==

The search will take three parameters:
* A start node, indicating the first node to expand
* A goal predicate, which determines whether a given vertex is a goal vertex (a vertex on which the search stops successfully)
* A partial result stack, describing the path (sequence of vertices) that the search has followed so far

In outline, the search looks like this:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;depth first search&gt;&gt;=
def depthFirstSearch(start, isGoal, result):
    &lt;&lt;ensure we're not stuck in a cycle&gt;&gt;

    result.append(start)

    &lt;&lt;check if we've found the goal&gt;&gt;
    &lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;

    # No path was found
    result.pop()
    return False
&lt;/codeblock&gt;

To expand each child, we simply call depth first search recursively on each child in order. If any of them return true, the final path will be in &lt;code&gt;result&lt;/code&gt; and we also return True:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;expand each child node in order, returning if we find the goal&gt;&gt;=
for v in start.successors:
    if depthFirstSearch(v, isGoal, result):
        return True
&lt;/codeblock&gt;

As our terminating condition, we check if the start node is a goal vertex by applying the goal predicate to it. If so, we return True immediately and the result is propagated back up to the initial caller:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;check if we've found the goal&gt;&gt;=
if isGoal(start):
    return True
&lt;/codeblock&gt;

Finally, if the graph we're processing might contain directed cycles (it's not a directed acyclic graph), we need to ensure we don't get stuck in an infinite recursion following a cycle. To do this, we simply search the list of visited nodes in &lt;code&gt;result&lt;/code&gt; for the start node and return False immediately if we've followed a cycle:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ensure we're not stuck in a cycle&gt;&gt;=
if start in result:
    return False
&lt;/codeblock&gt;

It's important of course that this be done before appending &lt;code&gt;start&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;. This completes the implementation.

== Sample code ==
[[Image:Petersen.png|right|framed|Petersen graph]]
This small test driver demonstrates use of the search function on the [http://mathworld.wolfram.com/PetersenGraph.html Petersen graph], a small graph with 10 vertices and diameter 2. We'll see that the path found by depth-first search can be much longer than the minimum 2 vertices.

First we have the code that generates the graph as a simple vector of vertices, labelling the vertices with sequential integers:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;generate Petersen graph&gt;&gt;=
def petersenGraph():
    v = [Vertex(i) for i in xrange(10)]
    &lt;&lt;add Petersen graph edges&gt;&gt;
    return v
&lt;/codeblock&gt;

Now we add the edges. We simply create a table of the edges and iterate over it. Note that since our data structure describes directed graphs, we need an edge in each direction for each edge of the graph:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;add Petersen graph edges&gt;&gt;=
edges = \
    [(0,1), (1,0), (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,0), (0,4),
     (5,6), (6,5), (6,7), (7,6), (7,8), (8,7), (8,9), (9,8), (9,5), (5,9),
     (5,0), (0,5), (6,2), (2,6), (7,4), (4,7), (8,1), (1,8), (9,3), (3,9)]
for a, b in edges:
    v[a].successors.append(v[b])
&lt;/codeblock&gt;

Now we can complete our sample:

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;main method&gt;&gt;=
if __name__ == &quot;__main__&quot;:
    v = petersenGraph()
    path = []
    if depthFirstSearch(v[0], (lambda v: v.data == 7), path):
        print &quot;Found path:&quot;, [u.data for u in path]
    else:
        print &quot;No path found&quot;

&lt;&lt;vertex.py&gt;&gt;=
&lt;&lt;vertex class&gt;&gt;

&lt;&lt;depth first search&gt;&gt;

&lt;&lt;generate Petersen graph&gt;&gt;

&lt;&lt;main method&gt;&gt;
&lt;/codeblock&gt;

When run, this produces the following path:

&lt;pre&gt;
Found path: [0, 1, 2, 3, 4, 7]
&lt;/pre&gt;

This is far from the optimal path, which is &quot;0 4 7&quot;.

== Improvements and tradeoffs ==

On large graphs, the cycle-checking step can become expensive, because the result list may become very long. One solution is to also maintain a set data structure holding the nodes visited so far. Another more common solution is to give each node a visited flag, which has the advantage that no node is ever expanded twice, but has the disadvantage that we need to make an initial pass to clear the flag on every node of the graph. Visited flags also make it difficult to make the algorithm threadsafe.

Another issue on large graphs is that depth-first search can easily form a very long call chain following a useless path. It's useful to include a threshold on how deep we want to search. By searching with incrementally larger thresholds, we get iterative deepening depth-first search, which finds much shorter paths in general than ordinary depth-first search.

[[Category:Depth-first search|Python]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
  </page>
  <page>
    <title>Derivatives Pricing</title>
    <id>2161</id>
    <revision>
      <id>5101</id>
      <timestamp>2006-05-23T06:57:12Z</timestamp>
      <contributor>
        <username>Lehalle</username>
        <id>24</id>
      </contributor>
      <text xml:space="preserve">==Asian Options Pricing==

Here is the [[Asian Option Pricing (Matlab)|Matlab implementation]] of the pricing of Asian options from the paper '''Unified Asian Pricing''' by [http://www.stat.columbia.edu/~vecer/ Jan Vecer] (2002), Risk, Vol. 15, No. 6, 113-116 .</text>
    </revision>
  </page>
  <page>
    <title>Desk calculator (Python)</title>
    <id>3049</id>
    <revision>
      <id>9356</id>
      <timestamp>2007-03-07T03:49:36Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{codedump}}
An interpreter for a [[:Category:Programming language:dc|dc]] dialect,
written in Python.
It lies somewhere between
a [http://en.wikipedia.org/wiki/Dc_(Unix) modern dc implementation]
and the Bell Labs [http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps 1971 version].
It lacks support
for input and output radix conversion
and for floating point;
however, it can produce arbitrary binary output,
and has been confirmed to work
with the following [[LiteratePrograms:About|LiteratePrograms]] articles:

* [[Fibonacci numbers (dc)]]
* [[Generating all rationals (dc)]]
* [[Merge sort (dc)]]
* [[Quine (dc)]]

== theory ==

An interpeter is basically
a left fold over the source code,
taking an initial state
into the final state
by applying each command in turn.

As &lt;code&gt;dc&lt;/code&gt; programs are self-tokenizing
&amp;mdash; the source is already a byte-code &amp;mdash;
the interpeter itself is very simple.

The complications arise in
providing the semantics of
the two major &lt;code&gt;dc&lt;/code&gt; datatypes
* [[:Category:Arbitrary-precision integer arithmetic|arbitrary-precision integers]]
* macro text / string data

== practice ==
=== data structures ===
* '''s'''tack
* '''c'''ontinuation
* '''d'''ictionary
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;data structures&gt;&gt;=
#############################################

s,c,d = [],&quot;&quot;,{}

&lt;&lt;stack elements&gt;&gt;
&lt;&lt;continuation utilities&gt;&gt;
&lt;/codeblock&gt;

=== the inner loop ===

&lt;codeblock language=&quot;python&quot;&gt;
#############################################
&lt;&lt;interpreter&gt;&gt;=
&lt;&lt;auxiliary commands&gt;&gt;
cmd = {
&lt;&lt;command table&gt;&gt;
}
def interp(str):	
	cpush(str)
	while len(c):
		cmds[cpop()]()

&lt;/codeblock&gt;

=== printing (I) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'p':	lambda: debugpr(s[-1:]),
'f':	lambda: debugpr(s),
&lt;&lt;auxiliary commands&gt;&gt;=
def debugpr(s):
	for v in s:
		print v
&lt;/codeblock&gt;
=== arithmetic ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'+':	lambda: s.append(NVal(s.pop(-2) + s.pop())),
'-':	lambda: s.append(NVal(s.pop(-2) - s.pop())),
'*':	lambda: s.append(NVal(s.pop(-2) * s.pop())),
'/':	lambda: s.append(NVal(s.pop(-2) //s.pop())),
'%':	lambda: s.append(NVal(s.pop(-2) % s.pop())),
'^':	lambda: s.append(NVal(s.pop(-2) **s.pop())),
'~':	lambda: s.extend(map(NVal,divmod(s.pop(-2),s.pop()))),
&lt;/codeblock&gt;
=== stack operations ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'd':	lambda: s.append(s[-1]),
'c':	lambda: s.__setitem__(slice( 0,None),[]),
'r':	lambda: s.__setitem__(slice(-3,None),s[-1:-3:-1]),
&lt;/codeblock&gt;
=== printing (II) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'n':	lambda: write(&quot;%s&quot; % s.pop()),
'P':	lambda: s.pop().prval(),
'Z':	lambda: s.append(NVal(s.pop().sizeof())),
'z':	lambda: s.append(len(s)),
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;stack elements&gt;&gt;=
class SVal(str):
	def execute(self):	cpush(self + '\0')
	def sizeof(self):	len(self)
	def prval(self):	write(self)

class NVal(long):
	def execute(self):	s.append(self)
	def sizeof(self):
		if self==0:	return 1
		else:		return int(math.log10(self))+1
	def prval(self):
		q,str = self,&quot;&quot;	
		while q &gt; 0:
			q,r = divmod(q,0x100)
			str = chr(r) + str
		write(str)

&lt;/codeblock&gt;

=== execution control ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;continuation utilities&gt;&gt;=
def cpop():
	global c
	r,c=c[0],c[1:]
	return r
def cpush(b):
	global c
	c = b+c
def ctrim(upto):
	global c
	try:	c = c[c.index(upto)+1:]
	except:	sys.exit(0)
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'#':	lambda: ctrim('\n'),
'q':	lambda: (ctrim('\0'),ctrim('\0')),
&lt;/codeblock&gt;
=== registers ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'l':	lambda: s.append(d[cpop()]),
's':	lambda: d.update([(cpop(),s.pop())]),
&lt;/codeblock&gt;
=== conditional branches ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'&gt;':	lambda: compare('&gt;'),
'&lt;':	lambda: compare('&lt;'),
'=':	lambda: compare('='),
'!':	lambda: compare('!'+cpop()),
&lt;&lt;auxiliary commands&gt;&gt;=
def compare(how):
	cmpfunc = {
	'&gt;':	lambda a,b: b &gt; a,
	'!&gt;':	lambda a,b: b &lt;= a,
	'&lt;':	lambda a,b: b &lt; a,
	'!&lt;':	lambda a,b: b &gt;= a,
	'=':	lambda a,b: b == a,
	'!=':	lambda a,b: b != a
	}
	if cmpfunc[how](s.pop(-2),s.pop()):
		d[cpop()].execute()
	else:
		cpop()
&lt;/codeblock&gt;
=== other control flow ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'x':	lambda: s.pop().execute(),
'?':	lambda: cpush(sys.stdin.readline()),
&lt;/codeblock&gt;
=== literals ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'[':	dostr,
'_':	lambda: donum(-1,0),
'0':	lambda: donum( 1,0),
'1':	lambda: donum( 1,1),
'2':	lambda: donum( 1,2),
'3':	lambda: donum( 1,3),
'4':	lambda: donum( 1,4),
'5':	lambda: donum( 1,5),
'6':	lambda: donum( 1,6),
'7':	lambda: donum( 1,7),
'8':	lambda: donum( 1,8),
'9':	lambda: donum( 1,9),
&lt;&lt;auxiliary commands&gt;&gt;=
def donum(sign,acc):
	digits = &quot;0123456789&quot;
	while c[0] in digits:
		acc = 10*acc + digits.index(cpop())
	acc *= sign
	s.append(NVal(acc))

def dostr():
	nest,acc = 1,[]
	while nest:
		c = cpop()
		if   c == ']': nest-=1
		elif c == '[': nest+=1
		if not nest:	break
		acc.append(c)
	s.append(SVal(&quot;&quot;.join(acc)))
&lt;/codeblock&gt;
=== the remainder ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
' ':	nop,
'\t':	nop,
'\r':	nop,
'\n':	nop,
'\0':	nop
&lt;&lt;auxiliary commands&gt;&gt;=
def nop(): pass
&lt;/codeblock&gt;

== wrapping up ==

Finally, we wrap everything up in a module

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;dc.py&gt;&gt;=
#############################################
import sys, math
write=sys.stdout.write
&lt;&lt;data structures&gt;&gt;
&lt;&lt;interpreter&gt;&gt;
&lt;&lt;command line interface&gt;&gt;
&lt;/codeblock&gt;

and provide a command line interface
allowing for either interactive or file input.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command line interface&gt;&gt;=
#############################################

if __name__==&quot;__main__&quot;:
	arg = sys.argv[1:]
	if not len(arg):
		while True:
			interp(sys.stdin.readline())
	while len(arg):
		if arg[0] == '-e':
			str = arg[1]
			arg = arg[2:]
		elif arg[0] == '-f':
			arg = arg[1:]
			continue	
		else:
			f = open(arg[0],&quot;rb&quot;)
			str = f.read()
			f.close()
			arg = arg[1:]
		interp(str)

&lt;/codeblock&gt;

so, for example, one may say

 dc.py -e 6581840dnP

or, having visited [[Merge sort (dc)]],

 dc.py -f mergesort.dc

[[Category:Language:Python]]
[[Category:Domain-specific]]</text>
    </revision>
    <revision>
      <id>9357</id>
      <timestamp>2007-03-07T03:52:17Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* the inner loop */ typo</comment>
      <text xml:space="preserve">{{codedump}}
An interpreter for a [[:Category:Programming language:dc|dc]] dialect,
written in Python.
It lies somewhere between
a [http://en.wikipedia.org/wiki/Dc_(Unix) modern dc implementation]
and the Bell Labs [http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps 1971 version].
It lacks support
for input and output radix conversion
and for floating point;
however, it can produce arbitrary binary output,
and has been confirmed to work
with the following [[LiteratePrograms:About|LiteratePrograms]] articles:

* [[Fibonacci numbers (dc)]]
* [[Generating all rationals (dc)]]
* [[Merge sort (dc)]]
* [[Quine (dc)]]

== theory ==

An interpeter is basically
a left fold over the source code,
taking an initial state
into the final state
by applying each command in turn.

As &lt;code&gt;dc&lt;/code&gt; programs are self-tokenizing
&amp;mdash; the source is already a byte-code &amp;mdash;
the interpeter itself is very simple.

The complications arise in
providing the semantics of
the two major &lt;code&gt;dc&lt;/code&gt; datatypes
* [[:Category:Arbitrary-precision integer arithmetic|arbitrary-precision integers]]
* macro text / string data

== practice ==
=== data structures ===
* '''s'''tack
* '''c'''ontinuation
* '''d'''ictionary
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;data structures&gt;&gt;=
#############################################

s,c,d = [],&quot;&quot;,{}

&lt;&lt;stack elements&gt;&gt;
&lt;&lt;continuation utilities&gt;&gt;
&lt;/codeblock&gt;

=== the inner loop ===

&lt;codeblock language=&quot;python&quot;&gt;
#############################################
&lt;&lt;interpreter&gt;&gt;=
&lt;&lt;auxiliary commands&gt;&gt;
cmds = {
&lt;&lt;command table&gt;&gt;
}
def interp(str):	
	cpush(str)
	while len(c):
		cmds[cpop()]()

&lt;/codeblock&gt;

=== printing (I) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'p':	lambda: debugpr(s[-1:]),
'f':	lambda: debugpr(s),
&lt;&lt;auxiliary commands&gt;&gt;=
def debugpr(s):
	for v in s:
		print v
&lt;/codeblock&gt;
=== arithmetic ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'+':	lambda: s.append(NVal(s.pop(-2) + s.pop())),
'-':	lambda: s.append(NVal(s.pop(-2) - s.pop())),
'*':	lambda: s.append(NVal(s.pop(-2) * s.pop())),
'/':	lambda: s.append(NVal(s.pop(-2) //s.pop())),
'%':	lambda: s.append(NVal(s.pop(-2) % s.pop())),
'^':	lambda: s.append(NVal(s.pop(-2) **s.pop())),
'~':	lambda: s.extend(map(NVal,divmod(s.pop(-2),s.pop()))),
&lt;/codeblock&gt;
=== stack operations ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'd':	lambda: s.append(s[-1]),
'c':	lambda: s.__setitem__(slice( 0,None),[]),
'r':	lambda: s.__setitem__(slice(-3,None),s[-1:-3:-1]),
&lt;/codeblock&gt;
=== printing (II) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'n':	lambda: write(&quot;%s&quot; % s.pop()),
'P':	lambda: s.pop().prval(),
'Z':	lambda: s.append(NVal(s.pop().sizeof())),
'z':	lambda: s.append(len(s)),
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;stack elements&gt;&gt;=
class SVal(str):
	def execute(self):	cpush(self + '\0')
	def sizeof(self):	len(self)
	def prval(self):	write(self)

class NVal(long):
	def execute(self):	s.append(self)
	def sizeof(self):
		if self==0:	return 1
		else:		return int(math.log10(self))+1
	def prval(self):
		q,str = self,&quot;&quot;	
		while q &gt; 0:
			q,r = divmod(q,0x100)
			str = chr(r) + str
		write(str)

&lt;/codeblock&gt;

=== execution control ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;continuation utilities&gt;&gt;=
def cpop():
	global c
	r,c=c[0],c[1:]
	return r
def cpush(b):
	global c
	c = b+c
def ctrim(upto):
	global c
	try:	c = c[c.index(upto)+1:]
	except:	sys.exit(0)
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'#':	lambda: ctrim('\n'),
'q':	lambda: (ctrim('\0'),ctrim('\0')),
&lt;/codeblock&gt;
=== registers ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'l':	lambda: s.append(d[cpop()]),
's':	lambda: d.update([(cpop(),s.pop())]),
&lt;/codeblock&gt;
=== conditional branches ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'&gt;':	lambda: compare('&gt;'),
'&lt;':	lambda: compare('&lt;'),
'=':	lambda: compare('='),
'!':	lambda: compare('!'+cpop()),
&lt;&lt;auxiliary commands&gt;&gt;=
def compare(how):
	cmpfunc = {
	'&gt;':	lambda a,b: b &gt; a,
	'!&gt;':	lambda a,b: b &lt;= a,
	'&lt;':	lambda a,b: b &lt; a,
	'!&lt;':	lambda a,b: b &gt;= a,
	'=':	lambda a,b: b == a,
	'!=':	lambda a,b: b != a
	}
	if cmpfunc[how](s.pop(-2),s.pop()):
		d[cpop()].execute()
	else:
		cpop()
&lt;/codeblock&gt;
=== other control flow ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'x':	lambda: s.pop().execute(),
'?':	lambda: cpush(sys.stdin.readline()),
&lt;/codeblock&gt;
=== literals ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'[':	dostr,
'_':	lambda: donum(-1,0),
'0':	lambda: donum( 1,0),
'1':	lambda: donum( 1,1),
'2':	lambda: donum( 1,2),
'3':	lambda: donum( 1,3),
'4':	lambda: donum( 1,4),
'5':	lambda: donum( 1,5),
'6':	lambda: donum( 1,6),
'7':	lambda: donum( 1,7),
'8':	lambda: donum( 1,8),
'9':	lambda: donum( 1,9),
&lt;&lt;auxiliary commands&gt;&gt;=
def donum(sign,acc):
	digits = &quot;0123456789&quot;
	while c[0] in digits:
		acc = 10*acc + digits.index(cpop())
	acc *= sign
	s.append(NVal(acc))

def dostr():
	nest,acc = 1,[]
	while nest:
		c = cpop()
		if   c == ']': nest-=1
		elif c == '[': nest+=1
		if not nest:	break
		acc.append(c)
	s.append(SVal(&quot;&quot;.join(acc)))
&lt;/codeblock&gt;
=== the remainder ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
' ':	nop,
'\t':	nop,
'\r':	nop,
'\n':	nop,
'\0':	nop
&lt;&lt;auxiliary commands&gt;&gt;=
def nop(): pass
&lt;/codeblock&gt;

== wrapping up ==

Finally, we wrap everything up in a module

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;dc.py&gt;&gt;=
#############################################
import sys, math
write=sys.stdout.write
&lt;&lt;data structures&gt;&gt;
&lt;&lt;interpreter&gt;&gt;
&lt;&lt;command line interface&gt;&gt;
&lt;/codeblock&gt;

and provide a command line interface
allowing for either interactive or file input.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command line interface&gt;&gt;=
#############################################

if __name__==&quot;__main__&quot;:
	arg = sys.argv[1:]
	if not len(arg):
		while True:
			interp(sys.stdin.readline())
	while len(arg):
		if arg[0] == '-e':
			str = arg[1]
			arg = arg[2:]
		elif arg[0] == '-f':
			arg = arg[1:]
			continue	
		else:
			f = open(arg[0],&quot;rb&quot;)
			str = f.read()
			f.close()
			arg = arg[1:]
		interp(str)

&lt;/codeblock&gt;

so, for example, one may say

 dc.py -e 6581840dnP

or, having visited [[Merge sort (dc)]],

 dc.py -f mergesort.dc

[[Category:Language:Python]]
[[Category:Domain-specific]]</text>
    </revision>
    <revision>
      <id>9359</id>
      <timestamp>2007-03-07T03:59:53Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{codedump}}
An interpreter for a [[:Category:Programming language:dc|dc]] dialect,
written in Python.
It lies somewhere between
a [http://en.wikipedia.org/wiki/Dc_(Unix) modern dc implementation]
and the Bell Labs [http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps 1971 version].
It lacks support
for input and output radix conversion
and for floating point;
however, it can produce arbitrary binary output,
and has been confirmed to work
with the following [[LiteratePrograms:About|LiteratePrograms]] articles:

* [[Fibonacci numbers (dc)]]
* [[Generating all rationals (dc)]]
* [[Merge sort (dc)]]
* [[Quine (dc)]]

== theory ==

An interpeter is basically
a left fold over the source code,
taking an initial state
into the final state
by applying each command in turn.

As &lt;code&gt;dc&lt;/code&gt; programs are self-tokenizing
&amp;mdash; the source is already a byte-code &amp;mdash;
the interpeter itself is very simple.

The complications arise in
providing the semantics of
the two major &lt;code&gt;dc&lt;/code&gt; datatypes
* [[:Category:Arbitrary-precision integer arithmetic|arbitrary-precision integers]]
* macro text / string data

== practice ==
=== data structures ===
* '''s'''tack
* '''c'''ontinuation
* '''d'''ictionary
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;data structures&gt;&gt;=
#############################################

s,c,d = [],&quot;&quot;,{}

&lt;&lt;stack elements&gt;&gt;
&lt;&lt;continuation utilities&gt;&gt;
&lt;/codeblock&gt;

=== the inner loop ===

&lt;codeblock language=&quot;python&quot;&gt;
#############################################
&lt;&lt;interpreter&gt;&gt;=
&lt;&lt;auxiliary commands&gt;&gt;
cmds = {
&lt;&lt;command table&gt;&gt;
}
def interp(str):	
	cpush(str)
	while len(c):
		cmds[cpop()]()

&lt;/codeblock&gt;

=== printing (I) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'p':	lambda: debugpr(s[-1:]),
'f':	lambda: debugpr(s),
&lt;&lt;auxiliary commands&gt;&gt;=
def debugpr(s):
	for v in s:
		print v
&lt;/codeblock&gt;
=== arithmetic ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'+':	lambda: s.append(NVal(s.pop(-2) + s.pop())),
'-':	lambda: s.append(NVal(s.pop(-2) - s.pop())),
'*':	lambda: s.append(NVal(s.pop(-2) * s.pop())),
'/':	lambda: s.append(NVal(s.pop(-2) //s.pop())),
'%':	lambda: s.append(NVal(s.pop(-2) % s.pop())),
'^':	lambda: s.append(NVal(s.pop(-2) **s.pop())),
'~':	lambda: s.extend(map(NVal,divmod(s.pop(-2),s.pop()))),
&lt;/codeblock&gt;
=== stack operations ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'd':	lambda: s.append(s[-1]),
'c':	lambda: s.__setitem__(slice( 0,None),[]),
'r':	lambda: s.__setitem__(slice(-3,None),s[-1:-3:-1]),
&lt;/codeblock&gt;
=== printing (II) ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'n':	lambda: write(&quot;%s&quot; % s.pop()),
'P':	lambda: s.pop().prval(),
'Z':	lambda: s.append(NVal(s.pop().sizeof())),
'z':	lambda: s.append(len(s)),
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;stack elements&gt;&gt;=
class SVal(str):
	def execute(self):	cpush(self + '\0')
	def sizeof(self):	len(self)
	def prval(self):	write(self)

class NVal(long):
	def execute(self):	s.append(self)
	def sizeof(self):
		if self==0:	return 1
		else:		return int(math.log10(self))+1
	def prval(self):
		q,str = self,&quot;&quot;	
		while q &gt; 0:
			q,r = divmod(q,0x100)
			str = chr(r) + str
		write(str)

&lt;/codeblock&gt;

=== execution control ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;continuation utilities&gt;&gt;=
def cpop():
	global c
	r,c=c[0],c[1:]
	return r
def cpush(b):
	global c
	c = b+c
def ctrim(upto):
	global c
	try:	c = c[c.index(upto)+1:]
	except:	sys.exit(0)
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'#':	lambda: ctrim('\n'),
'q':	lambda: (ctrim('\0'),ctrim('\0')),
&lt;/codeblock&gt;
=== registers ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'l':	lambda: s.append(d[cpop()]),
's':	lambda: d.update([(cpop(),s.pop())]),
&lt;/codeblock&gt;
=== conditional branches ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'&gt;':	lambda: compare('&gt;'),
'&lt;':	lambda: compare('&lt;'),
'=':	lambda: compare('='),
'!':	lambda: compare('!'+cpop()),
&lt;&lt;auxiliary commands&gt;&gt;=
def compare(how):
	cmpfunc = {
	'&gt;':	lambda a,b: b &gt; a,
	'!&gt;':	lambda a,b: b &lt;= a,
	'&lt;':	lambda a,b: b &lt; a,
	'!&lt;':	lambda a,b: b &gt;= a,
	'=':	lambda a,b: b == a,
	'!=':	lambda a,b: b != a
	}
	if cmpfunc[how](s.pop(-2),s.pop()):
		d[cpop()].execute()
	else:
		cpop()
&lt;/codeblock&gt;
=== other control flow ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'x':	lambda: s.pop().execute(),
'?':	lambda: cpush(sys.stdin.readline()),
&lt;/codeblock&gt;
=== literals ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'[':	dostr,
'_':	lambda: donum(-1,0),
'0':	lambda: donum( 1,0),
'1':	lambda: donum( 1,1),
'2':	lambda: donum( 1,2),
'3':	lambda: donum( 1,3),
'4':	lambda: donum( 1,4),
'5':	lambda: donum( 1,5),
'6':	lambda: donum( 1,6),
'7':	lambda: donum( 1,7),
'8':	lambda: donum( 1,8),
'9':	lambda: donum( 1,9),
&lt;&lt;auxiliary commands&gt;&gt;=
def donum(sign,acc):
	digits = &quot;0123456789&quot;
	while c[0] in digits:
		acc = 10*acc + digits.index(cpop())
	acc *= sign
	s.append(NVal(acc))

def dostr():
	nest,acc = 1,[]
	while nest:
		c = cpop()
		if   c == ']': nest-=1
		elif c == '[': nest+=1
		if not nest:	break
		acc.append(c)
	s.append(SVal(&quot;&quot;.join(acc)))
&lt;/codeblock&gt;
=== the remainder ===
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
' ':	nop,
'\t':	nop,
'\r':	nop,
'\n':	nop,
'\0':	nop
&lt;&lt;auxiliary commands&gt;&gt;=
def nop(): pass
&lt;/codeblock&gt;

== wrapping up ==

Finally, we wrap everything up in a module

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;dc.py&gt;&gt;=
#############################################
import sys, math
write=sys.stdout.write
&lt;&lt;data structures&gt;&gt;
&lt;&lt;interpreter&gt;&gt;
&lt;&lt;command line interface&gt;&gt;
&lt;/codeblock&gt;

and provide a command line interface
allowing for either interactive or file input.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command line interface&gt;&gt;=
#############################################

if __name__==&quot;__main__&quot;:
	arg = sys.argv[1:]
	if not len(arg):
		while True:
			interp(sys.stdin.readline())
	while len(arg):
		if arg[0] == '-e':
			str = arg[1]
			arg = arg[2:]
		elif arg[0] == '-f':
			arg = arg[1:]
			continue	
		else:
			f = open(arg[0],&quot;rb&quot;)
			str = f.read()
			f.close()
			arg = arg[1:]
		interp(str)

&lt;/codeblock&gt;

so, for example, one may say

 dc.py -e 6581840dnP

or, having visited [[Merge sort (dc)]],

 dc.py -f mergesort.dc

[[Category:Programming language:Python]]
[[Category:Domain-specific]]</text>
    </revision>
    <revision>
      <id>9363</id>
      <timestamp>2007-03-07T10:57:03Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>literated, -codedump</comment>
      <text xml:space="preserve">An interpreter for a [[:Category:Programming language:dc|dc]] dialect,
written in Python.
It lies somewhere between
a [http://en.wikipedia.org/wiki/Dc_(Unix) modern dc implementation]
and the Bell Labs [http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps 1971 version].
It lacks support
for input and output radix conversion
and for floating point;
however, it can produce arbitrary binary output,
and has been confirmed to work
with the following [[LiteratePrograms:About|LiteratePrograms]] articles:

* [[Fibonacci numbers (dc)]]
* [[Generating all rationals (dc)]]
* [[Merge sort (dc)]]
* [[Quine (dc)]]

== theory ==

An interpeter is basically
a left fold over the source code,
taking an initial state
into the final state
by applying each command in turn.

As &lt;code&gt;dc&lt;/code&gt; programs are self-tokenizing
&amp;mdash; the source is already a byte-code &amp;mdash;
the interpeter itself is very simple.

The complications arise in
providing the semantics of
the two major &lt;code&gt;dc&lt;/code&gt; datatypes
* [[:Category:Arbitrary-precision integer arithmetic|arbitrary-precision integers]]
* macro text / string data

== practice ==
=== data structures ===
There are three data structures in the interpreter:
* a '''s'''tack &amp;mdash; to store already-evaluated values
* a '''c'''ontinuation &amp;mdash; to store yet-to-be-evaluated code
* a '''d'''ictionary &amp;mdash; to provide the abstract registers
The decisions to implement
the stack and dictionary
with a list and dict
are rather obvious.
As dc commands are (mostly) single bytes,
the continuation is a list of bytes,
for which we use a string.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;data structures&gt;&gt;=
#############################################

s,c,d = [],&quot;&quot;,{}

&lt;&lt;stack elements&gt;&gt;
&lt;&lt;continuation utilities&gt;&gt;
&lt;/codeblock&gt;

=== the inner loop ===
The interpreter itself is equally simple:
while there are source bytecodes left in the continuation,
we look up the corresponding commands,
and execute them.
&lt;codeblock language=&quot;python&quot;&gt;
#############################################
&lt;&lt;interpreter&gt;&gt;=
&lt;&lt;auxiliary commands&gt;&gt;
cmds = {
&lt;&lt;command table&gt;&gt;
}
def interp(str):	
	cpush(str)
	while len(c):
		cmds[cpop()]()

&lt;/codeblock&gt;

=== printing (I) ===
For example, the codes '''p''' and '''f'''
correspond to commands
to print the top of the stack
and the entire stack, respectively.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'p':	lambda: debugpr(s[-1:]),
'f':	lambda: debugpr(s),
&lt;&lt;auxiliary commands&gt;&gt;=
def debugpr(s):
	for v in s:
		print v
&lt;/codeblock&gt;
=== arithmetic ===
Arithmetic operations are a little more complicated.
To implement each operation in the target language,
we perform the corresponding operation in the host language,
along with some explicit bookkeeping:
stack manipulation and ensuring that the results
are injected into our '''N'''umeric '''Val'''ue objects.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'+':	lambda: s.append(NVal(s.pop(-2) + s.pop())),
'-':	lambda: s.append(NVal(s.pop(-2) - s.pop())),
'*':	lambda: s.append(NVal(s.pop(-2) * s.pop())),
'/':	lambda: s.append(NVal(s.pop(-2) //s.pop())),
'%':	lambda: s.append(NVal(s.pop(-2) % s.pop())),
'^':	lambda: s.append(NVal(s.pop(-2) **s.pop())),
'~':	lambda: s.extend(map(NVal,divmod(s.pop(-2),s.pop()))),
&lt;/codeblock&gt;
''Question: what should be done to make this code more robust to changes in execution order?''
=== stack operations ===
The stack operations would be relatively straightforward,
if it were not for the need to avoid statements
in lambda expressions.
'''c'''lear and '''r'''everse/swap would be clearer as statements:
 c &amp;rarr; s[:]=[]
 r &amp;rarr; s[-3:]=s[-1:-3:-1] 
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'd':	lambda: s.append(s[-1]),
'c':	lambda: s.__setitem__(slice( 0,None),[]),
'r':	lambda: s.__setitem__(slice(-3,None),s[-1:-3:-1]),
&lt;/codeblock&gt;
=== printing (II) ===
The command '''n''' to print a value,
as well as '''z''', to push the current size of the stack,
are straightforward.
'''P''', to print, and '''Z''',
to determine the length of a value,
have different behaviors
depending upon whether or not
the top of the stack is
a number or a string.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'n':	lambda: write(&quot;%s&quot; % s.pop()),
'P':	lambda: s.pop().prval(),
'Z':	lambda: s.append(NVal(s.pop().sizeof())),
'z':	lambda: s.append(len(s)),
&lt;/codeblock&gt;

We model this polymorphism
by providing two distinct classes
for stack values.

As long as we have the two classes,
we can do some partial evaluation:
as the result of adding a number
to the continuation
will simply be that it is shifted
to the stack,
we avoid the intermediate steps
and place it there to begin with.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;stack elements&gt;&gt;=
class SVal(str):
	def execute(self):	cpush(self + '\0')
	def sizeof(self):	len(self)
	def prval(self):	write(self)

class NVal(long):
	def execute(self):	s.append(self)
	def sizeof(self):
		if self==0:	return 1
		else:		return int(math.log10(self))+1
	def prval(self):
		q,str = self,&quot;&quot;	
		while q &gt; 0:
			q,r = divmod(q,0x100)
			str = chr(r) + str
		write(str)

&lt;/codeblock&gt;

''Question: why is our task made easier by using '''long''' integers in Python, rather than C '''long'''s?''

''Question: if we did not append the extra NULL byte when executing a string, this implemenation would be properly tail-recursive.  Why do we not do so?'''

=== execution control ===
Supra, we saw that executing a macro
was as simple as pushing it onto the continuation,
&quot;scheduling&quot; it for evaluation
by the interpreter.

&quot;Pushing&quot; a function onto the continuation
is implemented by prepending it to the string.

Likewise, '''pop'''ping off the code for a command
and '''trim'''ming a continuation
(to provide an early exit or to skip over comments)
are implemented with easy string manipulations.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;continuation utilities&gt;&gt;=
def cpop():
	global c
	r,c=c[0],c[1:]
	return r
def cpush(b):
	global c
	c = b+c
def ctrim(upto):
	global c
	try:	c = c[c.index(upto)+1:]
	except:	sys.exit(0)
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'#':	lambda: ctrim('\n'),
'q':	lambda: (ctrim('\0'),ctrim('\0')),
&lt;/codeblock&gt;

Note that we have used null bytes
to delimit levels of macro invocation
in the continuation.

''Question: how is the double exit behavior of '''q''' related to the end-entire-method behavior of '''^''' in Smalltalk?'' 

Unfortunately, to support this behavior,
we cannot delete the nesting information
to support tail-call optimization.

Still, each tail call only adds 1 byte,
so [[Generating all rationals (dc)]] runs,
if not to &lt;math&gt;\infty&lt;/math&gt;,
at least for much longer than it does
in the Unix implementation.

=== registers ===

Continuations were somewhat involved; the dictionary is trivial.
'''l'''oad and '''s'''tore
manipulate the interpreter '''d'''ict
in the manner than one expects.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'l':	lambda: s.append(d[cpop()]),
's':	lambda: d.update([(cpop(),s.pop())]),
&lt;/codeblock&gt;
=== conditional branches ===

Taken conditional branches
require that the macro be looked up
in the dictionary,
and its value executed.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'&gt;':	lambda: compare('&gt;'),
'&lt;':	lambda: compare('&lt;'),
'=':	lambda: compare('='),
'!':	lambda: compare('!'+cpop()),
&lt;&lt;auxiliary commands&gt;&gt;=
def compare(how):
	cmpfunc = {
	'&gt;':	lambda a,b: b &gt; a,
	'!&gt;':	lambda a,b: b &lt;= a,
	'&lt;':	lambda a,b: b &lt; a,
	'!&lt;':	lambda a,b: b &gt;= a,
	'=':	lambda a,b: b == a,
	'!=':	lambda a,b: b != a
	}
	if cmpfunc[how](s.pop(-2),s.pop()):
		d[cpop()].execute()
	else:
		cpop()
&lt;/codeblock&gt;
=== other control flow ===
In contrast, e'''x'''ecuting from the stack,
or using '''?''' to execute user input,
are both straightforward.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'x':	lambda: s.pop().execute(),
'?':	lambda: cpush(sys.stdin.readline()),
&lt;/codeblock&gt;
''Question: what are the advantages of evaluating user input?  the disadvantages?''
=== literals ===
Of course, in order to operate on values,
we must have some way to specify them
in the first place.

Here we process numeric and string literals.
One might wish to take advantage of library routines
to do the lexing and value conversion,
but perhaps the character-by-character implementation
here better demonstrates
that the two forms of literals
are their own little [[:Category:Domain-specific|domain specific languages]],
and so we interpret them with the same strategy
as the outer interpreter:
a left fold.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'[':	dostr,
'_':	lambda: donum(-1,0),
'0':	lambda: donum( 1,0),
'1':	lambda: donum( 1,1),
'2':	lambda: donum( 1,2),
'3':	lambda: donum( 1,3),
'4':	lambda: donum( 1,4),
'5':	lambda: donum( 1,5),
'6':	lambda: donum( 1,6),
'7':	lambda: donum( 1,7),
'8':	lambda: donum( 1,8),
'9':	lambda: donum( 1,9),
&lt;&lt;auxiliary commands&gt;&gt;=
def donum(sign,acc):
	digits = &quot;0123456789&quot;
	while c[0] in digits:
		acc = 10*acc + digits.index(cpop())
	acc *= sign
	s.append(NVal(acc))

def dostr():
	nest,acc = 1,[]
	while nest:
		c = cpop()
		if   c == ']': nest-=1
		elif c == '[': nest+=1
		if not nest:	break
		acc.append(c)
	s.append(SVal(&quot;&quot;.join(acc)))
&lt;/codeblock&gt;
''Question: in theory, is it valid to say that the semantics of an algebraic construct (such as a literal value or an entire program) are given by means of a function folding over its syntax?''
=== the remainder ===
All that remains is to declare whitespace
to code for the &quot;identity&quot; operation
&amp;mdash; ie, it does nothing.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
' ':	nop,
'\t':	nop,
'\r':	nop,
'\n':	nop,
'\0':	nop
&lt;&lt;auxiliary commands&gt;&gt;=
def nop(): pass
&lt;/codeblock&gt;
Strictly speaking, this is not necessary,
but giving the programmer the choice of format
allows &lt;code&gt;dc&lt;/code&gt; code to be (a little)
less opaque.

Compare &lt;code&gt;[sa d la + sr la lr p d ls &gt;m]&lt;/code&gt;
with &lt;code&gt;[sadla+srlalrpdls&gt;m]&lt;/code&gt; &amp;mdash;
in a way, free whitespace
is the poor man's semantic hilighting.
== wrapping up ==

Finally, we wrap everything up in a module

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;dc.py&gt;&gt;=
#############################################
import sys, math
write=sys.stdout.write
&lt;&lt;data structures&gt;&gt;
&lt;&lt;interpreter&gt;&gt;
&lt;&lt;command line interface&gt;&gt;
&lt;/codeblock&gt;

and provide a command line interface
allowing for either interactive or file input.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command line interface&gt;&gt;=
#############################################

if __name__==&quot;__main__&quot;:
	arg = sys.argv[1:]
	if not len(arg):
		while True:
			interp(sys.stdin.readline())
	while len(arg):
		if arg[0] == '-e':
			str = arg[1]
			arg = arg[2:]
		elif arg[0] == '-f':
			arg = arg[1:]
			continue	
		else:
			f = open(arg[0],&quot;rb&quot;)
			str = f.read()
			f.close()
			arg = arg[1:]
		interp(str)

&lt;/codeblock&gt;

so, for example, one may say

 dc.py -e 6581840dnP

or, having visited [[Merge sort (dc)]],

 dc.py -f mergesort.dc

[[Category:Programming language:Python]]
[[Category:Domain-specific]]</text>
    </revision>
    <revision>
      <id>16662</id>
      <timestamp>2010-03-02T10:19:50Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">An interpreter for a [[:Category:Programming language:dc|dc]] dialect,
written in Python.
It lies somewhere between
a [http://en.wikipedia.org/wiki/Dc_(Unix) modern dc implementation]
and the Bell Labs [http://cm.bell-labs.com/cm/cs/who/dmr/man12.ps 1971 version].
It lacks support
for input and output radix conversion
and for floating point;
however, it can produce arbitrary binary output,
and has been confirmed to work
with the following [[LiteratePrograms:About|LiteratePrograms]] articles:

* [[Fibonacci numbers (dc)]]
* [[Generating all rationals (dc)]]
* [[Merge sort (dc)]]
* [[Quine (dc)]]

== theory ==

An interpeter is basically
a left fold over the source code,
taking an initial state
into the final state
by applying each command in turn.

As &lt;code&gt;dc&lt;/code&gt; programs are self-tokenizing
&amp;mdash; the source is already a byte-code &amp;mdash;
the interpeter itself is very simple.

The complications arise in
providing the semantics of
the two major &lt;code&gt;dc&lt;/code&gt; datatypes
* [[:Category:Arbitrary-precision integer arithmetic|arbitrary-precision integers]]
* macro text / string data

== practice ==
=== data structures ===
There are three data structures in the interpreter:
* a '''s'''tack &amp;mdash; to store already-evaluated values
* a '''c'''ontinuation &amp;mdash; to store yet-to-be-evaluated code
* a '''d'''ictionary &amp;mdash; to provide the abstract registers
The decisions to implement
the stack and dictionary
with a list and dict
are rather obvious.
As dc commands are (mostly) single bytes,
the continuation is a list of bytes,
for which we use a string.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;data structures&gt;&gt;=
#############################################

s,c,d = [],&quot;&quot;,{}

&lt;&lt;stack elements&gt;&gt;
&lt;&lt;continuation utilities&gt;&gt;
&lt;/codeblock&gt;

=== the inner loop ===
The interpreter itself is equally simple:
while there are source bytecodes left in the continuation,
we look up the corresponding commands,
and execute them.
&lt;codeblock language=&quot;python&quot;&gt;
#############################################
&lt;&lt;interpreter&gt;&gt;=
&lt;&lt;auxiliary commands&gt;&gt;
cmds = {
&lt;&lt;command table&gt;&gt;
}
def interp(str):	
	cpush(str)
	while len(c):
		cmds[cpop()]()

&lt;/codeblock&gt;

=== printing (I) ===
For example, the codes '''p''' and '''f'''
correspond to commands
to print the top of the stack
and the entire stack, respectively.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'p':	lambda: debugpr(s[-1:]),
'f':	lambda: debugpr(s),
&lt;&lt;auxiliary commands&gt;&gt;=
def debugpr(s):
	for v in s:
		print v
&lt;/codeblock&gt;
=== arithmetic ===
Arithmetic operations are a little more complicated.
To implement each operation in the target language,
we perform the corresponding operation in the host language,
along with some explicit bookkeeping:
stack manipulation and ensuring that the results
are injected into our '''N'''umeric '''Val'''ue objects.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'+':	lambda: s.append(NVal(s.pop(-2) + s.pop())),
'-':	lambda: s.append(NVal(s.pop(-2) - s.pop())),
'*':	lambda: s.append(NVal(s.pop(-2) * s.pop())),
'/':	lambda: s.append(NVal(s.pop(-2) //s.pop())),
'%':	lambda: s.append(NVal(s.pop(-2) % s.pop())),
'^':	lambda: s.append(NVal(s.pop(-2) **s.pop())),
'~':	lambda: s.extend(map(NVal,divmod(s.pop(-2),s.pop()))),
&lt;/codeblock&gt;
''Question: what should be done to make this code more robust to changes in execution order?''
=== stack operations ===
The stack operations would be relatively straightforward,
if it were not for the need to avoid statements
in lambda expressions.
'''c'''lear and '''r'''everse/swap would be clearer as statements:
 c &amp;rarr; s[:]=[]
 r &amp;rarr; s[-3:]=s[-1:-3:-1] 
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'd':	lambda: s.append(s[-1]),
'c':	lambda: s.__setitem__(slice( 0,None),[]),
'r':	lambda: s.__setitem__(slice(-3,None),s[-1:-3:-1]),
&lt;/codeblock&gt;
=== printing (II) ===
The command '''n''' to print a value,
as well as '''z''', to push the current size of the stack,
are straightforward.
'''P''', to print, and '''Z''',
to determine the length of a value,
have different behaviors
depending upon whether or not
the top of the stack is
a number or a string.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'n':	lambda: write(&quot;%s&quot; % s.pop()),
'P':	lambda: s.pop().prval(),
'Z':	lambda: s.append(NVal(s.pop().sizeof())),
'z':	lambda: s.append(len(s)),
&lt;/codeblock&gt;

We model this polymorphism
by providing two distinct classes
for stack values.

As long as we have the two classes,
we can do some partial evaluation:
as the result of adding a number
to the continuation
will simply be that it is shifted
to the stack,
we avoid the intermediate steps
and place it there to begin with.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;stack elements&gt;&gt;=
class SVal(str):
	def execute(self):	cpush(self + '\0')
	def sizeof(self):	len(self)
	def prval(self):	write(self)

class NVal(long):
	def execute(self):	s.append(self)
	def sizeof(self):
		if self==0:	return 1
		else:		return int(math.log10(self))+1
	def prval(self):
		q,str = self,&quot;&quot;	
		while q &gt; 0:
			q,r = divmod(q,0x100)
			str = chr(r) + str
		write(str)

&lt;/codeblock&gt;

''Question: why is our task made easier by using '''long''' integers in Python, rather than C '''long'''s?''

''Question: if we did not append the extra NULL byte when executing a string, this implemenation would be properly tail-recursive.  Why do we not do so?'''

=== execution control ===
Supra, we saw that executing a macro
was as simple as pushing it onto the continuation,
&quot;scheduling&quot; it for evaluation
by the interpreter.

&quot;Pushing&quot; a function onto the continuation
is implemented by prepending it to the string.

Likewise, '''pop'''ping off the code for a command
and '''trim'''ming a continuation
(to provide an early exit or to skip over comments)
are implemented with easy string manipulations.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;continuation utilities&gt;&gt;=
def cpop():
	global c
	r,c=c[0],c[1:]
	return r
def cpush(b):
	global c
	c = b+c
def ctrim(upto):
	global c
	try:	c = c[c.index(upto)+1:]
	except:	sys.exit(0)
&lt;/codeblock&gt;

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'#':	lambda: ctrim('\n'),
'q':	lambda: (ctrim('\0'),ctrim('\0')),
&lt;/codeblock&gt;

Note that we have used null bytes
to delimit levels of macro invocation
in the continuation.

''Question: how is the double exit behavior of '''q''' related to the end-entire-method behavior of '''^''' in Smalltalk?'' 

Unfortunately, to support this behavior,
we cannot delete the nesting information
to support tail-call optimization.

Still, each tail call only adds 1 byte,
so [[Generating all rationals (dc)]] runs,
if not to &lt;math&gt;\infty&lt;/math&gt;,
at least for much longer than it does
in the Unix implementation.

=== registers ===

Continuations were somewhat involved; the dictionary is trivial.
'''l'''oad and '''s'''tore
manipulate the interpreter '''d'''ict
in the manner than one expects.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'l':	lambda: s.append(d[cpop()]),
's':	lambda: d.update([(cpop(),s.pop())]),
&lt;/codeblock&gt;
=== conditional branches ===

Taken conditional branches
require that the macro be looked up
in the dictionary,
and its value executed.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'&gt;':	lambda: compare('&gt;'),
'&lt;':	lambda: compare('&lt;'),
'=':	lambda: compare('='),
'!':	lambda: compare('!'+cpop()),
&lt;&lt;auxiliary commands&gt;&gt;=
def compare(how):
	cmpfunc = {
	'&gt;':	lambda a,b: b &gt; a,
	'!&gt;':	lambda a,b: b &lt;= a,
	'&lt;':	lambda a,b: b &lt; a,
	'!&lt;':	lambda a,b: b &gt;= a,
	'=':	lambda a,b: b == a,
	'!=':	lambda a,b: b != a
	}
	if cmpfunc[how](s.pop(-2),s.pop()):
		d[cpop()].execute()
	else:
		cpop()
&lt;/codeblock&gt;
=== other control flow ===
In contrast, e'''x'''ecuting from the stack,
or using '''?''' to execute user input,
are both straightforward.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'x':	lambda: s.pop().execute(),
'?':	lambda: cpush(sys.stdin.readline()),
&lt;/codeblock&gt;
''Question: what are the advantages of evaluating user input?  the disadvantages?''
=== literals ===
Of course, in order to operate on values,
we must have some way to specify them
in the first place.

Here we process numeric and string literals.
One might wish to take advantage of library routines
to do the lexing and value conversion,
but perhaps the character-by-character implementation
here better demonstrates
that the two forms of literals
are their own little [[:Category:Domain-specific|domain specific languages]],
and so we interpret them with the same strategy
as the outer interpreter:
a left fold.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
'[':	dostr,
'_':	lambda: donum(-1,0),
'0':	lambda: donum( 1,0),
'1':	lambda: donum( 1,1),
'2':	lambda: donum( 1,2),
'3':	lambda: donum( 1,3),
'4':	lambda: donum( 1,4),
'5':	lambda: donum( 1,5),
'6':	lambda: donum( 1,6),
'7':	lambda: donum( 1,7),
'8':	lambda: donum( 1,8),
'9':	lambda: donum( 1,9),
&lt;&lt;auxiliary commands&gt;&gt;=
def donum(sign,acc):
	while c[0].isdigit():
		acc = 10*acc + int(cpop())
	acc *= sign
	s.append(NVal(acc))

def dostr():
	nest,acc = 1,[]
	while nest:
		c = cpop()
		if   c == ']': nest-=1
		elif c == '[': nest+=1
		if not nest:	break
		acc.append(c)
	s.append(SVal(&quot;&quot;.join(acc)))
&lt;/codeblock&gt;
''Question: in theory, is it valid to say that the semantics of an algebraic construct (such as a literal value or an entire program) are given by means of a function folding over its syntax?''
=== the remainder ===
All that remains is to declare whitespace
to code for the &quot;identity&quot; operation
&amp;mdash; ie, it does nothing.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command table&gt;&gt;=
' ':	nop,
'\t':	nop,
'\r':	nop,
'\n':	nop,
'\0':	nop
&lt;&lt;auxiliary commands&gt;&gt;=
def nop(): pass
&lt;/codeblock&gt;
Strictly speaking, this is not necessary,
but giving the programmer the choice of format
allows &lt;code&gt;dc&lt;/code&gt; code to be (a little)
less opaque.

Compare &lt;code&gt;[sa d la + sr la lr p d ls &gt;m]&lt;/code&gt;
with &lt;code&gt;[sadla+srlalrpdls&gt;m]&lt;/code&gt; &amp;mdash;
in a way, free whitespace
is the poor man's semantic hilighting.
== wrapping up ==

Finally, we wrap everything up in a module

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;dc.py&gt;&gt;=
#############################################
import sys, math
write=sys.stdout.write
&lt;&lt;data structures&gt;&gt;
&lt;&lt;interpreter&gt;&gt;
&lt;&lt;command line interface&gt;&gt;
&lt;/codeblock&gt;

and provide a command line interface
allowing for either interactive or file input.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;command line interface&gt;&gt;=
#############################################

if __name__==&quot;__main__&quot;:
	arg = sys.argv[1:]
	if not len(arg):
		while True:
			interp(sys.stdin.readline())
	while len(arg):
		if arg[0] == '-e':
			str = arg[1]
			arg = arg[2:]
		elif arg[0] == '-f':
			arg = arg[1:]
			continue	
		else:
			f = open(arg[0],&quot;rb&quot;)
			str = f.read()
			f.close()
			arg = arg[1:]
		interp(str)

&lt;/codeblock&gt;

so, for example, one may say

 dc.py -e 6581840dnP

or, having visited [[Merge sort (dc)]],

 dc.py -f mergesort.dc

[[Category:Programming language:Python]]
[[Category:Domain-specific]]</text>
    </revision>
  </page>
  <page>
    <title>Diary (Java)</title>
    <id>3022</id>
    <revision>
      <id>9076</id>
      <timestamp>2007-02-14T15:29:10Z</timestamp>
      <contributor>
        <username>322398</username>
        <id>137</id>
      </contributor>
      <text xml:space="preserve">==Diary==

This program is a simulation of a diary system where users can enter personal entries about thier thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

1)Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.

2)Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.</text>
    </revision>
    <revision>
      <id>9077</id>
      <timestamp>2007-02-14T15:29:46Z</timestamp>
      <contributor>
        <username>322398</username>
        <id>137</id>
      </contributor>
      <comment>/* Diary */</comment>
      <text xml:space="preserve">==Diary==

This program is for my degree. Please do not edit.This program is a simulation of a diary system where users can enter personal entries about thier thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

1)Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.

2)Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.</text>
    </revision>
    <revision>
      <id>9083</id>
      <timestamp>2007-02-14T16:22:43Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added {{develop}} macro and category</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is for my degree. Please do not edit.This program is a simulation of a diary system where users can enter personal entries about thier thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

1)Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.

2)Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]</text>
    </revision>
    <revision>
      <id>9089</id>
      <timestamp>2007-02-14T18:20:12Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Added new category</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is for my degree. Please do not edit.This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

1)Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.

2)Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9090</id>
      <timestamp>2007-02-14T19:14:31Z</timestamp>
      <contributor>
        <username>Cpjobling</username>
        <id>60</id>
      </contributor>
      <minor/>
      <comment>Wikified ordered list</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is for my degree. Please do not edit.This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9094</id>
      <timestamp>2007-02-15T17:42:45Z</timestamp>
      <contributor>
        <ip>137.44.1.200</ip>
      </contributor>
      <comment>/* Diary */</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9280</id>
      <timestamp>2007-02-22T18:35:38Z</timestamp>
      <contributor>
        <ip>208.47.133.246</ip>
      </contributor>
      <comment>/* Adding Entries */</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

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==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9282</id>
      <timestamp>2007-02-22T18:52:16Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition.An import statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list, which is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; and is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows us to perform one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;. If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9402</id>
      <timestamp>2007-03-12T15:12:47Z</timestamp>
      <contributor>
        <ip>137.44.1.200</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9440</id>
      <timestamp>2007-03-14T10:47:53Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>[[Diary (java)]] moved to [[Diary (Java)]]: Corrected spelling of Java</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9627</id>
      <timestamp>2007-04-02T22:00:11Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9628</id>
      <timestamp>2007-04-02T22:07:10Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <comment>/* Diary */</comment>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.


&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleteing an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>9629</id>
      <timestamp>2007-04-02T22:10:16Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.


&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding Entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9630</id>
      <timestamp>2007-04-02T22:12:24Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.


&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding Entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9631</id>
      <timestamp>2007-04-02T22:13:28Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.


&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding Entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>9632</id>
      <timestamp>2007-04-02T22:15:02Z</timestamp>
      <contributor>
        <ip>212.159.26.198</ip>
      </contributor>
      <text xml:space="preserve">{{develop}}

==Diary==

This program is a simulation of a diary system where users can enter personal entries about their thoughts and events in a chronological order. Users can also check the number of entries in thier diary, list all entires in the diary and delete any unwanted entries from it. This program is a good program to learn java from as it introduces the idea of using data structures to store information.


&lt;codeblock language=java&gt;
&lt;&lt;Defining the Class&gt;&gt;=
import java.util.ArrayList;
public class Diary
{
    private ArrayList&lt;String&gt; entries;
    &lt;&lt;Class Body&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock&gt;
&lt;&lt;Class Body&gt;&gt;=
&lt;&lt;Constructor&gt;&gt;
&lt;&lt;Adding Entries&gt;&gt;
&lt;&lt;Returning number of entries&gt;&gt;
&lt;&lt;Deleting an entry&gt;&gt;
&lt;&lt;Listing all entries&gt;&gt;
&lt;/codeblock&gt;

Notice that there is an &lt;code&gt;import&lt;/code&gt; statement before the class definition. An &lt;code&gt;import&lt;/code&gt; statement must always come before a class definition. This import statement gives access to a library class, called &lt;code&gt;ArrayList&lt;/code&gt;, which is required as the class uses a data structure known as an array list. This is described below. After writing this important import statement we can use the &lt;code&gt;ArrayList&lt;/code&gt; class as if it were one of our own, calling and implementing the methods that belong to it.

It is sensible to call a class a name that indicates what it does or how it behaves. This class is caled &lt;code&gt;Diary&lt;/code&gt; as it is easy to identify what it does from its name.

The first line of code in the body is a definition of the &lt;code&gt;entries&lt;/code&gt; field. This field is an &lt;code&gt;ArrayList&lt;/code&gt;. An ArrayList is known as a collection, meaning it can store an arbitrary number of elements, with each element being another object. This is useful as we wish to store an arbitrary number of diary entries. Because its purpose is to store entries, it has been called &lt;code&gt;entries&lt;/code&gt;. Notice it is a &lt;code&gt;private ArrayList&lt;/code&gt;, which means it cant be seen or used by other classes. It is also important to notice the &lt;code&gt;&lt;String&gt;&lt;/code&gt;. Because &lt;code&gt;ArrayList&lt;/code&gt; is a collection we must define what type of element is to be stored in it, which is achieved by placing &lt;code&gt;&lt;String&gt;&lt;/code&gt; in the definition.

==Constructor==
&lt;codeblock language=java&gt;
&lt;&lt;Constructor&gt;&gt;=
public Diary()
    {
        entries = new ArrayList&lt;String&gt;();
    }
&lt;/codeblock&gt;
Constructors should have the same name as the class they belong too. In this case the constructor is called &lt;code&gt;Diary&lt;/code&gt;, like the class it belongs too. Notice that the constructor takes no parameters as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; are empty.

An object of type &lt;code&gt;ArrayList&lt;/code&gt; is created in the first line of the body of the constructor for the &lt;code&gt;Diary&lt;/code&gt; class. This is stored in the &lt;code&gt;entries&lt;/code&gt; field. Notice that there is a need to specify what type of data is going to be stored in the &lt;code&gt;ArrayList&lt;/code&gt; as the &lt;code&gt;&lt;String&gt;&lt;/code&gt; is present. This is followed by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, to signify that there are no parameters being passed.

Before describing the methods used in the &lt;code&gt;Diary&lt;/code&gt; class it is useful to understand the benefits of using an &lt;code&gt;ArrayList&lt;/code&gt; for this simulation.

1)It can increase its capacity as required. This is useful because the user doesnt know how many entries they will be entering.

2)It keeps its own private count of how many items it is storing. The reason why this is useful will become aparant when a method is described later on.

3)It maintains the order of entries you enter into it. This is useful because a user of a diary often likes to look back in a diary to see previous entries at a certain date, eg thier 18th birthday. 

==Adding Entries==
The main idea of a diary system is to add entries. The method described below performs this task.
&lt;codeblock&gt;
&lt;&lt;Adding Entries&gt;&gt;=
public void storeEntry(String entry)
    {
        entries.add(entry);
    }
&lt;/codeblock&gt;
Looking at the method signature &lt;code&gt;storeEntry&lt;/code&gt;, it is easy to see this method is going to add an entry to the diary and is of type &lt;code&gt;void&lt;/code&gt;, meaning it is not going to return any value to the user. It has a parameter&lt;code&gt;entry&lt;/code&gt;, which is of type &lt;code&gt;String&lt;/code&gt;, this is passed from the user and represents the entry they wish to add to the diary. 

The body uses the &lt;code&gt;add&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class to store the value of the &lt;code&gt;entry&lt;/code&gt; parameter in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Returning number of entries==
It may also be useful to find out how many entries the diary is holding, which is achieved by the following method.
&lt;codeblock&gt;
&lt;&lt;Returning number of entries&gt;&gt;=
public int numberOfEntries()
    {
        return entries.size();
    }
&lt;/codeblock&gt;
The method signature has a realistic name &lt;code&gt;numberOfEntries&lt;/code&gt; as it is going to tell the user how many entries are in the diary. The method is of type &lt;code&gt;int&lt;/code&gt;, this indicates that it is going to return an integer value to the user by the end of the method. It has no parameters passed to it, as the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt; )&lt;/code&gt; are empty.

The body of the method is very basic. It uses the &lt;code&gt;size&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; to return the number of entries in the &lt;code&gt;entries ArrayList&lt;/code&gt;.

==Deleting an entry==
There may come a time when the user wishes to delete an entry from the diary, the method below allows them to do this.
&lt;codeblock&gt;
&lt;&lt;Deleting an entry&gt;&gt;=
public void removeEntry(int entryNumber)
    {
        if(entryNumber &lt; 0) {
            // This is not a valid entry number, so do nothing.
        }
        else if(entryNumber &lt; numberOfEntries()) {
            // This is a valid entry number.
            entries.remove(entryNumber);
        }
        else {
            // This is not a valid entry number, so do nothing.
        }
    }
&lt;/codeblock&gt;
The method signature indicates what the method is going to perform as it is called &lt;code&gt;removeEntry&lt;/code&gt;.It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. There is a parameter passed to it, called &lt;code&gt;entryNumber&lt;/code&gt;, which is of type &lt;code&gt;int&lt;/code&gt;, or integer.

The first line of the method body is an &lt;code&gt;if&lt;/code&gt; statement. This allows execution of one of two actions depending on the result of a check. In this case the check is to see if &lt;code&gt;entryNumber&lt;/code&gt;, which is the a number passed into the method by the user, is less than zero. If the number is less than 0 the method does nothing. If the number is greater than zero, the next line is executed, which is another check in the form of an &lt;code&gt;else if&lt;/code&gt; statement.

This checks if the &lt;code&gt;entryNumber&lt;/code&gt; is less than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method. If &lt;code&gt;entryNumber&lt;/code&gt; is less than the result then the &lt;code&gt;remove&lt;/code&gt; method of the &lt;code&gt;ArrayList&lt;/code&gt; class is used to remove the entry corresponding to the &lt;code&gt;entryNumber&lt;/code&gt; variable from the &lt;code&gt;entries ArrayList&lt;/code&gt;.

If the &lt;code&gt;entryNumber&lt;/code&gt; value is greater than the value returned by the &lt;code&gt;numberOfEntries&lt;/code&gt; method, the following &lt;code&gt;else&lt;/code&gt; statement is executed, which does nothing, as the value input by the user is not valid.

It is important to understand how the process of deleting an entry from the diary affects the index values of other entries in the collection. If an item with a low index number is removed, all following items are moved along by one position to fill the gap. This means thier index numbers will be  decreased by 1.

==Listing all entries==
Because a user may delete entries from the diary over time the index numbers may change quite significantly. It may be useful for the user to be able to list all entries, along with thier corresponding index values so they can see an up to date picture of the whole diary. The following method achieves this.
&lt;codeblock&gt;
&lt;&lt;Listing all entries&gt;&gt;=
public void listEntries()
    {
        for(String entry : entries) {
            System.out.println(entry);
        }
    }
&lt;/codeblock&gt;
This method has a realistic name &lt;code&gt;listEntries&lt;/code&gt;, which indicates what it does. It is of type &lt;code&gt;void&lt;/code&gt;, so it wont return any value to the user. It also takes no parameters, which is evident by &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt; being empty.

The body is taken up by a &lt;code&gt;for&lt;/code&gt; loop. A problem faces the programmer when it comes to writing a method such as this because the user wants to list all the entries in a collection, but at the time of writing code the programmer doesnt know how long the collection is going to be. A &lt;code&gt;for&lt;/code&gt; loop solves this by allowing a set of actions to be performed repeatedly, but without writing the actions out for everytime they need to be performed.

A &lt;code&gt;for&lt;/code&gt; loop contains two parts:

# Header- &lt;code&gt;for(String entry : entries)&lt;/code&gt;. This is where the loop details are defined. The first piece of code in the &lt;code&gt;(&lt;/code&gt; and &lt;code&gt;)&lt;/code&gt;, &lt;code&gt;String entry&lt;/code&gt; is known as a loop variable. This is a local variable that will be used to hold the list elements(in this case diary entries). This must be of type &lt;code&gt;String&lt;/code&gt; because the collection that is being used is of type &lt;code&gt;String&lt;/code&gt;. A colon is then used, followed by &lt;code&gt;entries&lt;/code&gt;, which is the collection that is being used in the &lt;code&gt;Diary&lt;/code&gt; class. This code stores one element in the collection &lt;code&gt;entries&lt;/code&gt; into the local variable &lt;code&gt;entry&lt;/code&gt;, starting at index 0, and increasing by 1 everytime the body of the &lt;code&gt;for&lt;/code&gt; loop is executed.
# Body- &lt;code&gt;System.out.println(entry);&lt;/code&gt;. This statement prints the value of the local variable &lt;code&gt;entry&lt;/code&gt; to the user each time the loop is executed.

[[Category:Introductory Examples|Java]]
[[Category:Programming language:Java]]

&lt;codeblock language=java&gt;
&lt;&lt;diary.java&gt;&gt;=
&lt;&lt;Defining the Class&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
  </page>
  <page>
    <title>Diary (java)</title>
    <id>3064</id>
    <revision>
      <id>9441</id>
      <timestamp>2007-03-14T10:47:53Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>[[Diary (java)]] moved to [[Diary (Java)]]: Corrected spelling of Java</comment>
      <text xml:space="preserve">#REDIRECT [[Diary (Java)]]</text>
    </revision>
  </page>
  <page>
    <title>Dijkstra's algorithm (C Plus Plus)</title>
    <id>2260</id>
    <revision>
      <id>5797</id>
      <timestamp>2006-06-03T09:40:04Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, cats, some details, will do rest later</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* prev_map (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, edge_weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; prev_map)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex v, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting v
        for (std::list&lt;edge&gt;::iterator iter = adjacency_map[v].begin();
             iter != adjacency_map[v].end();
             iter++)
        {
            vertex_t u = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. Changing this might affect which vertex we choose to visit next. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d[u] + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

This just means that we check the path going through ''u'' to see if it's the best one we've found so far:

We also need to initialize the output parameters so that at first all min distances are positive infinity and all &lt;code&gt;prev_map&lt;/code&gt; values are -1:

TODO: some code



[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5812</id>
      <timestamp>2006-06-03T21:18:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Complete implementation, sample code, link to Boost in alternatives</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, edge_weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::multiset&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, edge_weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].insert(edge(1,  79.83));
adjacency_map[0].insert(edge(5,  81.15));
adjacency_map[1].insert(edge(0,  79.75));
adjacency_map[1].insert(edge(2,  39.42));
adjacency_map[1].insert(edge(3, 103.00));
adjacency_map[2].insert(edge(1,  38.65));
adjacency_map[3].insert(edge(1, 102.53));
adjacency_map[3].insert(edge(5,  61.44));
adjacency_map[3].insert(edge(6,  96.79));
adjacency_map[4].insert(edge(5, 133.04));
adjacency_map[5].insert(edge(0,  81.77));
adjacency_map[5].insert(edge(3,  62.05));
adjacency_map[5].insert(edge(4, 134.47));
adjacency_map[5].insert(edge(6,  91.63));
adjacency_map[6].insert(edge(3,  97.24));
adjacency_map[6].insert(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5814</id>
      <timestamp>2006-06-03T21:20:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Missing include, chunk</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, edge_weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::multiset&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, edge_weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].insert(edge(1,  79.83));
adjacency_map[0].insert(edge(5,  81.15));
adjacency_map[1].insert(edge(0,  79.75));
adjacency_map[1].insert(edge(2,  39.42));
adjacency_map[1].insert(edge(3, 103.00));
adjacency_map[2].insert(edge(1,  38.65));
adjacency_map[3].insert(edge(1, 102.53));
adjacency_map[3].insert(edge(5,  61.44));
adjacency_map[3].insert(edge(6,  96.79));
adjacency_map[4].insert(edge(5, 133.04));
adjacency_map[5].insert(edge(0,  81.77));
adjacency_map[5].insert(edge(3,  62.05));
adjacency_map[5].insert(edge(4, 134.47));
adjacency_map[5].insert(edge(6,  91.63));
adjacency_map[6].insert(edge(3,  97.24));
adjacency_map[6].insert(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5815</id>
      <timestamp>2006-06-03T21:22:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>More missing chunk</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::multiset&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].insert(edge(1,  79.83));
adjacency_map[0].insert(edge(5,  81.15));
adjacency_map[1].insert(edge(0,  79.75));
adjacency_map[1].insert(edge(2,  39.42));
adjacency_map[1].insert(edge(3, 103.00));
adjacency_map[2].insert(edge(1,  38.65));
adjacency_map[3].insert(edge(1, 102.53));
adjacency_map[3].insert(edge(5,  61.44));
adjacency_map[3].insert(edge(6,  96.79));
adjacency_map[4].insert(edge(5, 133.04));
adjacency_map[5].insert(edge(0,  81.77));
adjacency_map[5].insert(edge(3,  62.05));
adjacency_map[5].insert(edge(4, 134.47));
adjacency_map[5].insert(edge(6,  91.63));
adjacency_map[6].insert(edge(3,  97.24));
adjacency_map[6].insert(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5816</id>
      <timestamp>2006-06-03T21:23:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>multiset-&gt;set</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].insert(edge(1,  79.83));
adjacency_map[0].insert(edge(5,  81.15));
adjacency_map[1].insert(edge(0,  79.75));
adjacency_map[1].insert(edge(2,  39.42));
adjacency_map[1].insert(edge(3, 103.00));
adjacency_map[2].insert(edge(1,  38.65));
adjacency_map[3].insert(edge(1, 102.53));
adjacency_map[3].insert(edge(5,  61.44));
adjacency_map[3].insert(edge(6,  96.79));
adjacency_map[4].insert(edge(5, 133.04));
adjacency_map[5].insert(edge(0,  81.77));
adjacency_map[5].insert(edge(3,  62.05));
adjacency_map[5].insert(edge(4, 134.47));
adjacency_map[5].insert(edge(6,  91.63));
adjacency_map[6].insert(edge(3,  97.24));
adjacency_map[6].insert(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5817</id>
      <timestamp>2006-06-03T21:24:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Qualify pair first less</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].insert(edge(1,  79.83));
adjacency_map[0].insert(edge(5,  81.15));
adjacency_map[1].insert(edge(0,  79.75));
adjacency_map[1].insert(edge(2,  39.42));
adjacency_map[1].insert(edge(3, 103.00));
adjacency_map[2].insert(edge(1,  38.65));
adjacency_map[3].insert(edge(1, 102.53));
adjacency_map[3].insert(edge(5,  61.44));
adjacency_map[3].insert(edge(6,  96.79));
adjacency_map[4].insert(edge(5, 133.04));
adjacency_map[5].insert(edge(0,  81.77));
adjacency_map[5].insert(edge(3,  62.05));
adjacency_map[5].insert(edge(4, 134.47));
adjacency_map[5].insert(edge(6,  91.63));
adjacency_map[6].insert(edge(3,  97.24));
adjacency_map[6].insert(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5818</id>
      <timestamp>2006-06-03T21:25:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>insert-&gt;push_back</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_edge_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
bool pair_first_less(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
{
    return p1.first &lt; p2.first;
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance, v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.remove(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = *prev;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt;&amp; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5819</id>
      <timestamp>2006-06-03T21:38:22Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix compiler errors</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;, pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5820</id>
      <timestamp>2006-06-03T21:39:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Break long line</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = iter-&gt;target;
            weight_t weight = iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5821</id>
      <timestamp>2006-06-03T21:40:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>One last compiler error</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible) and all &lt;code&gt;previous&lt;/code&gt; values are -1. We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
    previous[v] = -1;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5822</id>
      <timestamp>2006-06-03T21:50:45Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Don't want to initialize prev</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5823</id>
      <timestamp>2006-06-03T21:54:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add target to path</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5824</id>
      <timestamp>2006-06-03T22:00:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Missing &amp;</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edges are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5825</id>
      <timestamp>2006-06-03T22:01:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Clarify</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the lists of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5826</id>
      <timestamp>2006-06-03T22:03:14Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Simple graph representation */ Typo</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from each all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5827</id>
      <timestamp>2006-06-03T22:04:19Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>/* Simple graph representation */ Typo</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;codeblock&gt;d(u) + w(u, v) &amp;le; d(v)&lt;/codeblock&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5828</id>
      <timestamp>2006-06-03T22:04:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Wrong tag</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge, &lt;math&gt;d(u) + w(u, v) \le d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5829</id>
      <timestamp>2006-06-03T22:06:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Clarify</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep tracking of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5830</id>
      <timestamp>2006-06-03T22:08:30Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Typo</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, which each pair contains a vertex ''v'' along with &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance components:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5831</id>
      <timestamp>2006-06-03T22:11:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Clarify</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5838</id>
      <timestamp>2006-06-04T02:43:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Section</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5841</id>
      <timestamp>2006-06-04T05:51:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, wrong cats</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2)
    {
        return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11411</id>
      <timestamp>2007-10-29T14:32:10Z</timestamp>
      <contributor>
        <ip>134.130.102.7</ip>
      </contributor>
      <comment>/* Main algorithm */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2) const 
    {
       if(p1.first == p2.first) {
          return p1.second &lt; p2.second;
       }
       return p1.first &lt; p2.first; //Otherwise the initial vertex_queue will have the size 2 { 0,source ; inf;n }
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11412</id>
      <timestamp>2007-10-29T14:50:40Z</timestamp>
      <contributor>
        <username>Lutz</username>
        <id>1525</id>
      </contributor>
      <comment>/* Main algorithm */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2) const 
    {
       if(p1.first == p2.first) {
          //Otherwise the initial vertex_queue will have the size 2 { 0,source ; inf;n }
          return p1.second &lt; p2.second;
       }
       return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) {
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13421</id>
      <timestamp>2008-05-20T19:43:34Z</timestamp>
      <contributor>
        <ip>149.173.6.25</ip>
      </contributor>
      <comment>missing closing bracket added</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2) const 
    {
       if(p1.first == p2.first) {
          //Otherwise the initial vertex_queue will have the size 2 { 0,source ; inf;n }
          return p1.second &lt; p2.second;
       }
       return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());
}

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13422</id>
      <timestamp>2008-05-20T19:56:40Z</timestamp>
      <contributor>
        <ip>149.173.6.25</ip>
      </contributor>
      <comment>Ooops, my bad, removing the bracket I added &lt;blush&gt;</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2) const 
    {
       if(p1.first == p2.first) {
          //Otherwise the initial vertex_queue will have the size 2 { 0,source ; inf;n }
          return p1.second &lt; p2.second;
       }
       return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());


&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17172</id>
      <timestamp>2011-06-17T05:12:23Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;limits&gt; // for numeric_limits
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, but the STL's basic priority queue does not allow decreasing of keys of elements in the queue, which we need. Instead, we will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. The set is ordered by the min_distance component:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;pair first less comparator&gt;&gt;=
template &lt;typename T1, typename T2&gt;
struct pair_first_less
{
    bool operator()(std::pair&lt;T1,T2&gt; p1, std::pair&lt;T1,T2&gt; p2) const 
    {
       if(p1.first == p2.first) {
          //Otherwise the initial vertex_queue will have the size 2 { 0,source ; inf;n }
          return p1.second &lt; p2.second;
       }
       return p1.first &lt; p2.first;
    }
};

&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt;,
          pair_first_less&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());


&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17173</id>
      <timestamp>2011-06-17T05:44:42Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;limits&gt; // for numeric_limits
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We could do this using a heap data structure, but later on we will also need to decrease the distance of particular vertices, which will involve re-ordering that vertex in the heap. However, finding a particular element in a heap is a linear-time operation. To avoid this, we instead use a self-balancing binary search tree, which will also allow us to find the vertex of minimum distance, as well as find any particular vertex, quickly. We will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. Fortunately, C++'s &lt;code&gt;std::pair&lt;/code&gt; class already implements an ordering, which orders lexicographically (by first element, then by second element), which will work fine for us, as long as we use the distance as the first element of the pair.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());


&lt;&lt;simple graph type definition headers&gt;&gt;=
#include &lt;set&gt;
#include &lt;utility&gt; // for pair
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;simple graph type definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;pair first less comparator&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17174</id>
      <timestamp>2011-06-17T05:46:22Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;&lt;definition headers&gt;&gt;=
#include &lt;limits&gt; // for numeric_limits
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We could do this using a heap data structure, but later on we will also need to decrease the distance of particular vertices, which will involve re-ordering that vertex in the heap. However, finding a particular element in a heap is a linear-time operation. To avoid this, we instead use a self-balancing binary search tree, which will also allow us to find the vertex of minimum distance, as well as find any particular vertex, quickly. We will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. Fortunately, C++'s &lt;code&gt;std::pair&lt;/code&gt; class already implements an ordering, which orders lexicographically (by first element, then by second element), which will work fine for us, as long as we use the distance as the first element of the pair.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());


&lt;&lt;definition headers&gt;&gt;=
#include &lt;set&gt;
#include &lt;utility&gt; // for pair
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::pair&lt;weight_t, vertex_t&gt;(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17175</id>
      <timestamp>2011-06-17T05:48:54Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}

== Simple graph representation ==

The data structures supplied by C++'s Standard Template Library facilitate a straightforward implementation of Dijkstra's algorithm. For simplicity, we start with a simple graph representation where the vertices are numbered by sequential integers (0, 1, 2, ...) and the edge weights are &lt;code&gt;double&lt;/code&gt;s. We define a &lt;code&gt;struct&lt;/code&gt; representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef int vertex_t;
typedef double weight_t;

struct edge {
    vertex_t target;
    weight_t weight;
    edge(vertex_t arg_target, weight_t arg_weight)
        : target(arg_target), weight(arg_weight) { }
};
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will find an adjacency list representation most convenient. We will represent this as an ''adjacency map'', a mapping from each vertex to the list of edges exiting that vertex, as defined by the following &lt;code&gt;typedef&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
typedef std::map&lt;vertex_t, std::list&lt;edge&gt; &gt; adjacency_map_t;

&lt;&lt;definition headers&gt;&gt;=
#include &lt;map&gt;
#include &lt;list&gt;
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; map, which for each vertex ''v'' gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we use the previous array to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes two input parameters and two output parameters:
* source (in): The source vertex from which all shortest paths are found
* adjacency_map (in): The adjacency map specifying the connection between vertices and edge weights.
* min_distance (out): Will receive the shortest distance from &lt;code&gt;source&lt;/code&gt; to each vertex in the graph.
* previous (out): Receives a map that can be passed back into &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; later on to quickly get a shortest path from the source vertex to any desired vertex.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
void DijkstraComputePaths(vertex_t source,
                          adjacency_map_t&amp; adjacency_map,
                          std::map&lt;vertex_t, weight_t&gt;&amp; min_distance,
                          std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    &lt;&lt;initialize output parameters&gt;&gt;
    min_distance[source] = 0;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;
        // Visit each edge exiting u
        for (std::list&lt;edge&gt;::iterator edge_iter = adjacency_map[u].begin();
             edge_iter != adjacency_map[u].end();
             edge_iter++)
        {
            vertex_t v = edge_iter-&gt;target;
            weight_t weight = edge_iter-&gt;weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;min_distance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;min_distance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
weight_t distance_through_u = min_distance[u] + weight;
if (distance_through_u &lt; min_distance[v]) {
    &lt;&lt;remove v from queue&gt;&gt;
    min_distance[v] = distance_through_u;
    previous[v] = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

We also need to initialize the output parameters so that at first all min distances are positive infinity (as large as possible). We can visit all vertices by just iterating over the keys of &lt;code&gt;adjacency_map&lt;/code&gt;:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize output parameters&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    min_distance[v] = std::numeric_limits&lt; double &gt;::infinity();
}
&lt;&lt;definition headers&gt;&gt;=
#include &lt;limits&gt; // for numeric_limits
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We could do this using a heap data structure, but later on we will also need to decrease the distance of particular vertices, which will involve re-ordering that vertex in the heap. However, finding a particular element in a heap is a linear-time operation. To avoid this, we instead use a self-balancing binary search tree, which will also allow us to find the vertex of minimum distance, as well as find any particular vertex, quickly. We will use a &lt;code&gt;std::set&lt;/code&gt; of pairs, where each pair contains a vertex ''v'' along with its minimum distance &lt;code&gt;min_distance[v]&lt;/code&gt;. Fortunately, C++'s &lt;code&gt;std::pair&lt;/code&gt; class already implements an ordering, which orders lexicographically (by first element, then by second element), which will work fine for us, as long as we use the distance as the first element of the pair.

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;visit each vertex u, always visiting vertex with smallest min_distance first&gt;&gt;=
std::set&lt; std::pair&lt;weight_t, vertex_t&gt; &gt; vertex_queue;
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    vertex_queue.insert(std::make_pair(min_distance[v], v));
}

while (!vertex_queue.empty()) 
{
    vertex_t u = vertex_queue.begin()-&gt;second;
    vertex_queue.erase(vertex_queue.begin());


&lt;&lt;definition headers&gt;&gt;=
#include &lt;set&gt;
#include &lt;utility&gt; // for pair
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;begin()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertex_queue.erase(std::make_pair(min_distance[v], v));

&lt;&lt;re-add v to queue&gt;&gt;=
vertex_queue.insert(std::make_pair(min_distance[v], v));
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the linked list in the &lt;code&gt;previous&lt;/code&gt; map from the target back to the source:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
std::list&lt;vertex_t&gt; DijkstraGetShortestPathTo(
    vertex_t target, std::map&lt;vertex_t, vertex_t&gt;&amp; previous)
{
    std::list&lt;vertex_t&gt; path;
    std::map&lt;vertex_t, vertex_t&gt;::iterator prev;
    vertex_t vertex = target;
    path.push_front(vertex);
    while((prev = previous.find(vertex)) != previous.end())
    {
        vertex = prev-&gt;second;
        path.push_front(vertex);
    }
    return path;
}
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;dijkstra_example.cpp&gt;&gt;=
#include &lt;iostream&gt;
#include &lt;vector&gt;
#include &lt;string&gt;
&lt;&lt;definition headers&gt;&gt;

&lt;&lt;simple graph types&gt;&gt;

&lt;&lt;simple compute paths function&gt;&gt;

&lt;&lt;get shortest path function&gt;&gt;

int main()
{
    adjacency_map_t adjacency_map;
    std::vector&lt;std::string&gt; vertex_names;

    &lt;&lt;initialize adjacency map&gt;&gt;

    std::map&lt;vertex_t, weight_t&gt; min_distance;
    std::map&lt;vertex_t, vertex_t&gt; previous;
    DijkstraComputePaths(0, adjacency_map, min_distance, previous);
    &lt;&lt;print out shortest paths and distances&gt;&gt;
    return 0;
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (adjacency_map_t::iterator vertex_iter = adjacency_map.begin();
     vertex_iter != adjacency_map.end();
     vertex_iter++)
{
    vertex_t v = vertex_iter-&gt;first;
    std::cout &lt;&lt; &quot;Distance to &quot; &lt;&lt; vertex_names[v] &lt;&lt; &quot;: &quot; &lt;&lt; min_distance[v] &lt;&lt; std::endl;
    std::list&lt;vertex_t&gt; path =
        DijkstraGetShortestPathTo(v, previous);
    std::list&lt;vertex_t&gt;::iterator path_iter = path.begin();
    std::cout &lt;&lt; &quot;Path: &quot;;
    for( ; path_iter != path.end(); path_iter++)
    {
        std::cout &lt;&lt; vertex_names[*path_iter] &lt;&lt; &quot; &quot;;
    }
    std::cout &lt;&lt; std::endl;
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;initialize adjacency map&gt;&gt;=
vertex_names.push_back(&quot;Harrisburg&quot;);   // 0
vertex_names.push_back(&quot;Baltimore&quot;);    // 1
vertex_names.push_back(&quot;Washington&quot;);   // 2
vertex_names.push_back(&quot;Philadelphia&quot;); // 3
vertex_names.push_back(&quot;Binghamton&quot;);   // 4
vertex_names.push_back(&quot;Allentown&quot;);    // 5
vertex_names.push_back(&quot;New York&quot;);     // 6
adjacency_map[0].push_back(edge(1,  79.83));
adjacency_map[0].push_back(edge(5,  81.15));
adjacency_map[1].push_back(edge(0,  79.75));
adjacency_map[1].push_back(edge(2,  39.42));
adjacency_map[1].push_back(edge(3, 103.00));
adjacency_map[2].push_back(edge(1,  38.65));
adjacency_map[3].push_back(edge(1, 102.53));
adjacency_map[3].push_back(edge(5,  61.44));
adjacency_map[3].push_back(edge(6,  96.79));
adjacency_map[4].push_back(edge(5, 133.04));
adjacency_map[5].push_back(edge(0,  81.77));
adjacency_map[5].push_back(edge(3,  62.05));
adjacency_map[5].push_back(edge(4, 134.47));
adjacency_map[5].push_back(edge(6,  91.63));
adjacency_map[6].push_back(edge(3,  97.24));
adjacency_map[6].push_back(edge(5,  87.94));
&lt;/codeblock&gt;

== Alternatives ==

In an application that does a lot of graph manipulation, a good option is the [http://www.boost.org/libs/graph/doc/ Boost graph library], which includes [http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html support for Dijkstra's algorithm].

[[Category:Dijkstra's algorithm|C Plus Plus]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Dijkstra's algorithm (Inform 7)</title>
    <id>2984</id>
    <revision>
      <id>8854</id>
      <timestamp>2007-02-04T22:15:14Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{codedump}}
{{:Category:Dijkstra's algorithm}}
==theory==
Use the relation support in Inform 7 to code a well-known graph algorithm.
==practice==
===Dijkstra's algorithm===
TODO: literify.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is found;
	change the total distance of n to 0;
	run a relaxation step from n.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	run a relaxation step from n.

To run a relaxation step from (n - a node):
	repeat with m running through the nodes contacting n begin;
		relax m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''relax''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To relax (m - a found node) from (n - a node):
	now m is found.

To relax (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To relax (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		if some node is the precedent of m, now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]].  It may be possible to key on multiple fields in Inform 7, but here we take the brute-force approach of performing a symmetric scan over the entire table.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, Marseille, Narbonne, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
To slide the marker to (n - a node), in recursion:
	if n is the current node begin;
		say &quot;You take the marker from [n] and slide it&quot;;
	otherwise;
		slide the marker to the precedent of n, in recursion;
		if in recursion, say &quot; to [n]&quot;;
		otherwise say &quot;, winding up at [n].&quot;;
	end if:
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.txt&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>8855</id>
      <timestamp>2007-02-05T07:07:01Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* test data */ +&quot;oggsford&quot;</comment>
      <text xml:space="preserve">{{codedump}}
{{:Category:Dijkstra's algorithm}}
==theory==
Use the relation support in Inform 7 to code a well-known graph algorithm.
==practice==
===Dijkstra's algorithm===
TODO: literify.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is found;
	change the total distance of n to 0;
	run a relaxation step from n.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	run a relaxation step from n.

To run a relaxation step from (n - a node):
	repeat with m running through the nodes contacting n begin;
		relax m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''relax''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To relax (m - a found node) from (n - a node):
	now m is found.

To relax (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To relax (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		if some node is the precedent of m, now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7]  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;

===interaction===
In order to provide output and accept user input, we must make a few more definitions.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
To slide the marker to (n - a node), in recursion:
	if n is the current node begin;
		say &quot;You take the marker from [n] and slide it&quot;;
	otherwise;
		slide the marker to the precedent of n, in recursion;
		if in recursion, say &quot; to [n]&quot;;
		otherwise say &quot;, winding up at [n].&quot;;
	end if:
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.txt&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>8856</id>
      <timestamp>2007-02-05T07:44:05Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>todo done</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==
===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.txt&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>8989</id>
      <timestamp>2007-02-10T23:54:08Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* wrapping up */ use &quot;inform7&quot; extension</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==
===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>9312</id>
      <timestamp>2007-03-01T21:23:20Z</timestamp>
      <contributor>
        <ip>193.251.190.48</ip>
      </contributor>
      <comment>John</comment>
      <text xml:space="preserve" />
    </revision>
    <revision>
      <id>9313</id>
      <timestamp>2007-03-01T21:38:33Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/193.251.190.48|193.251.190.48]] ([[User_talk:193.251.190.48|193.251.190.48]]); changed back to last version by [[User:Dave|Dave]]</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==
===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>9820</id>
      <timestamp>2007-04-20T04:32:10Z</timestamp>
      <contributor>
        <ip>221.18.44.18</ip>
      </contributor>
      <comment>&lt;&gt;</comment>
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    </revision>
    <revision>
      <id>9822</id>
      <timestamp>2007-04-20T04:57:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==
===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>10038</id>
      <timestamp>2007-05-15T03:27:11Z</timestamp>
      <contributor>
        <ip>146.171.254.66</ip>
      </contributor>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==

I got this to work with the current version of Inform 7 by:
* replacing all instances of &quot;total distance&quot; with &quot;total_distance&quot; because otherwise the current version of Inform 7 says &quot;... this seems to be an attempt to total up the column of a table, whereas it's only legal to use 'total' for properties.&quot;
* repalcing &quot;decide on the total_distance of n + the distance between m and n.&quot; with &quot;let d be the total_distance of n plus the distance between m and n; decide on d.&quot; because otherwise the current version of Inform 7 says &quot;you wrote ... the outcome of a phrase to decide a value, but this was the wrong kind of value: an instruction to work something out rather than a number.&quot;

===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>10642</id>
      <timestamp>2007-07-05T07:58:42Z</timestamp>
      <contributor>
        <ip>74.93.196.181</ip>
      </contributor>
      <comment>qnhy ixdrjvzpe</comment>
      <text xml:space="preserve">pytvdj zhorefik tpwh djfwnbmla lioqp kfnbv ktvgsmbh</text>
    </revision>
    <revision>
      <id>10643</id>
      <timestamp>2007-07-05T13:09:44Z</timestamp>
      <contributor>
        <ip>213.162.248.20</ip>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==

I got this to work with the current version of Inform 7 by:
* replacing all instances of &quot;total distance&quot; with &quot;total_distance&quot; because otherwise the current version of Inform 7 says &quot;... this seems to be an attempt to total up the column of a table, whereas it's only legal to use 'total' for properties.&quot;
* repalcing &quot;decide on the total_distance of n + the distance between m and n.&quot; with &quot;let d be the total_distance of n plus the distance between m and n; decide on d.&quot; because otherwise the current version of Inform 7 says &quot;you wrote ... the outcome of a phrase to decide a value, but this was the wrong kind of value: an instruction to work something out rather than a number.&quot;

===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
    <revision>
      <id>10730</id>
      <timestamp>2007-07-22T23:59:16Z</timestamp>
      <contributor>
        <ip>69.151.98.190</ip>
      </contributor>
      <comment>Once you have your list, now you can repay the cards and start rebuilding your credit.</comment>
      <text xml:space="preserve">Hi, 
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Thanks</text>
    </revision>
    <revision>
      <id>10731</id>
      <timestamp>2007-07-23T00:22:44Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
==theory==
We use the relation support in [http://www.inform-fiction.org/I7/Inform%207.html Inform 7] to code a well-known graph algorithm.  Inform 7 is somewhat reminiscent of a cross between Prolog, COBOL, and DDL &amp;mdash; with the interesting property that phrases such as ''the nearest examined node contacting the current node'' may serve both as specification and as executable code.
==practice==

I got this to work with the current version of Inform 7 by:
* replacing all instances of &quot;total distance&quot; with &quot;total_distance&quot; because otherwise the current version of Inform 7 says &quot;... this seems to be an attempt to total up the column of a table, whereas it's only legal to use 'total' for properties.&quot;
* repalcing &quot;decide on the total_distance of n + the distance between m and n.&quot; with &quot;let d be the total_distance of n plus the distance between m and n; decide on d.&quot; because otherwise the current version of Inform 7 says &quot;you wrote ... the outcome of a phrase to decide a value, but this was the wrong kind of value: an instruction to work something out rather than a number.&quot;

===Dijkstra's algorithm===
Dijkstra's algorithm is a greedy algorithm that divides nodes up into three types:
* nodes for which we have definitely '''found''' the shortest path
* nodes which we have '''examined''', which have a shortest path thus far seen
* and, nodes which are yet '''unreached'''
We start by examining the source node, by definition at distance 0, with all the rest as yet ''unreached''.  Then we repeatedly run examination steps until converging by running out of ''examined'' nodes to consider.  On each iteration, we greedily convert the '''nearest examined''' node to a '''found''' node, and then examine all of its neighbors &amp;mdash; '''the nodes contacting n'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
Every turn: run Dijkstra's algorithm.

To run Dijkstra's algorithm:
	initialize Dijkstra's algorithm from the current node;
	while some of the nodes are examined begin;
		continue Dijkstra's algorithm;
	end while.
	
To initialize Dijkstra's algorithm from (n - a node):
	clear the state;
	now n is examined;
	change the total distance of n to 0.
	
To continue Dijkstra's algorithm:
	let n be the nearest examined node;
	now n is found;
	repeat with m running through the nodes contacting n begin;
		examine m from n;
	end repeat.
&lt;/codeblock&gt;
when we '''examine''' a path to a node, it may
* already have a confirmed shortest path
* be the first time we have encountered the node
* or, already have a provisional shortest path
in which case, we
* ignore it (perform a NOP to keep Inform happy)
* set its '''total distance''' and add it to the '''examined''' set along with a back-pointer
* or, do the above only if the new '''total distance''' would be shorter than the old.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To examine (m - a found node) from (n - a node): now m is found.

To examine (m - an unreached node) from (n - a node):
	now m is examined;
	change the total distance of m to the extension of n to m;
	now m follows n.
	
To examine (m - an examined node) from (n - a node):
	let d be the extension of n to m;
	if the total distance of m &gt; d begin;
		change the total distance of m to d;
		now m follows n;
	end if.
&lt;/codeblock&gt;
some ancillary details:
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;=
To clear the state:
	repeat with m running through nodes begin;
		now m is unreached;
		now m does not follow anything;
	end repeat;

To decide what number is the extension of (n - a node) to (m - a node):
	decide on the total distance of n + the distance between m and n.
&lt;/codeblock&gt;
===definitions===
There are a number of definitions we need to make for the code above to run &amp;mdash; both static properties, which are a function of the given graph:
* defining '''contact''' allows us to repeat over '''nodes contacting n'''.
* as it is constant, we will initialize the contact relation once, '''when play begins'''.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
A node is a kind of thing.
Contact relates nodes to each other.
The verb to contact (he contacts, they contact, he contacted, it is contacted, he is contacting) implies the contact relation.
&lt;/codeblock&gt;
and dynamic properties, which will change when we change the source node.
* the '''total distance''' holds the the length of the (currently estimated) shortest path from the source node.
* the '''10''' in the definition of '''near''' is arbitrary &amp;mdash; we provide this definition only so that we may use the superlative, and ask for the '''nearest examined node''' when we '''continue Dijkstra's algorithm'''. 
* defining the '''precedent''' allows us to extract the full path (in reverse order) to any given node from the source node.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;node properties&gt;&gt;=
The current node is a node that varies.

A node can be found, examined, or unreached.
A node has a number called the total distance.  
Definition: a node is near if its total distance is 10 or less.

Following relates various nodes to one node (called the precedent).
The verb to follow (he follows, they follow, he followed, it is followed, he is following) implies the following relation.
&lt;/codeblock&gt;
===test data===
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
We use the test data from [[Dijkstra's algorithm (Scala)]], and add Oxford, the home of [http://www.inform-fiction.org/I7/Inform%207.html Inform 7].  It may be possible to key on multiple fields, but as the table is small, here we take the brute-force approach of performing a symmetric scan.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;test data&gt;&gt;=
Barcelona, Geneve, Lausanne, London, Marseille, Narbonne, Oxford, Paris, and Toulouse are nodes.

Table of Intercity Distances
src	dst	distance
Barcelona	Narbonne	250
Geneve	Lausanne	64
Geneve	Marseille	260
Geneve	Narbonne	550
Geneve	Paris	540
Geneve	Toulouse	700
Lausanne	Paris	536
London	Oxford	95
London	Paris	440
Marseille	Narbonne	260
Narbonne	Toulouse	150
Paris	Toulouse	680

To decide what number is the distance between (n - a node) and (m - a node):
	repeat through the Table of Intercity Distances begin;
		if the src entry is n and the dst entry is m, decide on the distance entry;
		if the src entry is m and the dst entry is n, decide on the distance entry;
	end repeat.
	
&lt;/codeblock&gt;
===interaction===
In order to provide output and accept user input, we must make a few more definitions.  The recursion runs from the desired node back to the current node, but the output is generated upon return, yielding the path in-order from current to desired.
&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;user interaction&gt;&gt;=	
Definition: a node is initial if it is the current node.
To slide the marker from (n - an initial node):
	say &quot;You take the marker from [n] and slide it&quot;.
To slide the marker from (n - a node):
	slide the marker from the precedent of n;
	say &quot; to [n]&quot;.
To slide the marker to (n - a node):
	slide the marker from the precedent of n;
	say &quot;, winding up at [n].&quot;.
		
planning is an action applying to one visible thing.
understand &quot;[a node]&quot; as planning.
check planning:
	if the current node is the noun, say &quot;The marker is already at [the current node].&quot; instead.
carry out planning: 
	slide the marker to the noun;
	change the current node to the noun.
&lt;/codeblock&gt;
==wrapping up==

Finally we complete the game with the authoring boilerplate, an initial room for the player, some initialization code, and a small test-suite.

&lt;codeblock language=&quot;inform7&quot;&gt;
&lt;&lt;dijkstra.inform7&gt;&gt;=
&quot;Dijkstra's Algorithm&quot; by Dave

&lt;&lt;node properties&gt;&gt;
&lt;&lt;dijkstra's algorithm&gt;&gt;
&lt;&lt;test data&gt;&gt;
&lt;&lt;user interaction&gt;&gt;	
	
The Map Room is a room.
&quot;You are looking at a roadmap centered on the south of France[line break]Say 'relations' to examine the current graph state[line break]Say 'city name' to plan a trip from [the current node].&quot;. 
The marker and the roadmap are scenery in the Map Room.

When play begins:
	repeat through the Table of Intercity Distances begin;
		now the src entry contacts the dst entry;
		now the dst entry contacts the src entry;
	end repeat;
	repeat with n running through the nodes begin;
		move n to the Map Room;
	end repeat;
	change the current node to Barcelona;
	run Dijkstra's algorithm.
	
Test me with &quot;barcelona/lausanne/barcelona/paris/marseille&quot;
&lt;/codeblock&gt;

A sample run is as follows:

&lt;pre&gt;
Map Room
You are looking at a roadmap centered on the south of France
Say &quot;city name&quot; to plan a trip from Barcelona.

You can see Toulouse, Paris, Narbonne, Marseille, Lausanne, Geneve and Barcelona here.

&gt; barcelona
The marker is already at Barcelona.

&gt; lausanne
You take the marker from Barcelona and slide it to Narbonne to Marseille to Geneve, winding up at Lausanne.

&gt; barcelona
You take the marker from Lausanne and slide it to Geneve to Marseille to Narbonne, winding up at Barcelona.

&gt; paris
You take the marker from Barcelona and slide it to Narbonne to Toulouse, winding up at Paris.

&gt; marseille
You take the marker from Paris and slide it to Geneve, winding up at Marseille.

&gt;
&lt;/pre&gt;

[[Category:Programming language:Inform 7]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm|Inform 7]]</text>
    </revision>
  </page>
  <page>
    <title>Dijkstra's algorithm (Java)</title>
    <id>3297</id>
    <revision>
      <id>12310</id>
      <timestamp>2008-01-26T04:58:20Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName)
    { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple graph types&gt;&gt;=
class Edge
{
    public final int target;
    public final double weight;
    public Edge(int argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void DijkstraComputePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We do this using a priority queue. The Vertex class itself implements an ordering using the &lt;code&gt;compareTo&lt;/code&gt; method that uses the ordering of the &lt;code&gt;minDistance&lt;/code&gt; fields. The basic priority queue does not like when elements in the queue are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the priority queue. For simplicity, the queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.offer(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;, which works because the priority queue is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.offer(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; DijkstraGetShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        DijkstraComputePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = DijkstraGetShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12311</id>
      <timestamp>2008-01-26T04:59:07Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName)
    { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final int target;
    public final double weight;
    public Edge(int argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void DijkstraComputePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We do this using a priority queue. The Vertex class itself implements an ordering using the &lt;code&gt;compareTo&lt;/code&gt; method that uses the ordering of the &lt;code&gt;minDistance&lt;/code&gt; fields. The basic priority queue does not like when elements in the queue are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the priority queue. For simplicity, the queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.offer(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;, which works because the priority queue is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.offer(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; DijkstraGetShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        DijkstraComputePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = DijkstraGetShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12312</id>
      <timestamp>2008-01-26T05:00:00Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Simple graph representation */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName)
    { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;DijkstraComputePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void DijkstraComputePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We do this using a priority queue. The Vertex class itself implements an ordering using the &lt;code&gt;compareTo&lt;/code&gt; method that uses the ordering of the &lt;code&gt;minDistance&lt;/code&gt; fields. The basic priority queue does not like when elements in the queue are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the priority queue. For simplicity, the queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.offer(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;, which works because the priority queue is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.offer(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;DijkstraComputePaths()&lt;/code&gt;. &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; DijkstraGetShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        DijkstraComputePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = DijkstraGetShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12313</id>
      <timestamp>2008-01-26T05:07:21Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName)
    { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We do this using a priority queue. The Vertex class itself implements an ordering using the &lt;code&gt;compareTo&lt;/code&gt; method that uses the ordering of the &lt;code&gt;minDistance&lt;/code&gt; fields. The basic priority queue does not like when elements in the queue are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the priority queue. For simplicity, the queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.offer(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;, which works because the priority queue is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.offer(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12314</id>
      <timestamp>2008-01-26T11:05:38Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <comment>/* Simple graph representation */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We do this using a priority queue. The Vertex class itself implements an ordering using the &lt;code&gt;compareTo&lt;/code&gt; method that uses the ordering of the &lt;code&gt;minDistance&lt;/code&gt; fields. The basic priority queue does not like when elements in the queue are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the priority queue. For simplicity, the queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.offer(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;, which works because the priority queue is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.offer(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12318</id>
      <timestamp>2008-01-27T04:06:48Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>/* Main algorithm */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, with the minDistance as the priority; but Java's &lt;code&gt;PriorityQueue&lt;/code&gt; class does not offer an efficient way to decrease the priority of an element in the queue, which we need. Instead, we will use a &lt;code&gt;TreeSet&lt;/code&gt; ordered by the minDistance component. The set does not like it when the ordering of its elements are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the set. The set will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
SortedSet&lt;Vertex&gt; vertexQueue = new TreeSet&lt;Vertex&gt;();
vertexQueue.add(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.first();
    vertexQueue.remove(u);

&lt;&lt;imports&gt;&gt;=
import java.util.SortedSet;
import java.util.TreeSet;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;first()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.add(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14078</id>
      <timestamp>2008-07-22T17:58:28Z</timestamp>
      <contributor>
        <ip>198.240.130.75</ip>
      </contributor>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. Ideally we would do this using an available priority queue data structure, with the minDistance as the priority; but Java's &lt;code&gt;PriorityQueue&lt;/code&gt; class does not offer an efficient way to decrease the priority of an element in the queue, which we need. Instead, we will use a &lt;code&gt;TreeSet&lt;/code&gt; ordered by the minDistance component. The set does not like it when the ordering of its elements are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the set. The set will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing. 

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

Use a PriorityQueue instead of SortedSet as presented here. SortedSet will not allow adding nodes when the distance to reach that node is same as the distance to reach some other node already present in the Set.

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
SortedSet&lt;Vertex&gt; vertexQueue = new TreeSet&lt;Vertex&gt;();
vertexQueue.add(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.first();
    vertexQueue.remove(u);

&lt;&lt;imports&gt;&gt;=
import java.util.SortedSet;
import java.util.TreeSet;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;first()&lt;/code&gt;, which works because the set is ordered by minimum distance. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.add(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14309</id>
      <timestamp>2008-08-16T17:59:57Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>/* Main algorithm */ changed to PriorityQueue</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We use Java's &lt;code&gt;PriorityQueue&lt;/code&gt; class with the minDistance as the priority. The priority queue does not like it when the ordering of its elements are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the set. The queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.add(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.add(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15443</id>
      <timestamp>2008-11-13T16:13:18Z</timestamp>
      <contributor>
        <ip>137.222.229.32</ip>
      </contributor>
      <comment>/* Sample code */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We use Java's &lt;code&gt;PriorityQueue&lt;/code&gt; class with the minDistance as the priority. The priority queue does not like it when the ordering of its elements are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the set. The queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.add(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.add(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15444</id>
      <timestamp>2008-11-13T16:13:32Z</timestamp>
      <contributor>
        <ip>137.222.229.32</ip>
      </contributor>
      <comment>/* Sample code */</comment>
      <text xml:space="preserve">{{:Category:Dijkstra's algorithm}}
== Simple graph representation ==

We use a simple graph representation where the vertices are represented by a Vertex class.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex class&gt;&gt;=
class Vertex implements Comparable&lt;Vertex&gt;
{
    public final String name;
    public Edge[] adjacencies;
    public double minDistance = Double.POSITIVE_INFINITY;
    public Vertex previous;
    public Vertex(String argName) { name = argName; }
    public String toString() { return name; }
    &lt;&lt;Vertex comparator&gt;&gt;
}
&lt;/codeblock&gt;

Because we'll need to iterate over the successors of each vertex, we will keep a list of edges exiting each vertex. For use by the     algorithm later, we have two other fields:
* minDistance: The shortest distance from the source to this vertex in the graph. It is initialized to positive infinity (as large as possible).
* previous: A reference to the previous vertex to get a shortest path from the source vertex to this vertex.
In addition, later in the algorithm we will need to order the vertices. We made our class implement the &lt;code&gt;Comparable&lt;/code&gt; interface, and we will implement the actual comparison method later.

We also have a class representing an edge that stores its weight and target vertex (the vertex it points to):

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Edge class&gt;&gt;=
class Edge
{
    public final Vertex target;
    public final double weight;
    public Edge(Vertex argTarget, double argWeight)
    { target = argTarget; weight = argWeight; }
}
&lt;/codeblock&gt;

== Main algorithm ==

We're now prepared to define our method. We separate the computation into two stages:

# Compute the minimum distance from the source to each vertex in the graph. Simultaneously, keep track of the &lt;code&gt;previous&lt;/code&gt; reference for each vertex ''v'' that gives the previous vertex on the shortest path from the source vertex to ''v''. This is the expensive step.
# Later, any time we want to find a particular shortest path between the source vertex and a given vertex, we follow the previous references to quickly construct it.

For the first part, we write &lt;code&gt;computePaths&lt;/code&gt;, which takes as input the source vertex from which all shortest paths are found.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;simple compute paths function&gt;&gt;=
public static void computePaths(Vertex source)
{
    source.minDistance = 0.;
    &lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;
        // Visit each edge exiting u
        for (Edge e : u.adjacencies)
        {
            Vertex v = e.target;
            double weight = e.weight;
            &lt;&lt;relax the edge (u,v)&gt;&gt;
        }
    }
}
&lt;/codeblock&gt;

The outline of how the function works is shown above: we visit each vertex, looping over its out-edges and adjusting &lt;code&gt;minDistance&lt;/code&gt; as necessary. The critical operation is relaxing the edges, which is based on the following formula:

: if (''u'', ''v'') is an edge and ''u'' is on the shortest path to ''v'', &lt;math&gt;d(u) + w(u, v) = d(v)&lt;/math&gt;.

In other words, we can reach ''v'' by going from the source to ''u'', then following the edge (''u'',''v''). Eventually, we will visit every predecessor of ''v'' reachable from the source. The shortest path goes through one of these. We keep track of the shortest distance seen so far by setting &lt;code&gt;minDistance&lt;/code&gt; and the vertex it went through by setting &lt;code&gt;previous&lt;/code&gt;:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;relax the edge (u,v)&gt;&gt;=
double distanceThroughU = u.minDistance + weight;
if (distanceThroughU &lt; v.minDistance) {
    &lt;&lt;remove v from queue&gt;&gt;
    v.minDistance = distanceThroughU ;
    v.previous = u;
    &lt;&lt;re-add v to queue&gt;&gt;
}
&lt;/codeblock&gt;

Finally, we need a way to visit the vertices in order of their minimum distance. We use Java's &lt;code&gt;PriorityQueue&lt;/code&gt; class with the minDistance as the priority. The priority queue does not like it when the ordering of its elements are changed, so when we change the minimum distance of any vertex, we need to remove it and re-insert it into the set. The queue will only consist of those vertices that have finite distance (i.e. ones we have seen); if we come to a new vertex that is not in the queue, removing it will simply do nothing.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Vertex comparator&gt;&gt;=
public int compareTo(Vertex other)
{
    return Double.compare(minDistance, other.minDistance);
}

&lt;&lt;visit each vertex u, always visiting vertex with smallest minDistance first&gt;&gt;=
PriorityQueue&lt;Vertex&gt; vertexQueue = new PriorityQueue&lt;Vertex&gt;();
vertexQueue.add(source);

while (!vertexQueue.isEmpty()) {
    Vertex u = vertexQueue.poll();

&lt;&lt;imports&gt;&gt;=
import java.util.PriorityQueue;
&lt;/codeblock&gt;

We access and remove the smallest element using &lt;code&gt;poll()&lt;/code&gt;. If we change a vertex's minimum distance, we must update its key in the map as well:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;remove v from queue&gt;&gt;=
vertexQueue.remove(v);

&lt;&lt;re-add v to queue&gt;&gt;=
vertexQueue.add(v);
&lt;/codeblock&gt;

This completes &lt;code&gt;computePaths()&lt;/code&gt;. &lt;code&gt;getShortestPathTo()&lt;/code&gt; is much simpler, just following the chain of &lt;code&gt;previous&lt;/code&gt; references from the target back to the source:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;get shortest path function&gt;&gt;=
public static List&lt;Vertex&gt; getShortestPathTo(Vertex target)
{
    List&lt;Vertex&gt; path = new ArrayList&lt;Vertex&gt;();
    for (Vertex vertex = target; vertex != null; vertex = vertex.previous)
        path.add(vertex);

    Collections.reverse(path);
    return path;
}
&lt;&lt;imports&gt;&gt;=
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how we use the above functions:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Dijkstra.java&gt;&gt;=
&lt;&lt;imports&gt;&gt;

&lt;&lt;Vertex class&gt;&gt;

&lt;&lt;Edge class&gt;&gt;

public class Dijkstra
{
    &lt;&lt;simple compute paths function&gt;&gt;

    &lt;&lt;get shortest path function&gt;&gt;

    public static void main(String[] args)
    {
        &lt;&lt;initialize graph&gt;&gt;

        computePaths(v0);
        &lt;&lt;print out shortest paths and distances&gt;&gt;
    }
}
&lt;/codeblock&gt;

Printing out shortest paths is just a matter of iterating over the vertices and calling &lt;code&gt;DijkstraGetShortestPathTo()&lt;/code&gt; on each:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;print out shortest paths and distances&gt;&gt;=
for (Vertex v : vertices)
{
    System.out.println(&quot;Distance to &quot; + v + &quot;: &quot; + v.minDistance);
    List&lt;Vertex&gt; path = getShortestPathTo(v);
    System.out.println(&quot;Path: &quot; + path);
}
&lt;/codeblock&gt;

For this example, we choose vertices corresponding to some East Coast U.S. cities. We add edges corresponding to interstate highways, with the edge weight set to the driving distance between the cities in miles as determined by Mapquest:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;initialize graph&gt;&gt;=
Vertex v0 = new Vertex(&quot;Harrisburg&quot;);
Vertex v1 = new Vertex(&quot;Baltimore&quot;);
Vertex v2 = new Vertex(&quot;Washington&quot;);
Vertex v3 = new Vertex(&quot;Philadelphia&quot;);
Vertex v4 = new Vertex(&quot;Binghamton&quot;);
Vertex v5 = new Vertex(&quot;Allentown&quot;);
Vertex v6 = new Vertex(&quot;New York&quot;);
v0.adjacencies = new Edge[]{ new Edge(v1,  79.83),
                             new Edge(v5,  81.15) };
v1.adjacencies = new Edge[]{ new Edge(v0,  79.75),
                             new Edge(v2,  39.42),
                             new Edge(v3, 103.00) };
v2.adjacencies = new Edge[]{ new Edge(v1,  38.65) };
v3.adjacencies = new Edge[]{ new Edge(v1, 102.53),
                             new Edge(v5,  61.44),
                             new Edge(v6,  96.79) };
v4.adjacencies = new Edge[]{ new Edge(v5, 133.04) };
v5.adjacencies = new Edge[]{ new Edge(v0,  81.77),
                             new Edge(v3,  62.05),
                             new Edge(v4, 134.47),
                             new Edge(v6,  91.63) };
v6.adjacencies = new Edge[]{ new Edge(v3,  97.24),
                             new Edge(v5,  87.94) };
Vertex[] vertices = { v0, v1, v2, v3, v4, v5, v6 };
&lt;/codeblock&gt;

[[Category:Dijkstra's algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Dijkstra's algorithm (Scala)</title>
    <id>1947</id>
    <revision>
      <id>4386</id>
      <timestamp>2006-05-05T23:44:02Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <text xml:space="preserve">Here is an example of Dijkstra Shortest Path in Scala

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt; 
def minimumDistVertex( Q: HashSet[V]): V = (
   Q.toList.filter( dist.isDefinedAt) 
                .reduceLeft {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
)
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest path from source
        for( val Pair( city, dist) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) 
          Console.println( city + &quot;: &quot; + dist)
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; ?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
		&lt;test from=&quot;Marseille&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>4387</id>
      <timestamp>2006-05-05T23:54:05Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>Added categories</comment>
      <text xml:space="preserve">{{development}}
Here is an example of Dijkstra Shortest Path in Scala

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = (
   Q.toList.filter( dist.isDefinedAt) 
                .reduceLeft {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
)
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; ?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
		&lt;test from=&quot;Marseille&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;


[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4388</id>
      <timestamp>2006-05-05T23:57:47Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>added some initial text</comment>
      <text xml:space="preserve">Here is an example of Dijkstra Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = (
   Q.toList.filter( dist.isDefinedAt) 
                .reduceLeft {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
)
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; ?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
		&lt;test from=&quot;Marseille&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;


[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4389</id>
      <timestamp>2006-05-06T00:03:53Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>spacing</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = (

  Q.toList.filter( dist.isDefinedAt) reduceLeft
                     {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
)
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; ?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
		&lt;test from=&quot;Marseille&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;


[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4390</id>
      <timestamp>2006-05-06T00:14:52Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>Added testing</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;


&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = (

  Q.toList.filter( dist.isDefinedAt) reduceLeft
                     {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
)
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4393</id>
      <timestamp>2006-05-06T00:41:51Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  removed filter in minimumDistVertex routine ( rewritten)</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( Q.toList.forall(dist.isDefinedAt)) ;
           
  Q.toList reduceLeft {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4398</id>
      <timestamp>2006-05-06T05:49:34Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Shortest Path (Scala) moved to Dijkstra's shortest path algorithm (Scala)</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).toList ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( Q.toList.forall(dist.isDefinedAt)) ;
           
  Q.toList reduceLeft {(u: V, v: V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.toList) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4413</id>
      <timestamp>2006-05-06T13:07:30Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>reduced toList conversions</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u).elements ; !Settled.contains( v)) 
       
       if ( ! dist.isDefinedAt( v) || 
            dist(v) &gt; dist( u) + cost(Pair(u, v))) {
         
         dist.update( v, dist( u) + cost(Pair(u, v))) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  while (iter.hasNext) {
    val u = iter.next ;
    v = if (dist( u) &lt;= dist( v)) u else v ;
  }
  v
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]( 
   val vertices: HashSet[ V],
   val connections: HashSet[ Triple[V, V, Float]]
   ) {

   val cost = new HashMap[ Pair[V, V], Float] ;
   val adjacents = new HashMap[ V, HashSet[V]] ;
   
   // init structures
   def init = {
     
     for( val v &lt;- vertices.elements) {
       adjacents.update( v, new HashSet[V]) 
     }
     
     for( val Triple( u, v, c) &lt;- connections.toList) {
       cost.update( Pair( u, v), c) ;
       cost.update( Pair( v, u), c) ;
       adjacents( u) += v
       adjacents( v) += u
     }
   }
   
   init ;       
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val vertices = new HashSet[String] ;
      val connections = new HashSet[ Triple[ String, String, Float]] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      // load data
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        vertices += arc.attribute( &quot;from&quot;)
        vertices += arc.attribute( &quot;to&quot;)
        connections += Triple( arc.attribute(&quot;from&quot;), 
                               arc.attribute(&quot;to&quot;), 
                               java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;))) ;
      }
      
      // build model
      val roadMap = new WeightedGraph[ String]( vertices, connections) ;
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4414</id>
      <timestamp>2006-05-06T14:24:41Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>better graph class design</comment>
      <text xml:space="preserve">{{development}}
Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u); ! Settled.contains( v)) 

       if ( ! dist.isDefinedAt( v) || 
              dist(v) &gt; dist( u) + cost(u, v)) {
               
         dist.update( v, dist( u) + cost(u, v)) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  while (iter.hasNext) {
    val u = iter.next ;
    v = if (dist( u) &lt;= dist( v)) u else v ;
  }
  v
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 
  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
       
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;
       
  def addArc( from: V, to: V, c: Float) = {
         
    if (arcs.contains( from)) {
       val adj = arcs( from) ;
       adj.update( to, c) ;
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, c) ;
      arcs.update( from, adj) ;
    }
  }
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4415</id>
      <timestamp>2006-05-06T14:36:23Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>removed develop template</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u); ! Settled.contains( v)) 

       if ( ! dist.isDefinedAt( v) || 
              dist(v) &gt; dist( u) + cost(u, v)) {
               
         dist.update( v, dist( u) + cost(u, v)) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  while (iter.hasNext) {
    val u = iter.next ;
    v = if (dist( u) &lt;= dist( v)) u else v ;
  }
  v
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 
  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
       
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;
       
  def addArc( from: V, to: V, c: Float) = {
         
    if (arcs.contains( from)) {
       val adj = arcs( from) ;
       adj.update( to, c) ;
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, c) ;
      arcs.update( from, adj) ;
    }
  }
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4416</id>
      <timestamp>2006-05-06T14:44:07Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  added precondition</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {

   assume( arcs.contains( source), &quot;source not in graph&quot;)
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u); ! Settled.contains( v)) 

       if ( ! dist.isDefinedAt( v) || 
              dist(v) &gt; dist( u) + cost(u, v)) {
               
         dist.update( v, dist( u) + cost(u, v)) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  while (iter.hasNext) {
    val u = iter.next ;
    v = if (dist( u) &lt;= dist( v)) u else v ;
  }
  v
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 
  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
       
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;
       
  def addArc( from: V, to: V, c: Float) = {
         
    if (arcs.contains( from)) {
       val adj = arcs( from) ;
       adj.update( to, c) ;
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, c) ;
      arcs.update( from, adj) ;
    }
  }
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4417</id>
      <timestamp>2006-05-06T14:47:46Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  added comment</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

Actually returns minimum distances.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
def shortestPath( source: V) = {

   // check source exists in arcs origin vertices
   assume( arcs.contains( source), &quot;source not in graph&quot;)
   
   // initialize
   val dist = new HashMap[V, Float] ;  // distances
   val Q = new HashSet[V] ;            // priority queue
   val Settled = new HashSet[V] ;      // settled vertices
  
   &lt;&lt;minimumDistVertexDefinition&gt;&gt; 
   
   // start with source vertex
   Q += source ;
   dist.update( source, 0) ;
   
   while (! Q.isEmpty) {
  
     // extract minimal distance vertex from Q, add to Settled ones
     val u = minimumDistVertex( Q) ;
     Q -= u ;
     Settled += u ;
     
     // update neighbours distances
     // and add updated ones to Q
     
     for( val v &lt;- adjacents( u); ! Settled.contains( v)) 

       if ( ! dist.isDefinedAt( v) || 
              dist(v) &gt; dist( u) + cost(u, v)) {
               
         dist.update( v, dist( u) + cost(u, v)) ;
         Q += v ;
       }
   }
   
   // return distances
   dist
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  while (iter.hasNext) {
    val u = iter.next ;
    v = if (dist( u) &lt;= dist( v)) u else v ;
  }
  v
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 
  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
       
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;
       
  def addArc( from: V, to: V, c: Float) = {
         
    if (arcs.contains( from)) {
       val adj = arcs( from) ;
       adj.update( to, c) ;
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, c) ;
      arcs.update( from, adj) ;
    }
  }
   
  &lt;&lt;shortestPath&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
      
      // for each test source
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;
        
        // print shortest distance from source
        for( val Pair( city, distance) &lt;- roadMap.shortestPath( source)
                                                 .toList.sort( (x, y) =&gt; (x._2 &lt; y._2))) { 
          Console.println( city + &quot;: &quot; + distance)
        }  
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot;/&gt;
	&lt;/sources&gt;
&lt;/test&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Barcelona: 0.0
&gt;Narbonne: 250.0
&gt;Toulouse: 400.0
&gt;Marseille: 510.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;Paris: 1080.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Lausanne: 0.0
&gt;Geneve: 64.0
&gt;Marseille: 534.0
&gt;Paris: 604.0
&gt;Narbonne: 614.0
&gt;Toulouse: 764.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4421</id>
      <timestamp>2006-05-06T20:49:22Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>complete version</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @result  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/
def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors maps, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors
  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {
    var v = end ;
    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in graph&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    val u = minimumDistVertex( Q) ;
 
    // extract minimumDistVertex from Q, add to Settled ones
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (!endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  var v = iter.next ;          // min. dist. vertex

  iter.foldLeft( v) {(u:V, v:V) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, c: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, c) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, c) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
      
                                             
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {
        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test     
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;from&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test from=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test from=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne

&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4466</id>
      <timestamp>2006-05-07T13:23:20Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>comments, spacing, inferred types</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @result  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/
def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 
def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=
class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4469</id>
      <timestamp>2006-05-07T14:22:48Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>comments</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached: Boolean)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4476</id>
      <timestamp>2006-05-07T17:56:47Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>top page comment</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap of scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, instantiated to String in the Test module.

The Graph cost type is Float but could be Double or generalized.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached: Boolean)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4477</id>
      <timestamp>2006-05-07T18:00:38Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>grammatical correction</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap from scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, which the Test module instantiates as String.

The WeightedGraph cost type is Float but could be Int, Double or generalized.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached: Boolean)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4478</id>
      <timestamp>2006-05-07T18:44:40Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>text oops (scalar generalization not so easy)</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap from scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, which the Test module instantiates as String.

The WeightedGraph cost type is Float but could be Int, Double.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached: Boolean)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex
  Q += source ;
  dist.update( source, 0) ;
  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) 
   
        if ( ! dist.isDefinedAt( v) || 
               dist(v) &gt; dist( u) + cost(u, v)) {
          
          dist.update( v, dist( u) + cost(u, v)) ;
          Q += v ;
          pred.update( v, u) 
        }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall(dist.isDefinedAt)) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4521</id>
      <timestamp>2006-05-09T17:45:04Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  cosmetic corrections</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap from scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, which the Test module instantiates as String.

The WeightedGraph cost type is Float but could be Int, Double.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist.update( source, 0) ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {

        val actualMinDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || dist(v) &gt; actualMinDist) {
          
          dist.update( v, actualMinDist) ;
          pred.update( v, u) ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4522</id>
      <timestamp>2006-05-09T19:59:57Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  better name for variable</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap from scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, which the Test module instantiates as String.

The WeightedGraph cost type is Float but could be Int, Double.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist.update( source, 0) ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        // v-source distance through u  
        val v_u_s_Dist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || dist(v) &gt; v_u_s_Dist) {
          
          dist.update( v, v_u_s_Dist) ;
          pred.update( v, u) ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj.update( to, kost) 
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj.update( to, kost) ;
      arcs.update( from, adj) 
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4558</id>
      <timestamp>2006-05-11T16:02:06Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  alternate notation for HashMap 'update'</comment>
      <text xml:space="preserve">Here is an example of Dijkstra's Shortest Path in Scala.

== Shortest path ==

This procedural implementation uses sets and dictionaries of types HashSet and HashMap from scala.collection.mutable as imported in the test module.

The custom written WeightedGraph has a Vertex type parameter, which the Test module instantiates as String.

The WeightedGraph cost type is Float but could be Int, Double.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class WeightedGraph

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4564</id>
      <timestamp>2006-05-12T02:52:32Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>WP links +code tags</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;700&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest

&gt;from Barcelona
&gt;
&gt;Narbonne: 250.0
&gt;Geneve: 800.0
&gt;Lausanne: 864.0
&gt;--
&gt;from Lausanne
&gt;
&gt;Geneve: 64.0
&gt;Narbonne: 614.0
&gt;Barcelona: 864.0
&gt;--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4658</id>
      <timestamp>2006-05-13T18:15:56Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>better test output layout</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iter = Q.elements ;
  val w = iter.next ;          // first element

  iter.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one where The Scala Team is based.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4777</id>
      <timestamp>2006-05-15T08:12:44Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>complete name for a variable</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element

  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] is being developed.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4778</id>
      <timestamp>2006-05-15T08:16:37Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Test data */  oops</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element

  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4779</id>
      <timestamp>2006-05-15T08:20:20Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  comment</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml._ ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4780</id>
      <timestamp>2006-05-15T08:34:32Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Test module */  comment</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4781</id>
      <timestamp>2006-05-15T08:54:55Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Test module */  comment</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4782</id>
      <timestamp>2006-05-15T09:10:44Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  comment</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that instead of writing '''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )''' we can specify the function without the parameter, which function will be curried to the Q elements iterator values.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4783</id>
      <timestamp>2006-05-15T09:14:42Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  oops</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify the function ''dist.isDefinedAt'' without the parameter, which function will be curried to the Q elements iterator values.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4784</id>
      <timestamp>2006-05-15T11:16:04Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  oops</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify the function ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type f(v) =&gt; Boolean .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4785</id>
      <timestamp>2006-05-15T11:19:15Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  quoted expression</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify the function ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4786</id>
      <timestamp>2006-05-15T12:25:29Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */ better comment</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WheightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WheightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>4787</id>
      <timestamp>2006-05-15T16:40:00Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>sp</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedGraph&lt;/code&gt;

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedGraph&gt;&gt;=

class WeightedGraph[V]() { 

  // arcs = map to adjacents which in turn is a map to cost

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>5793</id>
      <timestamp>2006-06-03T09:15:08Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>more specific struct name: digraph instead of graph</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Shortest Path]]</text>
    </revision>
    <revision>
      <id>5803</id>
      <timestamp>2006-06-03T10:16:31Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix cat</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>5807</id>
      <timestamp>2006-06-03T18:38:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>[[Dijkstra's shortest path algorithm (Scala)]] moved to [[Dijkstra's algorithm (Scala)]]: Consistent with other names - if Wikipedia calls it Dijkstra's algorithm I think that's unambiguous enough</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==

Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==

&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>6003</id>
      <timestamp>2006-06-07T13:56:24Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>Add figures as an example</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adj = arcs( from) ;
        adj += to -&gt; kost
    }
    else {
      val adj = new HashMap[ V, Float] ;
      adj += to -&gt; kost ;
      arcs += from -&gt; adj
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>6509</id>
      <timestamp>2006-06-28T11:24:22Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Shortest path */  disambiguate variable name</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>6764</id>
      <timestamp>2006-07-11T12:44:51Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Dijkstra's algorithm (Scala)]] moved to [[Dijkstra's algorithm (Scala) on Wheels]]</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>6772</id>
      <timestamp>2006-07-11T12:45:35Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Dijkstra's algorithm (Scala) on Wheels]] moved to [[Dijkstra's algorithm (Scala) on Wheels on Wheels]]</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>6948</id>
      <timestamp>2006-07-11T14:26:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Dijkstra's algorithm (Scala) on Wheels on Wheels]] moved to [[Dijkstra's algorithm (Scala)]]: revert</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;)) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>13109</id>
      <timestamp>2008-04-16T20:56:21Z</timestamp>
      <contributor>
        <ip>83.215.27.89</ip>
      </contributor>
      <comment>/* Test module */</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0 ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;) ;
        val to = arc.attribute(&quot;to&quot;) ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;).get.toString) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;) ;
        val dest = test.attribute(&quot;dest&quot;) ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>16719</id>
      <timestamp>2010-05-03T22:22:18Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>scala version1 to v2 adjustments</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0F ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;                  // folder: test 

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;).toString ;
        val to = arc.attribute(&quot;to&quot;).toString ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;).get.toString) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;).toString ;
        val dest = test.attribute(&quot;dest&quot;).toString ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
&lt;pre&gt;
scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>16720</id>
      <timestamp>2010-05-03T22:29:28Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Testing */ added compilation line</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0F ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;                  // folder: test 

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;).toString ;
        val to = arc.attribute(&quot;to&quot;).toString ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;).get.toString) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;).toString ;
        val dest = test.attribute(&quot;dest&quot;).toString ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
Compile and run
&lt;pre&gt;
scalac test/ShortestPathTest.scala

scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
    <revision>
      <id>16870</id>
      <timestamp>2010-09-23T13:19:48Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">'''danielmayne1993@gmail.com  Message me!'''</text>
    </revision>
    <revision>
      <id>16900</id>
      <timestamp>2010-09-23T15:48:53Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Griba2010|Griba2010]]</comment>
      <text xml:space="preserve">Here is an example of [http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm Dijkstra's shortest path algorithm] in [http://en.wikipedia.org/wiki/Scala_programming_language Scala].

== Shortest path ==

This procedural implementation uses sets and dictionaries of types &lt;code&gt;HashSet&lt;/code&gt; and &lt;code&gt;HashMap&lt;/code&gt; from &lt;code&gt;scala.collection.mutable&lt;/code&gt; as imported in the test module.

The custom written &lt;code&gt;WeightedDiGraph&lt;/code&gt; has a &lt;code&gt;Vertex&lt;/code&gt; type parameter, which the Test module instantiates as &lt;code&gt;String&lt;/code&gt;.

The &lt;code&gt;WeightedDiGraph&lt;/code&gt; cost type is &lt;code&gt;Float&lt;/code&gt; but could be &lt;code&gt;Int&lt;/code&gt;, &lt;code&gt;Double&lt;/code&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;shortestPath&gt;&gt;=
/**
*  @param start
*  @param end
*  @return  route as list of pairs( node, shortest_distance), not including start
*           Nil if end not reached ( unconnected graph)
*/

def shortestPath( start: V, end: V): List[Pair[V, Float]] = {

  if (!arcs.contains( start)) 
    throw new MyException( &quot;shortestPath: &quot;+start+&quot; not in graph edge origins&quot;) ;
 
  if (!vertices.contains( end)) 
    throw new MyException( &quot;shortestPath: &quot;+end+&quot; not in graph vertices&quot;) ;

  // get shortest-distances, predecessors, end result
  val Triple( dist, pred, endReached) = dijkstra( start, end) ;
  
  // build path from end based on predecessors

  var path: List[Pair[V, Float]] = Nil ;

  if (endReached) {

    var v = end ;

    while ( v != start) {
      path = Pair(v, dist(v)) :: path ;

      // iterate on predecessor      
      v = pred( v)
    }
  }
  
  // return path
  path
}
&lt;/codeblock&gt;

Dijkstra's algorithm

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;dijkstra&gt;&gt;=
/**
*  @param start
*  @param end  (end vertex or null)
*  @return  Triple( distances, predecessors, endReached)
*/

def dijkstra( source: V, end: V) = {
  assume( arcs.contains( source), &quot;source not in arcs origins&quot;)
  if (end != null) assume( vertices.contains( end), &quot;end not in graph&quot;)
    
  // initialize
  val dist = new HashMap[V, Float] ;  // distances
  val Q = new HashSet[V] ;            // priority queue
  val Settled = new HashSet[V] ; // settled vertices
  val pred = new HashMap[V, V] ;    // predecessors
 
  &lt;&lt;minimumDistVertexDefinition&gt;&gt;
  
  // start with source vertex

  dist += source -&gt; 0F ;
  Q += source ;

  var endReached = false ;
  
  while (! Q.isEmpty &amp;&amp; ! endReached) {
 
    // extract minimumDistVertex from Q, add to Settled ones

    val u = minimumDistVertex( Q) ;
    Q -= u ;
    Settled += u ;
 
    if (end != null) endReached = (u == end) ;
    
    // update neighbours distances
    // and add updated ones to Q
    
    if (! endReached)
      for( val v &lt;- adjacents( u); ! Settled.contains( v)) {
        
        val vNewDist = dist( u) + cost(u, v) ;

        if ( ! dist.isDefinedAt( v) || vNewDist &lt; dist(v)) {
          
          dist += v -&gt; vNewDist ;
          pred += v -&gt; u ;
          Q += v ;
        }
      }
  }
  
  // return distances, predecessors, endReached
  Triple( dist, pred, endReached)
}
&lt;/codeblock&gt;

Minimum distance vertex from set.

Note that, in the assume precondition, instead of writing the usual anonymous function as actual parameter in ''Q.elements.forall( v =&gt; dist.isDefinedAt(v) )'' we can specify ''dist.isDefinedAt'' without the parameter, which is a function expression of the required type ''f(V) =&gt; Boolean'' .

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;minimumDistVertexDefinition&gt;&gt;= 

def minimumDistVertex( Q: HashSet[V]): V = {

  assume( ! Q.isEmpty &amp;&amp; Q.elements.forall( dist.isDefinedAt )) ;
           
  val iterator = Q.elements ;
  val w = iterator.next ;          // first element, because Q is not empty

  // calculate and return
  iterator.foldLeft( w) {(u, v) =&gt; if (dist( u) &lt;= dist( v)) u else v}
}
&lt;/codeblock&gt;

Our class &lt;code&gt;WeightedDiGraph&lt;/code&gt; will implement a directed graph with cost info.

It will implement arcs as a dictionary of origins and adjacents collection, which in turn will be a dictionary of destinations with the cost of the arc. 

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;WeightedDiGraph&gt;&gt;=

class WeightedDiGraph[V]() { 

  val arcs = new HashMap[ V, HashMap[ V, Float]] ;
  val vertices = new HashSet[ V] ;
  
  def adjacents( u: V) = arcs( u).keys ;
  def cost( u: V, v: V) = arcs(u)(v) ;

  def addArc( from: V, to: V, kost: Float) = {
    
    if (arcs.contains( from)) {
        val adjMap = arcs( from) ;
        adjMap += to -&gt; kost
    }
    else {
      val adjMap = new HashMap[ V, Float] ;
      adjMap += to -&gt; kost ;
      arcs += from -&gt; adjMap
    }
    
    vertices += from ;
    vertices += to 
  }
   
  &lt;&lt;shortestPath&gt;&gt;

  &lt;&lt;dijkstra&gt;&gt;
}
&lt;/codeblock&gt;

== Test module ==

We will load the XML test data file to a variable of type ''scala.xml.Node'', then we will apply an XPath like operator '''\''' that selects the Node childs of the specified element tag. A similar operator '''\\''' could be used to select descendants with the specified tag as in XPath.
&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;ShortestPathTest.scala&gt;&gt;=
package test;                  // folder: test 

import scala.collection.mutable.{HashSet, HashMap} ;
import scala.xml.XML ;

object ShortestPathTest {

  class MyException( msg: String) extends java.lang.RuntimeException( msg) ;

  &lt;&lt;WeightedDiGraph&gt;&gt;
  
  def main( args: Array[String]) = {
  
      val roadMap = new WeightedDiGraph[ String] ;
                                                   
      val test_data = XML.loadFile( &quot;test_data.xml&quot;) ;
      
      for( val arc &lt;- test_data \ &quot;graph&quot; \ &quot;arc&quot;) {

        val from = arc.attribute(&quot;from&quot;).toString ;
        val to = arc.attribute(&quot;to&quot;).toString ;
        val cost = java.lang.Float.parseFloat( arc.attribute(&quot;cost&quot;).get.toString) ;

        roadMap.addArc( from, to, cost) ;
        roadMap.addArc( to, from, cost) ;
      }
  
      // for each test entry in test_data
    
      for( val test &lt;- test_data \ &quot;sources&quot; \ &quot;test&quot;) {
        
        val source = test.attribute(&quot;source&quot;).toString ;
        val dest = test.attribute(&quot;dest&quot;).toString ;
        
        Console.println(&quot;from &quot; + source + &quot;\n&quot;) ;

        try {
          val route = roadMap.shortestPath( source, dest) ;

          if (route == Nil) {
            Console.println( &quot;No route to &quot; + dest)
          }
          else for( val Pair( city, distance) &lt;- route) {
            Console.println( city + &quot;: &quot; + distance)
          }
        }
        catch {
          case m: MyException =&gt; Console.println( &quot;MyException: &quot;+ m.getMessage)
          case e: Throwable =&gt; Console.println( e.getMessage) ;
        }
          
        Console.println( &quot;--&quot;) ;  
      }
  }
}
&lt;/codeblock&gt;

== Test data ==
[[Image:Europe cities2.png|thumb|right|Example of roadmap distance]]
Approx. roadmap distances.

Barcelona is my city, Lausanne (Switzerland) is the one that hosts the [http://lampwww.epfl.ch EPFL Polythecnics university] where [http://scala.epfl.ch/community/index.html The Scala programming language team] develops the language.

&lt;codeblock language=&quot;xml&quot;&gt;
&lt;&lt;test_data.xml&gt;&gt;=
&lt;?xml version=&quot;1.0&quot; encoding=&quot;ISO-8859-1&quot;?&gt;
&lt;test_data&gt;
	&lt;graph&gt;
		&lt;arc from=&quot;Barcelona&quot; to=&quot;Narbonne&quot; cost=&quot;250&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Marseille&quot; cost=&quot;260&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Toulouse&quot; cost=&quot;150&quot; /&gt;
		&lt;arc from=&quot;Narbonne&quot; to=&quot;Geneve&quot; cost=&quot;550&quot; /&gt;
		&lt;arc from=&quot;Marseille&quot; to=&quot;Geneve&quot; cost=&quot;470&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Paris&quot; cost=&quot;680&quot; /&gt;
		&lt;arc from=&quot;Toulouse&quot; to=&quot;Geneve&quot; cost=&quot;700&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Paris&quot; cost=&quot;540&quot; /&gt;
		&lt;arc from=&quot;Geneve&quot; to=&quot;Lausanne&quot; cost=&quot;64&quot; /&gt;
		&lt;arc from=&quot;Lausanne&quot; to=&quot;Paris&quot; cost=&quot;536&quot; /&gt;
	&lt;/graph&gt;
	&lt;sources&gt;
		&lt;test source=&quot;Barcelona&quot; dest=&quot;Lausanne&quot;/&gt;
		&lt;test source=&quot;Lausanne&quot; dest=&quot;Barcelona&quot;/&gt;
	&lt;/sources&gt;
&lt;/test_data&gt;
&lt;/codeblock&gt;

== Testing ==
[[Image:Europe shortest path.png|thumb|right|The shortest path between Barcelona and Lausanne]]
Compile and run
&lt;pre&gt;
scalac test/ShortestPathTest.scala

scala test.ShortestPathTest
&lt;/pre&gt;

will produce the output
&lt;pre&gt;
from Barcelona

Narbonne: 250.0
Geneve: 800.0
Lausanne: 864.0
--
from Lausanne

Geneve: 64.0
Narbonne: 614.0
Barcelona: 864.0
--
&lt;/pre&gt;

[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]
[[Category:Dijkstra's algorithm]]</text>
    </revision>
  </page>
  <page>
    <title>Dijkstra's shortest path algorithm (Scala)</title>
    <id>2262</id>
    <revision>
      <id>5808</id>
      <timestamp>2006-06-03T18:38:39Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>[[Dijkstra's shortest path algorithm (Scala)]] moved to [[Dijkstra's algorithm (Scala)]]: Consistent with other names - if Wikipedia calls it Dijkstra's algorithm I think that's unambiguous enough</comment>
      <text xml:space="preserve">#REDIRECT [[Dijkstra's algorithm (Scala)]]</text>
    </revision>
  </page>
  <page>
    <title>Dir (Windows)</title>
    <id>1913</id>
    <revision>
      <id>4234</id>
      <timestamp>2006-04-22T00:05:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Dir (Windows) moved to Directory listing (C, Windows): More descriptive name</comment>
      <text xml:space="preserve">#redirect [[Directory listing (C, Windows)]]</text>
    </revision>
  </page>
  <page>
    <title>Directory listing (C, Windows)</title>
    <id>3828</id>
    <revision>
      <id>4229</id>
      <timestamp>2006-04-21T21:39:08Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>A simple dir application who gives detailed output.</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes.

&lt;codeblock language=c&gt;
&lt;&lt;anotherdir.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;win.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  char	tmppath[512];
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
void main()
{
  char pathres[512];
  int  x = 0;

  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4233</id>
      <timestamp>2006-04-22T00:05:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Dir (Windows) moved to Directory listing (C, Windows)</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes.

&lt;codeblock language=c&gt;
&lt;&lt;anotherdir.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;win.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  char	tmppath[512];
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
void main()
{
  char pathres[512];
  int  x = 0;

  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4240</id>
      <timestamp>2006-04-22T00:47:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak to fix highlighting</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;anotherdir.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;win.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  char	tmppath[512];
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
void main()
{
  char pathres[512];
  int  x = 0;

  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4254</id>
      <timestamp>2006-04-22T17:45:40Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <minor/>
      <comment>Changed &quot;filename&quot; to match title</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;win.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  char	tmppath[512];
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
void main()
{
  char pathres[512];
  int  x = 0;

  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4286</id>
      <timestamp>2006-04-25T19:55:49Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ Cat:File management tools</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;win.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  char	tmppath[512];
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
void main()
{
  char pathres[512];
  int  x = 0;

  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>5929</id>
      <timestamp>2006-06-05T15:18:17Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>- unused vars, make main return int, #include&lt;windows.h&gt;</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %'16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : %'8d\n&quot;,attrib_a);
  printf(&quot;Compressed : %'8d\n&quot;,attrib_c);
  printf(&quot;Directory  : %'8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : %'8d\n&quot;,attrib_h);
  printf(&quot;Normal     : %'8d\n&quot;,attrib_n);
  printf(&quot;Offline    : %'8d\n&quot;,attrib_o);
  printf(&quot;Read only  : %'8d\n&quot;,attrib_r);
  printf(&quot;System     : %'8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : %'8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main()
{
  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>5930</id>
      <timestamp>2006-06-05T15:26:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>printf format specifiers</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : % 16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main()
{
  showdir(&quot;c:\\&quot;,1); /* recursive=1 - show all subdirs */

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>5931</id>
      <timestamp>2006-06-05T15:27:43Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Command line args.</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : % 16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
    strcat(outpath,&quot;\\&quot;);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main()
{
  int recursive=0;
  int ndirs=0;

  while(*++argv) {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;)) recursive=1;
    else {showdir(*argv, recursive); ++ndirs;}
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>6234</id>
      <timestamp>2006-06-13T14:08:45Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>argc and *argv[] was missing in main(), fixpath() only returns 1 if it changes anything</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : % 16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
  {
    strcat(outpath,&quot;\\&quot;);
    return 1;
  }

  return 0;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
  int recursive=0;
  int ndirs=0;

  while(*++argv)
  {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;))
      recursive=1;
    else
    {
      showdir(*argv, recursive);
      ++ndirs;
    }
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>13207</id>
      <timestamp>2008-04-22T13:01:49Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : % 16u bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
  {
    strcat(outpath,&quot;\\&quot;);
    return 1;
  }

  return 0;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
  int recursive=0;
  int ndirs=0;

  while(*++argv)
  {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;))
      recursive=1;
    else
    {
      showdir(*argv, recursive);
      ++ndirs;
    }
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>13334</id>
      <timestamp>2008-05-12T16:01:52Z</timestamp>
      <contributor>
        <username>Skim</username>
        <id>37</id>
      </contributor>
      <minor/>
      <comment>To right type.</comment>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(char *path, BOOL recursive);
int     fixpath(char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %16lu bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
  {
    strcat(outpath,&quot;\\&quot;);
    return 1;
  }

  return 0;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
  int recursive=0;
  int ndirs=0;

  while(*++argv)
  {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;))
      recursive=1;
    else
    {
      showdir(*argv, recursive);
      ++ndirs;
    }
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>16461</id>
      <timestamp>2009-06-15T06:31:11Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and it's subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(const char *path, BOOL recursive);
int     fixpath(const char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(const char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %16lu bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(const char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
  {
    strcat(outpath,&quot;\\&quot;);
    return 1;
  }

  return 0;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
  int recursive=0;
  int ndirs=0;

  while(*++argv)
  {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;))
      recursive=1;
    else
    {
      showdir(*argv, recursive);
      ++ndirs;
    }
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
    <revision>
      <id>16958</id>
      <timestamp>2010-10-21T14:37:56Z</timestamp>
      <contributor>
        <username>HarryDymond</username>
        <id>2141</id>
      </contributor>
      <text xml:space="preserve">{{develop}}

This code displays the content of a directory (and its subdirs). It shows detailed information about file attributes. 

&lt;codeblock language=c&gt;
&lt;&lt;directorylisting.c&gt;&gt;=

/*
**
** A simple &quot;dir&quot; application. Shows detailed info.
**
*/

#include &lt;windows.h&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &lt;string.h&gt;

//------------------------------------------------------------------------------------------------------------------
// Globals...
//------------------------------------------------------------------------------------------------------------------
WIN32_FIND_DATA *fd;

//------------------------------------------------------------------------------------------------------------------
// Protos...
//------------------------------------------------------------------------------------------------------------------
int     showdir(const char *path, BOOL recursive);
int     fixpath(const char *inpath, char *outpath);

//------------------------------------------------------------------------------------------------------------------
// showdir()
//------------------------------------------------------------------------------------------------------------------
int showdir(const char *_path,BOOL recursive)
{
  HANDLE fh;
  int    attrib_a=0;
  int    attrib_c=0;
  int    attrib_d=0;
  int    attrib_h=0;
  int    attrib_n=0;
  int    attrib_o=0;
  int    attrib_r=0;
  int    attrib_s=0;
  int    attrib_t=0;
  int    filecnt=0;
  char	 path[MAX_PATH];
  char	 tmppath[MAX_PATH];

  fd = malloc(sizeof(WIN32_FIND_DATA));

  fixpath(_path,path);
  strcat(path,&quot;*&quot;);

  printf(&quot;\nScanning: %s\n&quot;,path);

  fh = FindFirstFile((LPCSTR) path,fd);

  if(fh != INVALID_HANDLE_VALUE)
  {
    do
    {
      filecnt++;
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)
      {
        printf(&quot;[%-33.33s] &quot;,fd-&gt;cFileName);
        if((0 != strcmp(fd-&gt;cFileName,&quot;.&quot;)) &amp;&amp; (0 != strcmp(fd-&gt;cFileName,&quot;..&quot;)))
        {
          fixpath(_path,tmppath);
          strcat(tmppath,fd-&gt;cFileName);
          fixpath(tmppath,tmppath);
          if(recursive)
            showdir(tmppath,recursive);
        }
      }
      else
      {
        printf(&quot;%-35.35s &quot;  ,fd-&gt;cFileName);
      }

      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_ARCHIVE) 		printf(&quot;A&quot;) &amp;&amp; attrib_a++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_COMPRESSED) 	        printf(&quot;C&quot;) &amp;&amp; attrib_c++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_DIRECTORY)		printf(&quot;D&quot;) &amp;&amp; attrib_d++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_HIDDEN)			printf(&quot;H&quot;) &amp;&amp; attrib_h++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_NORMAL)			printf(&quot;N&quot;) &amp;&amp; attrib_n++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_OFFLINE)			printf(&quot;O&quot;) &amp;&amp; attrib_o++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_READONLY)		printf(&quot;R&quot;) &amp;&amp; attrib_r++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_SYSTEM)			printf(&quot;S&quot;) &amp;&amp; attrib_s++ ; else printf(&quot;-&quot;);
      if(fd-&gt;dwFileAttributes &amp; FILE_ATTRIBUTE_TEMPORARY)		printf(&quot;T&quot;) &amp;&amp; attrib_t++ ; else printf(&quot;-&quot;);

      //printf(&quot;Creation time    : %d\n&quot;,fd-&gt;ftCreationTime);
      //printf(&quot;Last access time : %d\n&quot;,fd-&gt;ftLastAccessTime);
      //printf(&quot;Last write time  : %d\n&quot;,fd-&gt;ftLastWriteTime);
      printf(&quot; Size : %16lu bytes\n&quot;,((fd-&gt;nFileSizeHigh * MAXDWORD)+fd-&gt;nFileSizeLow));

    }
    while(FindNextFile(fh,fd));
  }

  printf(&quot;\nStatistics : (%d files)\n&quot;,filecnt);
  printf(&quot;Archived   : % 8d\n&quot;,attrib_a);
  printf(&quot;Compressed : % 8d\n&quot;,attrib_c);
  printf(&quot;Directory  : % 8d\n&quot;,attrib_d);
  printf(&quot;Hidden     : % 8d\n&quot;,attrib_h);
  printf(&quot;Normal     : % 8d\n&quot;,attrib_n);
  printf(&quot;Offline    : % 8d\n&quot;,attrib_o);
  printf(&quot;Read only  : % 8d\n&quot;,attrib_r);
  printf(&quot;System     : % 8d\n&quot;,attrib_s);
  printf(&quot;Temporary  : % 8d\n&quot;,attrib_t);

  FindClose(fh);

  return 1;
}

//------------------------------------------------------------------------------------------------------------------
// fixpath() - Adds \ to the end of a path if not present.
//------------------------------------------------------------------------------------------------------------------
int fixpath(const char *inpath, char *outpath)
{
  int   n=0;

  strcpy(outpath,inpath);

  while(inpath[n]) n++;

  if(inpath[n-1] != '\\')
  {
    strcat(outpath,&quot;\\&quot;);
    return 1;
  }

  return 0;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------
int main(int argc, char *argv[])
{
  int recursive=0;
  int ndirs=0;

  while(*++argv)
  {
    if(!strcmp(*argv, &quot;-r&quot;) || !strcmp(*argv, &quot;/r&quot;))
      recursive=1;
    else
    {
      showdir(*argv, recursive);
      ++ndirs;
    }
  }
  if(!ndirs) showdir(&quot;.&quot;, recursive);

  return 0;
}

&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]
[[Category:File management tools]]</text>
    </revision>
  </page>
  <page>
    <title>Disjoint set data structure (C)</title>
    <id>1729</id>
    <revision>
      <id>2922</id>
      <timestamp>2006-03-08T09:27:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Initial implementation in C, simple and enhanced versions</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. For simplicity we'll assume that our elements are ''int''s:

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct {
    int value;
    struct forest_node_simple* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(int value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    forest_node_simple *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s2));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));
    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct {
    int value;
    struct forest_node* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSetSimple(int value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSetSimple(int value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;union_find.h&gt;

int main() {
    forest_node *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s2));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2924</id>
      <timestamp>2006-03-08T09:29:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix structs</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. For simplicity we'll assume that our elements are ''int''s:

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct {
    int value;
    forest_node_simple* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(int value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    forest_node_simple *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s2));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));
    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct {
    int value;
    forest_node* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSetSimple(int value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSetSimple(int value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;union_find.h&gt;

int main() {
    forest_node *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s2));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2925</id>
      <timestamp>2006-03-08T09:39:27Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Forgot #define, other fixes</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. For simplicity we'll assume that our elements are ''int''s:

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    int value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(int value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    forest_node_simple *s1=MakeSetSimple(1),
    forest_node_simple *s2=MakeSetSimple(2),
    forest_node_simple *s3=MakeSetSimple(3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    int value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(int value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(int value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    forest_node *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2926</id>
      <timestamp>2006-03-08T09:40:48Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix punct</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. For simplicity we'll assume that our elements are ''int''s:

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    int value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(int value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    forest_node_simple *s1=MakeSetSimple(1);
    forest_node_simple *s2=MakeSetSimple(2);
    forest_node_simple *s3=MakeSetSimple(3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    int value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(int value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(int value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    forest_node *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2927</id>
      <timestamp>2006-03-08T09:43:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>int -&gt; void*</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    forest_node_simple *s1=MakeSetSimple(1);
    forest_node_simple *s2=MakeSetSimple(2);
    forest_node_simple *s3=MakeSetSimple(3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    forest_node *s1=MakeSet(1), *s2=MakeSet(2), *s3=MakeSet(3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2928</id>
      <timestamp>2006-03-08T09:45:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix compiler errors</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This already guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2930</id>
      <timestamp>2006-03-08T09:50:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Enhancements */ Name</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2931</id>
      <timestamp>2006-03-08T09:51:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Enhancements */ +There are more efficient approaches that don't require two passes...</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>2973</id>
      <timestamp>2006-03-08T20:26:33Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Note about internal storage</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

When using this data structure in a real application, another option is to embed the forest node properties directly into the structure representing each element (this is known as ''internal storage'').

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>9784</id>
      <timestamp>2007-04-17T04:06:27Z</timestamp>
      <contributor>
        <ip>192.8.220.5</ip>
      </contributor>
      <comment>/* Disjoint set forests */</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

okl;k;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>9786</id>
      <timestamp>2007-04-17T04:49:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

When using this data structure in a real application, another option is to embed the forest node properties directly into the structure representing each element (this is known as ''internal storage'').

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    forest_node* temp;
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>12354</id>
      <timestamp>2008-01-29T09:16:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* Enhancements */ move ''temp'' declaration to top of scope</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

When using this data structure in a real application, another option is to embed the forest node properties directly into the structure representing each element (this is known as ''internal storage'').

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    forest_node* temp;
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>13049</id>
      <timestamp>2008-04-12T05:34:37Z</timestamp>
      <contributor>
        <ip>74.53.104.146</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

http://www.fagictkxbluepill.com/site1/ [url=http://www.fagicizmbluepill.com/site2/]site2[/url] &lt;a href=&quot;http://www.fagickbpbluepill.com/site3/&quot;&gt;site3&lt;/a&gt; &lt;a href=http://www.fagicmdebluepill.com/site4/&gt;site4&lt;/a&gt; [url=&quot;http://www.fagicopvbluepill.com/site5/&quot;]site5[/url] [LINK http://www.fagicjnbbluepill.com/site6/]site6[/LINK] phuir

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    forest_node* temp;
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>13051</id>
      <timestamp>2008-04-12T07:48:29Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

When using this data structure in a real application, another option is to embed the forest node properties directly into the structure representing each element (this is known as ''internal storage'').

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    forest_node* temp;
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = temp;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
    <revision>
      <id>13366</id>
      <timestamp>2008-05-16T18:05:53Z</timestamp>
      <contributor>
        <ip>79.43.56.27</ip>
      </contributor>
      <comment>bug fixed</comment>
      <text xml:space="preserve">{{Category:Disjoint set data structure}}

== Disjoint set forests ==

In a ''disjoint set forest'', we represent each partition using a tree (not necessarily a binary tree). The nodes of the tree have no child pointers, but do have parent pointers. We use void pointers for the values to allow any value to be placed in the data structure (in other languages one would use generics here):

&lt;codeblock language=c&gt;
&lt;&lt;forest node simple&gt;&gt;=
typedef struct forest_node_simple_t {
    void* value;
    struct forest_node_simple_t* parent;
} forest_node_simple;
&lt;/codeblock&gt;

When using this data structure in a real application, another option is to embed the forest node properties directly into the structure representing each element (this is known as ''internal storage'').

Given any node in the tree, we can reach the root by following parent pointers; we let this root node represent the partition as a whole. This gives us our initial find operation:

&lt;codeblock language=c&gt;
&lt;&lt;simple find operation&gt;&gt;=
forest_node_simple* FindSimple(forest_node_simple* node) {
    while (node-&gt;parent != NULL) {
        node = node-&gt;parent;
    }
    return node;
}
&lt;/codeblock&gt;

Merging two trees into one tree is also simple; we just find the root of one of them and attach it to the root of the other by setting its parent pointer:

&lt;codeblock language=c&gt;
&lt;&lt;simple union operation&gt;&gt;=
/* Given the root elements of two trees, merge the trees into one tree */
void UnionSimple(forest_node_simple* node1, forest_node_simple* node2) {
    node2-&gt;parent = node1; /* or node1-&gt;parent = node2; */
}
&lt;/codeblock&gt;

Finally, MakeSet allocates a new node with no parent and places the given value in it:

&lt;codeblock language=c&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;=
forest_node_simple* MakeSetSimple(void* value) {
    forest_node_simple* node = malloc(sizeof(forest_node_simple));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    return node;
}
&lt;/codeblock&gt;

The &lt;code&gt;malloc()&lt;/code&gt; function requires stdlib.h:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;
&lt;/codeblock&gt;

Here's an example of how it might be used:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_simple.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;assert.h&gt;

&lt;&lt;forest node simple&gt;&gt;
&lt;&lt;simple MakeSet operation&gt;&gt;
&lt;&lt;simple find operation&gt;&gt;
&lt;&lt;simple union operation&gt;&gt;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node_simple* s1=MakeSetSimple(&amp;i1);
    forest_node_simple* s2=MakeSetSimple(&amp;i2);
    forest_node_simple* s3=MakeSetSimple(&amp;i3);

    assert(FindSimple(s1) == s1);
    UnionSimple(s1, s2);
    assert(FindSimple(s1) == FindSimple(s2));
    assert(FindSimple(s1) != FindSimple(s3));
    UnionSimple(s2, s3);
    assert(FindSimple(s1) == FindSimple(s2) &amp;&amp;
           FindSimple(s1) == FindSimple(s3));

    return 0;
}
&lt;/codeblock&gt;

== Enhancements ==

Although simple, the algorithm described so far has the problem that the tree can, over many merge operations, develop a large height. Since the find operation takes time proportional to tree height, this can lead to linear worst-case time. Recalling that we can attach either root to the other during a merge, we would ideally always attach the tree of smaller height to the root of the tree of larger height. Unfortunately, height is expensive to calculate, especially without child pointers. Instead, we'll use a rough estimate of height called the ''rank'', stored in the tree's root node:

&lt;codeblock language=c&gt;
&lt;&lt;forest node&gt;&gt;=
typedef struct forest_node_t {
    void* value;
    struct forest_node_t* parent;
    int rank;
} forest_node;
&lt;/codeblock&gt;

Rank is defined as follows:

* MakeSet always produces a tree of rank 0:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* MakeSet(void* value);
&lt;&lt;MakeSet operation&gt;&gt;=
forest_node* MakeSet(void* value) {
    forest_node* node = malloc(sizeof(forest_node));
    node-&gt;value = value;
    node-&gt;parent = NULL;
    node-&gt;rank = 0;
    return node;
}
&lt;/codeblock&gt;

* If rank(s) &amp;ne; rank(t), then rank(Union(s,t)) is the larger of rank(s) and rank(t). In this case, we attach the tree with smaller rank to the root of the tree with larger rank.
* If rank(s) = rank(t), then rank(Union(s,t)) = rank(s) + 1 = rank(t) + 1.

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
void Union(forest_node* node1, forest_node* node2);
&lt;&lt;union operation&gt;&gt;=
void Union(forest_node* node1, forest_node* node2) {
    if (node1-&gt;rank &gt; node2-&gt;rank) {
        node2-&gt;parent = node1;
    } else if (node2-&gt;rank &gt; node1-&gt;rank) {
        node1-&gt;parent = node2;
    } else { /* they are equal */
        node2-&gt;parent = node1;
        node1-&gt;rank++;
    }
}
&lt;/codeblock&gt;

This technique, known as the ''union find heuristic'', guarantees logarithmic height, which is reasonably efficient. But we can do even better by using a technique called ''path compression''. The idea is that all nodes we visit when traversing up from a node to the root are in the same tree, and so they might as well be pointing directly at the root. We make a second pass and update their parent pointers, speeding up future searches involving these nodes dramatically:

&lt;codeblock language=c&gt;
&lt;&lt;declarations&gt;&gt;=
forest_node* Find(forest_node* node);
&lt;&lt;find operation&gt;&gt;=
forest_node* Find(forest_node* node) {
    forest_node* temp;
    /* Find the root */
    forest_node* root = node;
    while (root-&gt;parent != NULL) {
        root = root-&gt;parent;
    }
    /* Update the parent pointers */
    while (node-&gt;parent != NULL) {
        temp = node-&gt;parent;
        node-&gt;parent = root;
        node = temp;
    }
    return root;
}
&lt;/codeblock&gt;

There are more efficient approaches that don't require two passes, but these are more complicated and we won't consider them here.

We can wrap all this up in a source and header files for reuse:

&lt;codeblock language=c&gt;
&lt;&lt;union_find.h&gt;&gt;=
#ifndef _UNION_FIND_H_
#define _UNION_FIND_H_

&lt;&lt;forest node&gt;&gt;
&lt;&lt;declarations&gt;&gt;

#endif /* #ifndef _UNION_FIND_H_ */

&lt;&lt;union_find.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &quot;union_find.h&quot;

&lt;&lt;MakeSet operation&gt;&gt;
&lt;&lt;union operation&gt;&gt;
&lt;&lt;find operation&gt;&gt;
&lt;/codeblock&gt;

Here's some sample usage much like our previous example:

&lt;codeblock language=c&gt;
&lt;&lt;union_find_example.c&gt;&gt;=
#include &lt;assert.h&gt;
#include &quot;union_find.h&quot;

int main() {
    int i1=1, i2=2, i3=3;
    forest_node *s1=MakeSet(&amp;i1), *s2=MakeSet(&amp;i2), *s3=MakeSet(&amp;i3);
    assert(Find(s1) == s1);
    Union(s1, s2);
    assert(Find(s1) == Find(s2));
    assert(Find(s1) != Find(s3));
    Union(s2, s3);
    assert(Find(s1) == Find(s2) &amp;&amp;
           Find(s1) == Find(s3));
    return 0;
}
&lt;/codeblock&gt;

This completes the implementation.

[[Category:Programming language:C]]
[[Category:Environment:Portable]]
[[Category:Disjoint set data structure]]</text>
    </revision>
  </page>
  <page>
    <title>Divisors (C)</title>
    <id>3992</id>
    <revision>
      <id>17035</id>
      <timestamp>2011-02-02T00:58:16Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <comment>added C code with short description</comment>
      <text xml:space="preserve">{{Category:Number Theory}}

This implements the divisors function from number theory in C. Divisors lists the divisors 'd' of a given number n.

&lt;codeblock language=c&gt;
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

int main(int argc, char *argv[])
{
  int d, n;
  n=atoi(argv[1]);

  if(n&gt;1) {
    printf(&quot;1, &quot;);
    for(d=2; d&lt;n; d++) {
      if(n % d == 0) {
        printf(&quot;%d, &quot;,d);
      }
    }
    printf(&quot;%d\n&quot;,n);
  } else if(n==1) {
    printf(&quot;1\n&quot;);
  } else {
    printf(&quot;ERROR: use positive integers only\n&quot;);
  }

  return(0);
}
&lt;/codeblock&gt;


Here are some running examples.
&lt;pre&gt;
$ divisors 12
1, 2, 3, 4, 6, 12
$ divisors 120 
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
$ divisors 6
1, 2, 3, 6
$ divisors 5
1, 5
&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>17049</id>
      <timestamp>2011-02-07T21:07:44Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">{{Category:Number Theory}}

This implements the divisors function from number theory in C. Divisors lists the divisors 'd' of a given number n.

&lt;codeblock language=c&gt;
#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

int main(int argc, char *argv[])
{
  int d, n;
  n=atoi(argv[1]);

  if(n&gt;1) {
    printf(&quot;1, &quot;);
    for(d=2; d&lt;n; d++) {
      if(n % d == 0) {
        printf(&quot;%d, &quot;,d);
      }
    }
    printf(&quot;%d\n&quot;,n);
  } else if(n==1) {
    printf(&quot;1\n&quot;);
  } else {
    printf(&quot;ERROR: use positive integers only\n&quot;);
  }

  return(0);
}
&lt;/codeblock&gt;


Here are some running examples.
&lt;pre&gt;
$ divisors 12
1, 2, 3, 4, 6, 12
$ divisors 120 
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
$ divisors 6
1, 2, 3, 6
$ divisors 5
1, 5
&lt;/pre&gt;


[[Category:Programming language:C]]
[[Category:Mathematics|C]]
[[Category:Number Theory:C]]</text>
    </revision>
  </page>
  <page>
    <title>Doubly linked list (Java)</title>
    <id>2285</id>
    <revision>
      <id>6023</id>
      <timestamp>2006-06-08T13:33:09Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;


&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	public DoublyLinkedList() {
		this.head = new Node(null);
		this.tail = new Node(null);
		this.head.setPrev(null);
		this.head.setNext(this.tail);
		this.tail.setPrev(this.head);
		this.tail.setNext(null);
		this.length = 0;
	}

	public int size() {
		return this.length;
	}
	
	public boolean isEmpty() {
		return this.length == 0;
	}
	
	public Node get(int index) throws IndexOutOfBoundsException {
		if (index &lt; 0 || index &gt; this.length) {
			throw new IndexOutOfBoundsException();
		} else {
			Node cursor = this.head;
			for (int i = 0; i &lt; index; i++) {
				cursor = cursor.getNext();
			}
			return cursor;
		}
	}
	
	public Object remove(int index) throws IndexOutOfBoundsException {
		if (index == 0) {
			throw new IndexOutOfBoundsException();
		} else {
			Node result = this.get(index);
			result.getNext().setPrev(result.getPrev());
			result.getPrev().setNext(result.getNext());
			return result.getValue();
		}
	}
	
	public void add(int index, Object value) throws IndexOutOfBoundsException {
		Node cursor = this.get(index);
		Node temp = new Node(value);
		temp.setPrev(cursor);
		temp.setNext(cursor.getNext());
		cursor.getNext().setPrev(temp);
		cursor.setNext(temp);
		this.length++;
	}

	public void addHead(Object value) {
		this.add(0, value);
	}

	public void addTail(Object value) {
		this.add(this.length, value);
	}

	public String toString() {
		StringBuffer result = new StringBuffer();
		result.append(&quot;(head) - &quot;);
		Node temp = this.head;
		while (temp.getNext() != this.tail) {
			temp = temp.getNext();
			result.append(temp.getValue() + &quot; - &quot;);
		}
		result.append(&quot;(tail)&quot;);
		return result.toString();
	}

	public static void main(String argv[]) {
		DoublyLinkedList list = new DoublyLinkedList();
		list.addHead(new Integer(1));
		list.addHead(new Integer(2));
		list.addTail(new Integer(9));
		list.addHead(new Integer(3));
		list.addTail(new Integer(11));
		list.add(2, new Integer(0));
		System.out.println(list);
		list.remove(list.size());
		System.out.println(list);
	}

	private Node head;
	private Node tail;
	private int length;
}
&lt;/codeblock&gt;
==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Python]]</text>
    </revision>
    <revision>
      <id>6024</id>
      <timestamp>2006-06-08T13:45:15Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* List */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;


&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Python]]</text>
    </revision>
    <revision>
      <id>6026</id>
      <timestamp>2006-06-08T14:26:08Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Node */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. We use &lt;code&gt;Object&lt;/code&gt; class to store any arbitrary data types.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Python]]</text>
    </revision>
    <revision>
      <id>6028</id>
      <timestamp>2006-06-08T14:57:40Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* List */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. We use &lt;code&gt;Object&lt;/code&gt; class to store any arbitrary data types.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

====Constructor====
The constructor sets up an empty list.
# Generate both &lt;code&gt;head&lt;/code&gt; and &lt;code&gt;tail&lt;/code&gt; node.
# Connect the two nodes.
# Initialize the &lt;code&gt;length&lt;/code&gt; variable.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Python]]</text>
    </revision>
    <revision>
      <id>6029</id>
      <timestamp>2006-06-08T15:07:56Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Execution result */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. We use &lt;code&gt;Object&lt;/code&gt; class to store any arbitrary data types.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

====Constructor====
The constructor sets up an empty list.
# Generate both &lt;code&gt;head&lt;/code&gt; and &lt;code&gt;tail&lt;/code&gt; node.
# Connect the two nodes.
# Initialize the &lt;code&gt;length&lt;/code&gt; variable.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>6682</id>
      <timestamp>2006-07-11T12:41:18Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Doubly linked list (Java)]] moved to [[Doubly linked list (Java) on Wheels]]</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. We use &lt;code&gt;Object&lt;/code&gt; class to store any arbitrary data types.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

====Constructor====
The constructor sets up an empty list.
# Generate both &lt;code&gt;head&lt;/code&gt; and &lt;code&gt;tail&lt;/code&gt; node.
# Connect the two nodes.
# Initialize the &lt;code&gt;length&lt;/code&gt; variable.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>6858</id>
      <timestamp>2006-07-11T14:16:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Doubly linked list (Java) on Wheels]] moved to [[Doubly linked list (Java)]]: revert</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. We use &lt;code&gt;Object&lt;/code&gt; class to store any arbitrary data types.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private Object value;
private Node prev;
private Node next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(Object value) {
	this.value = value;
}

Node(Object value, Node prev, Node next) {
	this.value = value;
	this.setPrev(prev);
	this.setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node prev) {
	this.prev = prev;
}

void setNext(Node next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node getPrev() {
	return this.prev;
}

Node getNext() {
	return this.next;
}

Object getValue() {
	return this.value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node head;
private Node tail;
private int length;
&lt;/codeblock&gt;

====Constructor====
The constructor sets up an empty list.
# Generate both &lt;code&gt;head&lt;/code&gt; and &lt;code&gt;tail&lt;/code&gt; node.
# Connect the two nodes.
# Initialize the &lt;code&gt;length&lt;/code&gt; variable.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
public DoublyLinkedList() {
	this.head = new Node(null);
	this.tail = new Node(null);
	this.head.setPrev(null);
	this.head.setNext(this.tail);
	this.tail.setPrev(this.head);
	this.tail.setNext(null);
	this.length = 0;
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; this.length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node cursor = this.head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public Object remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node result = this.get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		this.length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, Object value) throws IndexOutOfBoundsException {
	Node cursor = this.get(index);
	Node temp = new Node(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	this.length++;
}

public void addHead(Object value) {
	this.add(0, value);
}

public void addTail(Object value) {
	this.add(this.length, value);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return this.length;
}
	
public boolean isEmpty() {
	return this.length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node temp = this.head;
	while (temp.getNext() != this.tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList list = new DoublyLinkedList();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>11973</id>
      <timestamp>2008-01-09T00:57:01Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>15775</id>
      <timestamp>2009-01-04T12:25:52Z</timestamp>
      <contributor>
        <ip>212.239.17.140</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

http://www.message_dronro.com/

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>15776</id>
      <timestamp>2009-01-04T15:42:50Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/212.239.17.140|212.239.17.140]] ([[User_talk:212.239.17.140|212.239.17.140]]); changed back to last version by [[User:Spoon!|Spoon!]]</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16026</id>
      <timestamp>2009-01-24T09:04:53Z</timestamp>
      <contributor>
        <ip>72.197.139.55</ip>
      </contributor>
      <comment>/* Constructor */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;
Check

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16027</id>
      <timestamp>2009-01-24T09:06:01Z</timestamp>
      <contributor>
        <ip>72.197.139.55</ip>
      </contributor>
      <comment>/* Constructor */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16032</id>
      <timestamp>2009-01-25T02:37:53Z</timestamp>
      <contributor>
        <ip>67.110.213.10</ip>
      </contributor>
      <comment>/* Code */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work.
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16033</id>
      <timestamp>2009-01-25T08:16:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <comment>/* Code */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16109</id>
      <timestamp>2009-02-05T17:08:31Z</timestamp>
      <contributor>
        <ip>131.216.48.244</ip>
      </contributor>
      <comment>/* Add a node */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
        System.out.println(&quot;LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL&quot;);
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
        System.out.println(&quot;LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL&quot;);
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
        System.out.println(&quot;LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL&quot;);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16110</id>
      <timestamp>2009-02-05T17:24:40Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/131.216.48.244|131.216.48.244]] ([[User_talk:131.216.48.244|131.216.48.244]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16111</id>
      <timestamp>2009-02-05T17:35:09Z</timestamp>
      <contributor>
        <ip>131.216.48.244</ip>
      </contributor>
      <comment>/* Add a node */</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
System.out.println(&quot;LOL&quot;);
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16112</id>
      <timestamp>2009-02-05T18:43:17Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/131.216.48.244|131.216.48.244]] ([[User_talk:131.216.48.244|131.216.48.244]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
    <revision>
      <id>16871</id>
      <timestamp>2010-09-23T13:21:03Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">'''YEEEEEEEEEEEE HAAAAAAAAAAAA!'''</text>
    </revision>
    <revision>
      <id>16899</id>
      <timestamp>2010-09-23T15:48:39Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">This is a simple implementation of a [http://en.wikipedia.org/wiki/Linked_list#Doubly-linked_list doubly-linked list]. Although Java SDK provides &lt;code&gt;LinkedList&lt;/code&gt; class, it is not difficult to write a doubly-linked list class from scratch.

A doubly linked list is composed of two classes - the list itself and the node in the list.
==Code==
I would like to point out that this code as of jdk-1.6.0 does not work. -- anon
:That's true. We need to go back to the pre-Generic version. -- [[User:Derek Ross|Derek Ross]] | [[User talk:Derek Ross|Talk]] 03:16, 25 January 2009 (EST)
===Node===
The Node class is not defined as a public class; rather, it is defined as '''package friendly.''' It means that this class is visible only inside of this package.
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
class Node&lt;E&gt; {
	&lt;&lt;Node_constructor&gt;&gt;

	&lt;&lt;Node_setter&gt;&gt;

	&lt;&lt;Node_getter&gt;&gt;

	&lt;&lt;Node_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Doubly-linked-node.png|framed|right|A node in a doubly linked list]]
* &lt;code&gt;value&lt;/code&gt; stores the data in a node. Its type is a generic type parameter &lt;code&gt;E&lt;/code&gt;, so we can ensure that we are storing the right data type.
* &lt;code&gt;prev&lt;/code&gt; points to the previous node in a doubly linked list.
* &lt;code&gt;next&lt;/code&gt; points to the next node in a doubly linked list.
&lt;codeblock language=java&gt;
&lt;&lt;Node_data&gt;&gt;=
private E value;
private Node&lt;E&gt; prev;
private Node&lt;E&gt; next;
&lt;/codeblock&gt;

====Constructor====
&lt;codeblock language=java&gt;
&lt;&lt;Node_constructor&gt;&gt;=
Node(E value) {
	this.value = value;
}

Node(E value, Node&lt;E&gt; prev, Node&lt;E&gt; next) {
	this.value = value;
	setPrev(prev);
	setNext(next);
}
&lt;/codeblock&gt;

====Setter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_setter&gt;&gt;=
void setPrev(Node&lt;E&gt; prev) {
	this.prev = prev;
}

void setNext(Node&lt;E&gt; next) {
	this.next = next;
}
&lt;/codeblock&gt;

====Getter====
&lt;codeblock language=java&gt;
&lt;&lt;Node_getter&gt;&gt;=
Node&lt;E&gt; getPrev() {
	return prev;
}

Node&lt;E&gt; getNext() {
	return next;
}

E getValue() {
	return value;
}
&lt;/codeblock&gt;

===List===
&lt;codeblock language=java&gt;
&lt;&lt;DoublyLinkedList.java&gt;&gt;=
public class DoublyLinkedList&lt;E&gt; {
	&lt;&lt;List_construct&gt;&gt;

	&lt;&lt;List_get&gt;&gt;

	&lt;&lt;List_remove&gt;&gt;
	
	&lt;&lt;List_add&gt;&gt;

	&lt;&lt;List_utils&gt;&gt;

	&lt;&lt;List_test&gt;&gt;

	&lt;&lt;List_data&gt;&gt;
}
&lt;/codeblock&gt;

====Data====
[[Image:Empty Doubly linked list.png|framed|right|An empty doubly linked list.]]
* &lt;code&gt;head&lt;/code&gt;: a dummy node for the head of a list
* &lt;code&gt;tail&lt;/code&gt;: a dummy node for the end of a list
* &lt;code&gt;length&lt;/code&gt;: the length of nodes in a list, initialized to 0.
&lt;codeblock language=java&gt;
&lt;&lt;List_data&gt;&gt;=
private Node&lt;E&gt; head = new Node&lt;E&gt;(null);
private Node&lt;E&gt; tail = new Node&lt;E&gt;(null);
private int length = 0;
&lt;/codeblock&gt;

====Initializer block====
The initializer block connects the head and tail nodes. We could do this in a constructor; but it is not necessary in this case because the initialization is not dependent on any inputs.
&lt;codeblock language=java&gt;
&lt;&lt;List_construct&gt;&gt;=
{
	head.setPrev(null);
	head.setNext(tail);
	tail.setPrev(head);
	tail.setNext(null);
}
&lt;/codeblock&gt;

====Get a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_get&gt;&gt;=
public Node&lt;E&gt; get(int index) throws IndexOutOfBoundsException {
	if (index &lt; 0 || index &gt; length) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; cursor = head;
		for (int i = 0; i &lt; index; i++) {
			cursor = cursor.getNext();
		}
		return cursor;
	}
}
&lt;/codeblock&gt;

====Remove a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_remove&gt;&gt;=
public E remove(int index) throws IndexOutOfBoundsException {
	if (index == 0) {
		throw new IndexOutOfBoundsException();
	} else {
		Node&lt;E&gt; result = get(index);
		result.getNext().setPrev(result.getPrev());
		result.getPrev().setNext(result.getNext());
		length--;
		return result.getValue();
	}
}
&lt;/codeblock&gt;

====Add a node====
&lt;codeblock language=java&gt;
&lt;&lt;List_add&gt;&gt;=
public void add(int index, E value) throws IndexOutOfBoundsException {
	Node&lt;E&gt; cursor = get(index);
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addHead(E value) {
	Node&lt;E&gt; cursor = head;
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}

public void addTail(E value) {
	Node&lt;E&gt; cursor = tail.getPrev();
	Node&lt;E&gt; temp = new Node&lt;E&gt;(value);
	temp.setPrev(cursor);
	temp.setNext(cursor.getNext());
	cursor.getNext().setPrev(temp);
	cursor.setNext(temp);
	length++;
}
&lt;/codeblock&gt;

====Utilities====
&lt;codeblock language=java&gt;
&lt;&lt;List_utils&gt;&gt;=
public int size() {
	return length;
}
	
public boolean isEmpty() {
	return length == 0;
}
	
public String toString() {
	StringBuffer result = new StringBuffer();
	result.append(&quot;(head) - &quot;);
	Node&lt;E&gt; temp = head;
	while (temp.getNext() != tail) {
		temp = temp.getNext();
		result.append(temp.getValue() + &quot; - &quot;);
	}
	result.append(&quot;(tail)&quot;);
	return result.toString();
}
&lt;/codeblock&gt;

====Test====
&lt;codeblock language=java&gt;
&lt;&lt;List_test&gt;&gt;=
public static void main(String argv[]) {
	DoublyLinkedList&lt;Integer&gt; list = new DoublyLinkedList&lt;Integer&gt;();
	list.addHead(new Integer(1));
	list.addHead(new Integer(2));
	list.addTail(new Integer(9));
	list.addHead(new Integer(3));
	list.addTail(new Integer(11));
	list.add(2, new Integer(0));
	System.out.println(list);
	list.remove(list.size());
	System.out.println(list);
}
&lt;/codeblock&gt;

==Execution result==

[[Category:Programming language:Java]]
[[Category:Environment:Portable]]
[[Category:Doubly linked list|Java]]</text>
    </revision>
  </page>
  <page>
    <title>Drawing Petersen graph (Pic)</title>
    <id>2284</id>
    <revision>
      <id>6019</id>
      <timestamp>2006-06-08T08:31:39Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">[[Image:Petersen.png|framed|A Petersen graph]]
The [http://en.wikipedia.org/wiki/Petersen_graph Petersen graph] is a graph possessing ten vertices, all of which have degree three. This article explains how to draw a Petersen graph using pic, a small language to create 'box-and-arrow' diagram.

==How to convert PIC document to graphic file format==
A pic document can be converted to various graphic file format such as EPS and PNG following these steps.
# Write a pic document.
# Convert it to TeX picture commands.
# Embed it into a LaTeX document.
# Compile it to a EPS document.
# Convert EPS document to any graphic file format.
The exact steps is omitted because a detailed explanation is available at [[Hello World (Pic)]].

==Code==
===Main source code===
Every pic source begins with &lt;code&gt;.PS&lt;/code&gt; and ends with &lt;code&gt;.PE&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;petersen.pic&gt;&gt;=
.PS

&lt;&lt;init&gt;&gt;

&lt;&lt;points&gt;&gt;

&lt;&lt;lines&gt;&gt;

.PE
&lt;/codeblock&gt;

===Initialization===
The default unit in pic is inch.
* &lt;code&gt;circlerad&lt;/code&gt;: the radius of a circle - used for each node in graph
* &lt;code&gt;fillval&lt;/code&gt;: the gray scale used to fill a shape.
* &lt;code&gt;r1&lt;/code&gt;: the distance from the center of a Petersen graph to five inner vertices.
* &lt;code&gt;r2&lt;/code&gt;: the distance from the center of a Petersen graph to five outer vertices.
* &lt;code&gt;pi&lt;/code&gt;: 3.141592
&lt;codeblock language=pic&gt;
&lt;&lt;init&gt;&gt;=
circlerad = .12
fillval = .95
r1 = .5
r2 = 2 * r1
pi = atan2(0, -1)
&lt;/codeblock&gt;

===Drawing Vertices===
We will use a rectangular coordinate system to draw ten vertices in a Petersen graph. We choose the center of a Petersen graph as origin for convenience. The drawing process is simply drawing two pentagons.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
O: (0,0)

P0: circle fill &quot;0&quot; at O + (0, r2)
P1: circle fill &quot;1&quot; at O + (r2 * cos(9 * pi / 10),  r2 * sin(9 * pi / 10))
P2: circle fill &quot;2&quot; at O + (r2 * cos(13 * pi / 10), r2 * sin(13 * pi / 10))
P3: circle fill &quot;3&quot; at O + (r2 * cos(17 * pi / 10), r2 * sin(17 * pi / 10))
P4: circle fill &quot;4&quot; at O + (r2 * cos(pi / 10),      r2 * sin(pi / 10))

P5: circle fill &quot;5&quot; at O + (0, r1)
P8: circle fill &quot;8&quot; at O + (r1 * cos(9 * pi / 10),  r1 * sin(9 * pi / 10))
P6: circle fill &quot;6&quot; at O + (r1 * cos(13 * pi / 10), r1 * sin(13 * pi / 10))
P9: circle fill &quot;9&quot; at O + (r1 * cos(17 * pi / 10), r1 * sin(17 * pi / 10))
P7: circle fill &quot;7&quot; at O + (r1 * cos(pi / 10),      r1 * sin(pi / 10))
&lt;/codeblock&gt;
Each circle is named for later use.

===Connecting each vertices===
Finally, we connec each vertices. Thanks to the &lt;code&gt;chop&lt;/code&gt; command, we could easily chop off each line.

&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P1 chop
line from P1 chop to P2 chop
line from P2 chop to P3 chop
line from P3 chop to P4 chop
line from P4 chop to P0 chop

line from P0 chop to P5 chop
line from P1 chop to P8 chop
line from P2 chop to P6 chop
line from P3 chop to P9 chop
line from P4 chop to P7 chop

line from P5 chop to P6 chop
line from P6 chop to P7 chop
line from P7 chop to P8 chop
line from P8 chop to P9 chop
line from P9 chop to P5 chop
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6020</id>
      <timestamp>2006-06-08T08:48:54Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">[[Image:Petersen.png|framed|A Petersen graph]]
The [http://en.wikipedia.org/wiki/Petersen_graph Petersen graph] is a graph possessing ten vertices, all of which have degree three. This article explains how to draw a Petersen graph using pic, a small language to create 'box-and-arrow' diagrams.

==How to convert PIC document to graphic file format==
A pic document can be converted to various graphic file format such as EPS and PNG following these steps.
# Write a pic document.
# Convert it to TeX picture commands.
# Embed it into a LaTeX document.
# Compile it to a EPS document.
# Convert EPS document to any graphic file format.
The exact steps are omitted because a detailed explanation is available at [[Hello World (Pic)]].

==Code==
===Main source code===
Every pic source begins with &lt;code&gt;.PS&lt;/code&gt; and ends with &lt;code&gt;.PE&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;petersen.pic&gt;&gt;=
.PS

&lt;&lt;init&gt;&gt;

&lt;&lt;points&gt;&gt;

&lt;&lt;lines&gt;&gt;

.PE
&lt;/codeblock&gt;
We initialize several variables, draw ten vertices, and finally connect every vertices.

===Initialization===
We initialize several system variables that will be used throughout the code. The default unit in pic is inch.
* &lt;code&gt;circlerad&lt;/code&gt;: the radius of a circle - used for each node in graph
* &lt;code&gt;fillval&lt;/code&gt;: the gray scale used to fill a shape.
* &lt;code&gt;r1&lt;/code&gt;: the distance from the center of a Petersen graph to five inner vertices.
* &lt;code&gt;r2&lt;/code&gt;: the distance from the center of a Petersen graph to five outer vertices.
* &lt;code&gt;pi&lt;/code&gt;: &lt;math&gt;\pi&lt;/math&gt;
&lt;codeblock language=pic&gt;
&lt;&lt;init&gt;&gt;=
circlerad = .12
fillval = .95
r1 = .5
r2 = 2 * r1
pi = atan2(0, -1)
&lt;/codeblock&gt;

===Drawing ten vertices===
We will use a rectangular coordinate system to draw ten vertices in a Petersen graph. The drawing process is simply plotting five points in each pentagons.

We choose the center of a Petersen graph as origin for convenience.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
O: (0,0)
&lt;/codeblock&gt;
Then we draw five circles for an outer pentagon.
&lt;codeblock&gt;
P0: circle fill &quot;0&quot; at O + (0, r2)
P1: circle fill &quot;1&quot; at O + (r2 * cos(9 * pi / 10),  r2 * sin(9 * pi / 10))
P2: circle fill &quot;2&quot; at O + (r2 * cos(13 * pi / 10), r2 * sin(13 * pi / 10))
P3: circle fill &quot;3&quot; at O + (r2 * cos(17 * pi / 10), r2 * sin(17 * pi / 10))
P4: circle fill &quot;4&quot; at O + (r2 * cos(pi / 10),      r2 * sin(pi / 10))
&lt;/codeblock&gt;
Finally, we draw five circles for an inner pentagon.
&lt;codeblock&gt;
P5: circle fill &quot;5&quot; at O + (0, r1)
P8: circle fill &quot;8&quot; at O + (r1 * cos(9 * pi / 10),  r1 * sin(9 * pi / 10))
P6: circle fill &quot;6&quot; at O + (r1 * cos(13 * pi / 10), r1 * sin(13 * pi / 10))
P9: circle fill &quot;9&quot; at O + (r1 * cos(17 * pi / 10), r1 * sin(17 * pi / 10))
P7: circle fill &quot;7&quot; at O + (r1 * cos(pi / 10),      r1 * sin(pi / 10))
&lt;/codeblock&gt;
Each circle is named for later use.

===Connecting each vertex===
The last step is connecting each circle. Thanks to the &lt;code&gt;chop&lt;/code&gt; command, we could easily chop off each line.

First, we draw an outer pentagon connecting every two contiguous vertices.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P1 chop
line from P1 chop to P2 chop
line from P2 chop to P3 chop
line from P3 chop to P4 chop
line from P4 chop to P0 chop
&lt;/codeblock&gt;

Next, we connect each corresponding vertex between two pentagons.
&lt;codeblock&gt;
line from P0 chop to P5 chop
line from P1 chop to P8 chop
line from P2 chop to P6 chop
line from P3 chop to P9 chop
line from P4 chop to P7 chop
&lt;/codeblock&gt;

Finally, we draw a set of star-shaped lines for an inner pentagon.
&lt;codeblock&gt;
line from P5 chop to P6 chop
line from P6 chop to P7 chop
line from P7 chop to P8 chop
line from P8 chop to P9 chop
line from P9 chop to P5 chop
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6022</id>
      <timestamp>2006-06-08T10:45:33Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>fix chunk names</comment>
      <text xml:space="preserve">[[Image:Petersen.png|framed|A Petersen graph]]
The [http://en.wikipedia.org/wiki/Petersen_graph Petersen graph] is a graph possessing ten vertices, all of which have degree three. This article explains how to draw a Petersen graph using pic, a small language to create 'box-and-arrow' diagrams.

==How to convert PIC document to graphic file format==
A pic document can be converted to various graphic file format such as EPS and PNG following these steps.
# Write a pic document.
# Convert it to TeX picture commands.
# Embed it into a LaTeX document.
# Compile it to a EPS document.
# Convert EPS document to any graphic file format.
The exact steps are omitted because a detailed explanation is available at [[Hello World (Pic)]].

==Code==
===Main source code===
Every pic source begins with &lt;code&gt;.PS&lt;/code&gt; and ends with &lt;code&gt;.PE&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;petersen.pic&gt;&gt;=
.PS

&lt;&lt;init&gt;&gt;

&lt;&lt;points&gt;&gt;

&lt;&lt;lines&gt;&gt;

.PE
&lt;/codeblock&gt;
We initialize several variables, draw ten vertices, and finally connect every vertices.

===Initialization===
We initialize several system variables that will be used throughout the code. The default unit in pic is inch.
* &lt;code&gt;circlerad&lt;/code&gt;: the radius of a circle - used for each node in graph
* &lt;code&gt;fillval&lt;/code&gt;: the gray scale used to fill a shape.
* &lt;code&gt;r1&lt;/code&gt;: the distance from the center of a Petersen graph to five inner vertices.
* &lt;code&gt;r2&lt;/code&gt;: the distance from the center of a Petersen graph to five outer vertices.
* &lt;code&gt;pi&lt;/code&gt;: &lt;math&gt;\pi&lt;/math&gt;
&lt;codeblock language=pic&gt;
&lt;&lt;init&gt;&gt;=
circlerad = .12
fillval = .95
r1 = .5
r2 = 2 * r1
pi = atan2(0, -1)
&lt;/codeblock&gt;

===Drawing ten vertices===
We will use a rectangular coordinate system to draw ten vertices in a Petersen graph. The drawing process is simply plotting five points in each pentagons.

We choose the center of a Petersen graph as origin for convenience.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
O: (0,0)
&lt;/codeblock&gt;
Then we draw five circles for an outer pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P0: circle fill &quot;0&quot; at O + (0, r2)
P1: circle fill &quot;1&quot; at O + (r2 * cos(9 * pi / 10),  r2 * sin(9 * pi / 10))
P2: circle fill &quot;2&quot; at O + (r2 * cos(13 * pi / 10), r2 * sin(13 * pi / 10))
P3: circle fill &quot;3&quot; at O + (r2 * cos(17 * pi / 10), r2 * sin(17 * pi / 10))
P4: circle fill &quot;4&quot; at O + (r2 * cos(pi / 10),      r2 * sin(pi / 10))
&lt;/codeblock&gt;
Finally, we draw five circles for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P5: circle fill &quot;5&quot; at O + (0, r1)
P8: circle fill &quot;8&quot; at O + (r1 * cos(9 * pi / 10),  r1 * sin(9 * pi / 10))
P6: circle fill &quot;6&quot; at O + (r1 * cos(13 * pi / 10), r1 * sin(13 * pi / 10))
P9: circle fill &quot;9&quot; at O + (r1 * cos(17 * pi / 10), r1 * sin(17 * pi / 10))
P7: circle fill &quot;7&quot; at O + (r1 * cos(pi / 10),      r1 * sin(pi / 10))
&lt;/codeblock&gt;
Each circle is named for later use.

===Connecting each vertex===
The last step is connecting each circle. Thanks to the &lt;code&gt;chop&lt;/code&gt; command, we could easily chop off each line.

First, we draw an outer pentagon connecting every two contiguous vertices.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P1 chop
line from P1 chop to P2 chop
line from P2 chop to P3 chop
line from P3 chop to P4 chop
line from P4 chop to P0 chop
&lt;/codeblock&gt;

Next, we connect each corresponding vertex between two pentagons.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P5 chop
line from P1 chop to P8 chop
line from P2 chop to P6 chop
line from P3 chop to P9 chop
line from P4 chop to P7 chop
&lt;/codeblock&gt;

Finally, we draw a set of star-shaped lines for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P5 chop to P6 chop
line from P6 chop to P7 chop
line from P7 chop to P8 chop
line from P8 chop to P9 chop
line from P9 chop to P5 chop
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6840</id>
      <timestamp>2006-07-11T12:47:54Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Drawing Petersen graph (Pic)]] moved to [[Drawing Petersen graph (Pic) on Wheels]]</comment>
      <text xml:space="preserve">[[Image:Petersen.png|framed|A Petersen graph]]
The [http://en.wikipedia.org/wiki/Petersen_graph Petersen graph] is a graph possessing ten vertices, all of which have degree three. This article explains how to draw a Petersen graph using pic, a small language to create 'box-and-arrow' diagrams.

==How to convert PIC document to graphic file format==
A pic document can be converted to various graphic file format such as EPS and PNG following these steps.
# Write a pic document.
# Convert it to TeX picture commands.
# Embed it into a LaTeX document.
# Compile it to a EPS document.
# Convert EPS document to any graphic file format.
The exact steps are omitted because a detailed explanation is available at [[Hello World (Pic)]].

==Code==
===Main source code===
Every pic source begins with &lt;code&gt;.PS&lt;/code&gt; and ends with &lt;code&gt;.PE&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;petersen.pic&gt;&gt;=
.PS

&lt;&lt;init&gt;&gt;

&lt;&lt;points&gt;&gt;

&lt;&lt;lines&gt;&gt;

.PE
&lt;/codeblock&gt;
We initialize several variables, draw ten vertices, and finally connect every vertices.

===Initialization===
We initialize several system variables that will be used throughout the code. The default unit in pic is inch.
* &lt;code&gt;circlerad&lt;/code&gt;: the radius of a circle - used for each node in graph
* &lt;code&gt;fillval&lt;/code&gt;: the gray scale used to fill a shape.
* &lt;code&gt;r1&lt;/code&gt;: the distance from the center of a Petersen graph to five inner vertices.
* &lt;code&gt;r2&lt;/code&gt;: the distance from the center of a Petersen graph to five outer vertices.
* &lt;code&gt;pi&lt;/code&gt;: &lt;math&gt;\pi&lt;/math&gt;
&lt;codeblock language=pic&gt;
&lt;&lt;init&gt;&gt;=
circlerad = .12
fillval = .95
r1 = .5
r2 = 2 * r1
pi = atan2(0, -1)
&lt;/codeblock&gt;

===Drawing ten vertices===
We will use a rectangular coordinate system to draw ten vertices in a Petersen graph. The drawing process is simply plotting five points in each pentagons.

We choose the center of a Petersen graph as origin for convenience.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
O: (0,0)
&lt;/codeblock&gt;
Then we draw five circles for an outer pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P0: circle fill &quot;0&quot; at O + (0, r2)
P1: circle fill &quot;1&quot; at O + (r2 * cos(9 * pi / 10),  r2 * sin(9 * pi / 10))
P2: circle fill &quot;2&quot; at O + (r2 * cos(13 * pi / 10), r2 * sin(13 * pi / 10))
P3: circle fill &quot;3&quot; at O + (r2 * cos(17 * pi / 10), r2 * sin(17 * pi / 10))
P4: circle fill &quot;4&quot; at O + (r2 * cos(pi / 10),      r2 * sin(pi / 10))
&lt;/codeblock&gt;
Finally, we draw five circles for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P5: circle fill &quot;5&quot; at O + (0, r1)
P8: circle fill &quot;8&quot; at O + (r1 * cos(9 * pi / 10),  r1 * sin(9 * pi / 10))
P6: circle fill &quot;6&quot; at O + (r1 * cos(13 * pi / 10), r1 * sin(13 * pi / 10))
P9: circle fill &quot;9&quot; at O + (r1 * cos(17 * pi / 10), r1 * sin(17 * pi / 10))
P7: circle fill &quot;7&quot; at O + (r1 * cos(pi / 10),      r1 * sin(pi / 10))
&lt;/codeblock&gt;
Each circle is named for later use.

===Connecting each vertex===
The last step is connecting each circle. Thanks to the &lt;code&gt;chop&lt;/code&gt; command, we could easily chop off each line.

First, we draw an outer pentagon connecting every two contiguous vertices.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P1 chop
line from P1 chop to P2 chop
line from P2 chop to P3 chop
line from P3 chop to P4 chop
line from P4 chop to P0 chop
&lt;/codeblock&gt;

Next, we connect each corresponding vertex between two pentagons.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P5 chop
line from P1 chop to P8 chop
line from P2 chop to P6 chop
line from P3 chop to P9 chop
line from P4 chop to P7 chop
&lt;/codeblock&gt;

Finally, we draw a set of star-shaped lines for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P5 chop to P6 chop
line from P6 chop to P7 chop
line from P7 chop to P8 chop
line from P8 chop to P9 chop
line from P9 chop to P5 chop
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7000</id>
      <timestamp>2006-07-11T14:29:34Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Drawing Petersen graph (Pic) on Wheels]] moved to [[Drawing Petersen graph (Pic)]]: revert</comment>
      <text xml:space="preserve">[[Image:Petersen.png|framed|A Petersen graph]]
The [http://en.wikipedia.org/wiki/Petersen_graph Petersen graph] is a graph possessing ten vertices, all of which have degree three. This article explains how to draw a Petersen graph using pic, a small language to create 'box-and-arrow' diagrams.

==How to convert PIC document to graphic file format==
A pic document can be converted to various graphic file format such as EPS and PNG following these steps.
# Write a pic document.
# Convert it to TeX picture commands.
# Embed it into a LaTeX document.
# Compile it to a EPS document.
# Convert EPS document to any graphic file format.
The exact steps are omitted because a detailed explanation is available at [[Hello World (Pic)]].

==Code==
===Main source code===
Every pic source begins with &lt;code&gt;.PS&lt;/code&gt; and ends with &lt;code&gt;.PE&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;petersen.pic&gt;&gt;=
.PS

&lt;&lt;init&gt;&gt;

&lt;&lt;points&gt;&gt;

&lt;&lt;lines&gt;&gt;

.PE
&lt;/codeblock&gt;
We initialize several variables, draw ten vertices, and finally connect every vertices.

===Initialization===
We initialize several system variables that will be used throughout the code. The default unit in pic is inch.
* &lt;code&gt;circlerad&lt;/code&gt;: the radius of a circle - used for each node in graph
* &lt;code&gt;fillval&lt;/code&gt;: the gray scale used to fill a shape.
* &lt;code&gt;r1&lt;/code&gt;: the distance from the center of a Petersen graph to five inner vertices.
* &lt;code&gt;r2&lt;/code&gt;: the distance from the center of a Petersen graph to five outer vertices.
* &lt;code&gt;pi&lt;/code&gt;: &lt;math&gt;\pi&lt;/math&gt;
&lt;codeblock language=pic&gt;
&lt;&lt;init&gt;&gt;=
circlerad = .12
fillval = .95
r1 = .5
r2 = 2 * r1
pi = atan2(0, -1)
&lt;/codeblock&gt;

===Drawing ten vertices===
We will use a rectangular coordinate system to draw ten vertices in a Petersen graph. The drawing process is simply plotting five points in each pentagons.

We choose the center of a Petersen graph as origin for convenience.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
O: (0,0)
&lt;/codeblock&gt;
Then we draw five circles for an outer pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P0: circle fill &quot;0&quot; at O + (0, r2)
P1: circle fill &quot;1&quot; at O + (r2 * cos(9 * pi / 10),  r2 * sin(9 * pi / 10))
P2: circle fill &quot;2&quot; at O + (r2 * cos(13 * pi / 10), r2 * sin(13 * pi / 10))
P3: circle fill &quot;3&quot; at O + (r2 * cos(17 * pi / 10), r2 * sin(17 * pi / 10))
P4: circle fill &quot;4&quot; at O + (r2 * cos(pi / 10),      r2 * sin(pi / 10))
&lt;/codeblock&gt;
Finally, we draw five circles for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;points&gt;&gt;=
P5: circle fill &quot;5&quot; at O + (0, r1)
P8: circle fill &quot;8&quot; at O + (r1 * cos(9 * pi / 10),  r1 * sin(9 * pi / 10))
P6: circle fill &quot;6&quot; at O + (r1 * cos(13 * pi / 10), r1 * sin(13 * pi / 10))
P9: circle fill &quot;9&quot; at O + (r1 * cos(17 * pi / 10), r1 * sin(17 * pi / 10))
P7: circle fill &quot;7&quot; at O + (r1 * cos(pi / 10),      r1 * sin(pi / 10))
&lt;/codeblock&gt;
Each circle is named for later use.

===Connecting each vertex===
The last step is connecting each circle. Thanks to the &lt;code&gt;chop&lt;/code&gt; command, we could easily chop off each line.

First, we draw an outer pentagon connecting every two contiguous vertices.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P1 chop
line from P1 chop to P2 chop
line from P2 chop to P3 chop
line from P3 chop to P4 chop
line from P4 chop to P0 chop
&lt;/codeblock&gt;

Next, we connect each corresponding vertex between two pentagons.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P0 chop to P5 chop
line from P1 chop to P8 chop
line from P2 chop to P6 chop
line from P3 chop to P9 chop
line from P4 chop to P7 chop
&lt;/codeblock&gt;

Finally, we draw a set of star-shaped lines for an inner pentagon.
&lt;codeblock&gt;
&lt;&lt;lines&gt;&gt;=
line from P5 chop to P6 chop
line from P6 chop to P7 chop
line from P7 chop to P8 chop
line from P8 chop to P9 chop
line from P9 chop to P5 chop
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Drawing convex hull (Pic)</title>
    <id>2296</id>
    <revision>
      <id>6069</id>
      <timestamp>2006-06-09T12:06:22Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">The [[convex hull]] of a set of points ''Q'' is the smallest polygon that embraces every point in ''Q''. This article explains how to draw a convex hull diagram using pic. The exact steps to convert a pic document into a graphic format is available at [[Hello World (Pic)]].

==Plotting random points==
[[Image:Scattered_Points.png|framed|Thirteen random points in a 2-D plane.]]
We first choose thirteen points and scatter them to a 2-dimensional plane.
  P1: ( 1,  3)
  P2: ( 2,  7)
  P3: ( 9, -2)
  P4: (-5,  7)
  P5: (-7,  2)
  P6: (-1,  3)
  P7: ( 4,  6)
  P8: (-3, -4)
  P9: ( 6,  0)
 P10: (-2,  8)
 P11: ( 0, -5)
 P12: ( 5,  8)
 P13: (-4, -1)

We draw a circle at each coordinate. Note that we need the label for each point for later use.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
P1: circle fill at (1, 3)
P2: circle fill at (2, 7)
P3: circle fill at (9, -2)
P4: circle fill at (-5, 7)
P5: circle fill at (-7, 2)
P6: circle fill at (-1, 3)
P7: circle fill at (4, 6)
P8: circle fill at (-3, -4)
P9: circle fill at (6, 0)
P10: circle fill at (-2, 8)
P11: circle fill at (0, -5)
P12: circle fill at (5, 8)
P13: circle fill at (-4, -1)
&lt;/codeblock&gt;

We place the name of each point at every coordinate. Note that special &lt;code&gt;pic&lt;/code&gt; commands such as &lt;code&gt;below&lt;/code&gt;, &lt;code&gt;above&lt;/code&gt;, &lt;code&gt;ljust&lt;/code&gt;, and &lt;code&gt;rjust&lt;/code&gt; really come in handy.
&lt;codeblock languaeg=pic&gt;
&lt;&lt;names&gt;&gt;=
&quot;$p_1$&quot; at P1  below ljust
&quot;$p_2$&quot; at P2  below ljust
&quot;$p_3$&quot; at P3  below ljust
&quot;$p_4$&quot; at P4  below ljust
&quot;$p_5$&quot; at P5  below rjust
&quot;$p_6$&quot; at P6  below ljust
&quot;$p_7$&quot; at P7  below ljust
&quot;$p_8$&quot; at P8  below rjust
&quot;$p_9$&quot; at P9  below ljust
&quot;$p_{10}$&quot; at P10 below ljust
&quot;$p_{11}$&quot; at P11 below ljust
&quot;$p_{12}$&quot; at P12 above ljust
&quot;$p_{13}$&quot; at P13 below ljust
&lt;/codeblock&gt;

Embedding the information on points and names completes a whole &lt;code&gt;pic&lt;/code&gt; document. We could reduce the size of &lt;code&gt;pic&lt;/code&gt; document by adjusting &lt;code&gt;scale&lt;/code&gt; variables. The &lt;code&gt;circlerad&lt;/code&gt; variable defines the default radius of every circle in a document.

&lt;codeblock language=pic&gt;
&lt;&lt;Scattered_points.pic&gt;&gt;=
.PS
scale = 8
circlerad = 0.2

&lt;&lt;points&gt;&gt;

&lt;&lt;names&gt;&gt;

.PE
&lt;/codeblock&gt;

==Drawing convex hull==
[[Image:Convex_hull.png|framed|The convex hull of a set of given points.]]
In addition to points and names, we need to draw a polygon embracing every points in a graph.

&lt;codeblock language=pic&gt;
&lt;&lt;Scattered_points.pic&gt;&gt;=
.PS
scale = 8
circlerad = 0.2

&lt;&lt;points&gt;&gt;

&lt;&lt;names&gt;&gt;

&lt;&lt;lines&gt;&gt;
.PE
&lt;/codeblock&gt;
The convex hull is drawn in dashed line. The &lt;code&gt;pic&lt;/code&gt; command for dashed pattern is &lt;code&gt;dashed&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line dashed from P11 to P3
line dashed from P3  to P12
line dashed from P12 to P10
line dashed from P10 to P4
line dashed from P4  to P5
line dashed from P5  to P8
line dashed from P8  to P11
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7051</id>
      <timestamp>2006-07-25T20:02:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>WP link</comment>
      <text xml:space="preserve">The [http://en.wikipedia.org/wiki/Convex_hull convex hull] of a set of points ''Q'' is the smallest polygon that embraces every point in ''Q''. This article explains how to draw a convex hull diagram using pic. The exact steps to convert a pic document into a graphic format is available at [[Hello World (Pic)]].

==Plotting random points==
[[Image:Scattered_Points.png|framed|Thirteen random points in a 2-D plane.]]
We first choose thirteen points and scatter them to a 2-dimensional plane.
  P1: ( 1,  3)
  P2: ( 2,  7)
  P3: ( 9, -2)
  P4: (-5,  7)
  P5: (-7,  2)
  P6: (-1,  3)
  P7: ( 4,  6)
  P8: (-3, -4)
  P9: ( 6,  0)
 P10: (-2,  8)
 P11: ( 0, -5)
 P12: ( 5,  8)
 P13: (-4, -1)

We draw a circle at each coordinate. Note that we need the label for each point for later use.
&lt;codeblock language=pic&gt;
&lt;&lt;points&gt;&gt;=
P1: circle fill at (1, 3)
P2: circle fill at (2, 7)
P3: circle fill at (9, -2)
P4: circle fill at (-5, 7)
P5: circle fill at (-7, 2)
P6: circle fill at (-1, 3)
P7: circle fill at (4, 6)
P8: circle fill at (-3, -4)
P9: circle fill at (6, 0)
P10: circle fill at (-2, 8)
P11: circle fill at (0, -5)
P12: circle fill at (5, 8)
P13: circle fill at (-4, -1)
&lt;/codeblock&gt;

We place the name of each point at every coordinate. Note that special &lt;code&gt;pic&lt;/code&gt; commands such as &lt;code&gt;below&lt;/code&gt;, &lt;code&gt;above&lt;/code&gt;, &lt;code&gt;ljust&lt;/code&gt;, and &lt;code&gt;rjust&lt;/code&gt; really come in handy.
&lt;codeblock languaeg=pic&gt;
&lt;&lt;names&gt;&gt;=
&quot;$p_1$&quot; at P1  below ljust
&quot;$p_2$&quot; at P2  below ljust
&quot;$p_3$&quot; at P3  below ljust
&quot;$p_4$&quot; at P4  below ljust
&quot;$p_5$&quot; at P5  below rjust
&quot;$p_6$&quot; at P6  below ljust
&quot;$p_7$&quot; at P7  below ljust
&quot;$p_8$&quot; at P8  below rjust
&quot;$p_9$&quot; at P9  below ljust
&quot;$p_{10}$&quot; at P10 below ljust
&quot;$p_{11}$&quot; at P11 below ljust
&quot;$p_{12}$&quot; at P12 above ljust
&quot;$p_{13}$&quot; at P13 below ljust
&lt;/codeblock&gt;

Embedding the information on points and names completes a whole &lt;code&gt;pic&lt;/code&gt; document. We could reduce the size of &lt;code&gt;pic&lt;/code&gt; document by adjusting &lt;code&gt;scale&lt;/code&gt; variables. The &lt;code&gt;circlerad&lt;/code&gt; variable defines the default radius of every circle in a document.

&lt;codeblock language=pic&gt;
&lt;&lt;Scattered_points.pic&gt;&gt;=
.PS
scale = 8
circlerad = 0.2

&lt;&lt;points&gt;&gt;

&lt;&lt;names&gt;&gt;

.PE
&lt;/codeblock&gt;

==Drawing convex hull==
[[Image:Convex_hull.png|framed|The convex hull of a set of given points.]]
In addition to points and names, we need to draw a polygon embracing every points in a graph.

&lt;codeblock language=pic&gt;
&lt;&lt;Scattered_points.pic&gt;&gt;=
.PS
scale = 8
circlerad = 0.2

&lt;&lt;points&gt;&gt;

&lt;&lt;names&gt;&gt;

&lt;&lt;lines&gt;&gt;
.PE
&lt;/codeblock&gt;
The convex hull is drawn in dashed line. The &lt;code&gt;pic&lt;/code&gt; command for dashed pattern is &lt;code&gt;dashed&lt;/code&gt;.
&lt;codeblock language=pic&gt;
&lt;&lt;lines&gt;&gt;=
line dashed from P11 to P3
line dashed from P3  to P12
line dashed from P12 to P10
line dashed from P10 to P4
line dashed from P4  to P5
line dashed from P5  to P8
line dashed from P8  to P11
&lt;/codeblock&gt;

[[Category:Programming language:Pic]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Drawing on map projections (Python)</title>
    <id>2281</id>
    <revision>
      <id>6004</id>
      <timestamp>2006-06-07T15:08:26Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">{{develop}}
[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|} 

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>6005</id>
      <timestamp>2006-06-07T17:00:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+[[Category:Uses library:Matplotlib]]</comment>
      <text xml:space="preserve">{{develop}}
[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|} 

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>6013</id>
      <timestamp>2006-06-08T00:31:15Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Data */</comment>
      <text xml:space="preserve">{{develop}}
[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from matplotlib.toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;==
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>6014</id>
      <timestamp>2006-06-08T00:33:14Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Code */</comment>
      <text xml:space="preserve">{{develop}}
[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from matplotlib.toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;=
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>6015</id>
      <timestamp>2006-06-08T00:42:01Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* External links */</comment>
      <text xml:space="preserve">{{develop}}
[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from matplotlib.toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;=
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==Result==
[[Image:Europe_cities.png|thumb|Seven cities in Europe]]

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>6016</id>
      <timestamp>2006-06-08T00:42:35Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>Remove {{develop}} tag.</comment>
      <text xml:space="preserve">[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
It is quite easy to install each library. The install procedure is avilable at [http://matplotlib.sourceforge.net/installing.html Installing matplotlib].

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from matplotlib.toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;=
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==Result==
[[Image:Europe_cities.png|thumb|Seven cities in Europe]]

==External links==
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>15715</id>
      <timestamp>2008-12-31T04:04:23Z</timestamp>
      <contributor>
        <ip>71.167.67.33</ip>
      </contributor>
      <comment>links</comment>
      <text xml:space="preserve">[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
** [http://matplotlib.sourceforge.net/installing.html Installing matplotlib]
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
** [http://matplotlib.sourceforge.net/basemap/doc/html/users/installing.html Installing basemap]
It is quite easy to install each library. The install procedures are available at the above links.

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from matplotlib.toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;=
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==Result==
[[Image:Europe_cities.png|thumb|Seven cities in Europe]]

==External links==
* [http://matplotlib.sourceforge.net/basemap/doc/html/ Matplotlib Basemap Toolkit documentation]
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
    <revision>
      <id>16977</id>
      <timestamp>2010-12-14T13:16:38Z</timestamp>
      <contributor>
        <username>Luizirber</username>
        <id>2183</id>
      </contributor>
      <comment>/* Library information */</comment>
      <text xml:space="preserve">[http://www.python.org/ Python] and [http://matplotlib.sourceforge.net/toolkits.html basemap matplotlib toolkit] provide an efficient way to draw a collection of shapes over real world maps. This article explains how to draw a simple roadmap among some cities in Western Europe. This roadmap is used as an example of [[Dijkstra's algorithm (Scala)|Dijkstra's shortest path algorithm]].

==Requirement==
* [http://www.python.org Python]
* [http://matplotlib.sourceforge.net/ Matplotlib] - python 2D plotting library
** [http://matplotlib.sourceforge.net/installing.html Installing matplotlib]
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html Basemap toolkit]
** [http://matplotlib.sourceforge.net/basemap/doc/html/users/installing.html Installing basemap]
It is quite easy to install each library. The install procedures are available at the above links.

==How to draw==
===Data===
The example roadmap contains seven european cities -- [http://en.wikipedia.org/Barcelona Barcelona], [http://en.wikipedia.org/wiki/Narbonne Narbonne], [http://en.wikipedia.org/wiki/Paris Paris], [http://en.wikipedia.org/wiki/Toulouse Toulouse], [http://en.wikipedia.org/wiki/Lausanne Lausanne], [http://en.wikipedia.org/wiki/Marseille Marseille] and [http://en.wikipedia.org/wiki/Geneva Geneva]. We need to know their coordinates in order to plot their locations on projection map. The exact coordinates can be found at each city's artcle in [http://www.wikipedia.org wikipedia].

{|class='wikitable'
|+ Seven cities and their coordinates
!City
!Latitude 
!Longitude
|-
|Barcelona
|41°23' N
|2º11' E
|-
|Narbonne
|43°11'N
|3°00'E
|-
|Paris
|48°52′N
|2°19′E
|-
|Toulouse
|43°36′N,
|1°26′E
|-
|Lausanne
|46°31′N
|6°38′E
|-
|Marseille
|43°17′N
|5°22′E
|-
|Geneva
|46°12′N
|6°09′E
|}

==Code==
===Library information===
First, we declare some libraries we are going to use. We also use [http://antigrain.com/ AGG] backend to draw a map in a raster graphic format.
&lt;codeblock language=python&gt;
&lt;&lt;include&gt;&gt;=
import matplotlib
matplotlib.use('Agg')

from mpl_toolkits.basemap import Basemap
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
&lt;/codeblock&gt;

===Basemap set-up===
The next step is basemap set-up. Each argument means:
* &lt;code&gt;llcrnrlon&lt;/code&gt;: longitude of lower left hand corner of the desired map domain.
* &lt;code&gt;llcrnrlat&lt;/code&gt;: latitude of lower left hand corner of the desired map domain.
* &lt;code&gt;urcrnrlon&lt;/code&gt;: longitude of lower upper right corner of the desired map domain.
* &lt;code&gt;urcrnrlat&lt;/code&gt;: latitude of upper right hand corner of the desired map domain.
* &lt;code&gt;resolution&lt;/code&gt;: resolution of boundary data. 'l' stands for 'low.'
* &lt;code&gt;projection&lt;/code&gt;: we will use [http://en.wikipedia.org/wiki/Transverse_Mercator_projection Transverse Mercator projection] -- one of 17 projection maps basemap toolkits supports.
* &lt;code&gt;lon_0&lt;/code&gt;: central longitude of the desired map domain.
* &lt;code&gt;lat_0&lt;/code&gt;: central latitude of the desired map domain.

&lt;codeblock language=python&gt;
&lt;&lt;basemap&gt;&gt;=
m = Basemap(llcrnrlon=1, \
            llcrnrlat=40.6, \
            urcrnrlon=8.8, \
            urcrnrlat = 49.6, \
            resolution = 'l', \
            projection = 'tmerc', \
            lon_0 = 4.9, \
            lat_0 = 45.1)
&lt;/codeblock&gt;

===Canvas set-up===
Now we set up canvas, add an axis, and reset figure size to have same aspect ratio as map. The width of '8' inches is just a heuristic number.
&lt;codeblock language=python&gt;
&lt;&lt;figure_setup&gt;&gt;=
fig = Figure()
canvas = FigureCanvas(fig)
m.ax = fig.add_axes([0, 0, 1, 1])
fig.set_figsize_inches((8/m.aspect, 8.))
&lt;/codeblock&gt;

===Coordinate Data of Cities===
The coordinates of seven cities are stored in list.
&lt;codeblock language=python&gt;
&lt;&lt;data&gt;&gt;=
lats = [41.38, 43.18, 48.87, 43.60, 46.52, 43.28, 46.20]
lons = [ 2.18,  3.00,  2.32,  1.43,  6.63,  5.37,  6.15]
name = ['Barcelona', 'Narbonne', 'Paris', 'Toulouse', 'Lausanne', 'Marseille', 'Geneva']
&lt;/codeblock&gt;

===Draw and Save===
We draw coastlines as well as political boundaries and fill the continent. Then convert both latitude and longitude into map domain coordinates. Finally, we plot each city with a blue dot and save the map in PNG format.
&lt;codeblock language=python&gt;
&lt;&lt;draw&gt;&gt;=
m.drawcoastlines(color='gray')
m.drawcountries(color='gray')
m.fillcontinents(color='beige')
x, y = m(lons, lats)
m.plot(x, y, 'bo')
canvas.print_figure('map.png', dpi=100)
&lt;/codeblock&gt;

===The Whole Code===
&lt;codeblock language=python&gt;
&lt;&lt;draw_europe.py&gt;&gt;=
&lt;&lt;include&gt;&gt;
def main():
    &lt;&lt;basemap&gt;&gt;

    &lt;&lt;figure_setup&gt;&gt;

    &lt;&lt;data&gt;&gt;

    &lt;&lt;draw&gt;&gt;

if __name__ == &quot;__main__&quot;:
    main()

&lt;/codeblock&gt;

==Result==
[[Image:Europe_cities.png|thumb|Seven cities in Europe]]

==External links==
* [http://matplotlib.sourceforge.net/basemap/doc/html/ Matplotlib Basemap Toolkit documentation]
* [http://matplotlib.sourceforge.net/matplotlib.toolkits.basemap.basemap.html basemap documentation] - from matplotlib homepage
* [http://matplotlib.sourceforge.net/screenshots.html Screenshot of Matplotlib] - sample code and figure

[[Category:Environment:Portable]]
[[Category:Programming language:Python]]
[[Category:Uses library:Matplotlib]]</text>
    </revision>
  </page>
  <page>
    <title>Dynamic tray icon (Windows)</title>
    <id>1908</id>
    <revision>
      <id>4215</id>
      <timestamp>2006-04-21T19:00:48Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Dynamic tray icon for windows.</comment>
      <text xml:space="preserve">== Dynamic tray icon in windows ==

This code is a good(?) example on how to create a dyanmic icon in the windows tray. It allows you to draw on top of a template icon or redraw it completely.

&lt;codeblock language=c&gt;
&lt;&lt;dynamic_tray_icon.c&gt;&gt;=

/*
**
** Dynamic tray icon example
**
*/

#include &lt;windows.h&gt;
#include &lt;shellapi.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// replaceicon() - draws stuff on top of a template icon. Destroys the input icon and returns a new one
//
// Inputs
// 						hIcon  : Handle to a icon
// 						value  : 0 - 100
//						clear  : 1 = clear icon first, 0 = don't clear icon first
// returns
// 						Failure: 0
//						Success: Handle to a icon
//------------------------------------------------------------------------------------------------------------------

HICON replaceicon(HICON hIcon, int value, BOOL clear)
{
  ICONINFO  uInfo;
  INT       lRes;
  HDC       hMemDc;
  HGDIOBJ   hOldBMP;
  HICON     hNewIcon;
  RECT      rectDraw;
  BITMAP    uBitmap;
  LOGFONT   font;
  HBRUSH    hBrush1;
  HBRUSH    hBrush2;

  lRes = GetIconInfo(hIcon, &amp;uInfo);
  if(!lRes)
    return 0;

  hMemDc = CreateCompatibleDC(NULL);
  if(!hMemDc)
    return 0;

  if(!GetObject(uInfo.hbmColor , sizeof(BITMAP), &amp;uBitmap))
    return 0;

  rectDraw.left  =                   0 ; rectDraw.top                       = 0 ;
  rectDraw.right = uBitmap.bmWidth - 1 ; rectDraw.bottom = uBitmap.bmHeight - 1 ;

  hOldBMP = SelectObject(hMemDc, uInfo.hbmColor);

  // ---

  RECT		bar;

  bar.left      = rectDraw.left;
  bar.right     = rectDraw.right;
  bar.top       = rectDraw.bottom  - (value * ((rectDraw.bottom - rectDraw.top)) / 100);
  bar.bottom    = rectDraw.bottom;

  if(clear)
    FillRect(hMemDc,&amp;rectDraw,(HBRUSH) (hBrush1=CreateSolidBrush(RGB( 64,  0, 64 ))));

  FillRect(hMemDc,&amp;bar,     (HBRUSH) (hBrush2=CreateSolidBrush(RGB( 220,32,255 ))));

  if(hBrush1)
    DeleteObject(hBrush1);
  if(hBrush2)
    DeleteObject(hBrush2);

  // ---

  char string[8];

  font.lfHeight             = uBitmap.bmHeight;
  font.lfWidth              = uBitmap.bmWidth/4;
  font.lfEscapement         = 0;
  font.lfOrientation        = 0;
  font.lfWeight             = 0; //FW_BOLD;
  font.lfItalic             = 0;
  font.lfUnderline          = 0;
  font.lfStrikeOut          = 0;
  font.lfCharSet            = ANSI_CHARSET;
  font.lfOutPrecision       = OUT_DEFAULT_PRECIS;
  font.lfClipPrecision      = CLIP_DEFAULT_PRECIS;
  font.lfQuality            = ANTIALIASED_QUALITY; //DEFAULT_QUALITY;
  font.lfPitchAndFamily     = DEFAULT_PITCH;
  strcpy(font.lfFaceName,   &quot;Tahoma&quot;);

       SelectObject(hMemDc, CreateFontIndirect(&amp;font));
          SetBkMode(hMemDc, TRANSPARENT);
            SetROP2(hMemDc, R2_COPYPEN);
  SetStretchBltMode(hMemDc, COLORONCOLOR);
       SetTextColor(hMemDc, RGB(235,235,255));
            sprintf(string, &quot;%d&quot;,value);

  lRes = DrawText(hMemDc, string, strlen(string), &amp;rectDraw, DT_CENTER | DT_VCENTER | DT_SINGLELINE);

  // ---

  if(!lRes)
    return 0;

  if(NULL || HGDI_ERROR == SelectObject(hMemDc, hOldBMP))
    return 0;

  hNewIcon = CreateIconIndirect(&amp;uInfo);

  if(!hNewIcon)
    return 0;

  DestroyIcon(hIcon);
  hIcon = hNewIcon;

  if(hMemDc)
   DeleteDC(hMemDc);

  if(uInfo.hbmMask)
    DeleteObject(uInfo.hbmMask);

  if(uInfo.hbmColor)
    DeleteObject(uInfo.hbmColor);

  return hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Add, modify or removes the tray icon. A value of 0 means remove
//------------------------------------------------------------------------------------------------------------------

HICON settrayicon(HICON hIcon,int value)
{
  NOTIFYICONDATA   icon;
  static BOOL      firstrun=1;

  ZeroMemory(&amp;icon,sizeof(NOTIFYICONDATA));
  icon.cbSize               = sizeof(NOTIFYICONDATA);
  icon.uID                  = 0;
  icon.hWnd                 = GetDesktopWindow();
  icon.uFlags               = NIF_ICON | NIF_TIP | NIF_MESSAGE;
  icon.hIcon                = hIcon;
  sprintf(icon.szTip,&quot;Value = %d&quot;,value);

  icon.hIcon = replaceicon(icon.hIcon, value, 1); // Modify the icon

  if(!icon.hIcon)
    printf(&quot;***ERROR: replaceicon()\n&quot;), exit(0);

  Shell_NotifyIcon(value==0?NIM_DELETE:firstrun?NIM_ADD,firstrun=0:NIM_MODIFY,&amp;icon);
  Sleep(0);

  return icon.hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------

int main(void)
{
  HICON		icon;

  icon = LoadImage(0,&quot;c:\\Progs\\Developing\\lcc\\projects\\DriveGleam\\Icons\\Drives\\full_idle.ico&quot;
                    ,IMAGE_ICON,32,32,LR_LOADFROMFILE);

  for(int x=0; x&lt;100; x+=3)
  {
    icon = settrayicon(icon,x); // add/update the icon
    sleep(200);                 // Let us se what happens
  }

  settrayicon(icon,0); // remove the icon
  return 0;
}


&lt;/codeblock&gt;

{{develop}}</text>
    </revision>
    <revision>
      <id>4217</id>
      <timestamp>2006-04-21T19:37:02Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Minor fixes, move develop tag</comment>
      <text xml:space="preserve">{{develop}}

This code is an example of how to create a dynamic icon in the Windows system tray. It allows you to draw on top of a template icon or redraw it completely.

&lt;codeblock language=c&gt;
&lt;&lt;dynamic_tray_icon.c&gt;&gt;=

/*
**
** Dynamic tray icon example
**
*/

#include &lt;windows.h&gt;
#include &lt;shellapi.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// replaceicon() - draws stuff on top of a template icon. Destroys the input icon and returns a new one
//
// Inputs
// 						hIcon  : Handle to a icon
// 						value  : 0 - 100
//						clear  : 1 = clear icon first, 0 = don't clear icon first
// returns
// 						Failure: 0
//						Success: Handle to a icon
//------------------------------------------------------------------------------------------------------------------

HICON replaceicon(HICON hIcon, int value, BOOL clear)
{
  ICONINFO  uInfo;
  INT       lRes;
  HDC       hMemDc;
  HGDIOBJ   hOldBMP;
  HICON     hNewIcon;
  RECT      rectDraw;
  BITMAP    uBitmap;
  LOGFONT   font;
  HBRUSH    hBrush1;
  HBRUSH    hBrush2;

  lRes = GetIconInfo(hIcon, &amp;uInfo);
  if(!lRes)
    return 0;

  hMemDc = CreateCompatibleDC(NULL);
  if(!hMemDc)
    return 0;

  if(!GetObject(uInfo.hbmColor , sizeof(BITMAP), &amp;uBitmap))
    return 0;

  rectDraw.left  =                   0 ; rectDraw.top                       = 0 ;
  rectDraw.right = uBitmap.bmWidth - 1 ; rectDraw.bottom = uBitmap.bmHeight - 1 ;

  hOldBMP = SelectObject(hMemDc, uInfo.hbmColor);

  // ---

  RECT		bar;

  bar.left      = rectDraw.left;
  bar.right     = rectDraw.right;
  bar.top       = rectDraw.bottom  - (value * ((rectDraw.bottom - rectDraw.top)) / 100);
  bar.bottom    = rectDraw.bottom;

  if(clear)
    FillRect(hMemDc,&amp;rectDraw,(HBRUSH) (hBrush1=CreateSolidBrush(RGB( 64,  0, 64 ))));

  FillRect(hMemDc,&amp;bar,     (HBRUSH) (hBrush2=CreateSolidBrush(RGB( 220,32,255 ))));

  if(hBrush1)
    DeleteObject(hBrush1);
  if(hBrush2)
    DeleteObject(hBrush2);

  // ---

  char string[8];

  font.lfHeight             = uBitmap.bmHeight;
  font.lfWidth              = uBitmap.bmWidth/4;
  font.lfEscapement         = 0;
  font.lfOrientation        = 0;
  font.lfWeight             = 0; //FW_BOLD;
  font.lfItalic             = 0;
  font.lfUnderline          = 0;
  font.lfStrikeOut          = 0;
  font.lfCharSet            = ANSI_CHARSET;
  font.lfOutPrecision       = OUT_DEFAULT_PRECIS;
  font.lfClipPrecision      = CLIP_DEFAULT_PRECIS;
  font.lfQuality            = ANTIALIASED_QUALITY; //DEFAULT_QUALITY;
  font.lfPitchAndFamily     = DEFAULT_PITCH;
  strcpy(font.lfFaceName,   &quot;Tahoma&quot;);

       SelectObject(hMemDc, CreateFontIndirect(&amp;font));
          SetBkMode(hMemDc, TRANSPARENT);
            SetROP2(hMemDc, R2_COPYPEN);
  SetStretchBltMode(hMemDc, COLORONCOLOR);
       SetTextColor(hMemDc, RGB(235,235,255));
            sprintf(string, &quot;%d&quot;,value);

  lRes = DrawText(hMemDc, string, strlen(string), &amp;rectDraw, DT_CENTER | DT_VCENTER | DT_SINGLELINE);

  // ---

  if(!lRes)
    return 0;

  if(NULL || HGDI_ERROR == SelectObject(hMemDc, hOldBMP))
    return 0;

  hNewIcon = CreateIconIndirect(&amp;uInfo);

  if(!hNewIcon)
    return 0;

  DestroyIcon(hIcon);
  hIcon = hNewIcon;

  if(hMemDc)
   DeleteDC(hMemDc);

  if(uInfo.hbmMask)
    DeleteObject(uInfo.hbmMask);

  if(uInfo.hbmColor)
    DeleteObject(uInfo.hbmColor);

  return hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Add, modify or removes the tray icon. A value of 0 means remove
//------------------------------------------------------------------------------------------------------------------

HICON settrayicon(HICON hIcon,int value)
{
  NOTIFYICONDATA   icon;
  static BOOL      firstrun=1;

  ZeroMemory(&amp;icon,sizeof(NOTIFYICONDATA));
  icon.cbSize               = sizeof(NOTIFYICONDATA);
  icon.uID                  = 0;
  icon.hWnd                 = GetDesktopWindow();
  icon.uFlags               = NIF_ICON | NIF_TIP | NIF_MESSAGE;
  icon.hIcon                = hIcon;
  sprintf(icon.szTip,&quot;Value = %d&quot;,value);

  icon.hIcon = replaceicon(icon.hIcon, value, 1); // Modify the icon

  if(!icon.hIcon)
    printf(&quot;***ERROR: replaceicon()\n&quot;), exit(0);

  Shell_NotifyIcon(value==0?NIM_DELETE:firstrun?NIM_ADD,firstrun=0:NIM_MODIFY,&amp;icon);
  Sleep(0);

  return icon.hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------

int main(void)
{
  HICON		icon;

  icon = LoadImage(0,&quot;c:\\Progs\\Developing\\lcc\\projects\\DriveGleam\\Icons\\Drives\\full_idle.ico&quot;
                    ,IMAGE_ICON,32,32,LR_LOADFROMFILE);

  for(int x=0; x&lt;100; x+=3)
  {
    icon = settrayicon(icon,x); // add/update the icon
    sleep(200);                 // Let us se what happens
  }

  settrayicon(icon,0); // remove the icon
  return 0;
}


&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>4218</id>
      <timestamp>2006-04-21T19:37:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>A couple categories</comment>
      <text xml:space="preserve">{{develop}}

This code is an example of how to create a dynamic icon in the Windows system tray. It allows you to draw on top of a template icon or redraw it completely.

&lt;codeblock language=c&gt;
&lt;&lt;dynamic_tray_icon.c&gt;&gt;=

/*
**
** Dynamic tray icon example
**
*/

#include &lt;windows.h&gt;
#include &lt;shellapi.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// replaceicon() - draws stuff on top of a template icon. Destroys the input icon and returns a new one
//
// Inputs
// 						hIcon  : Handle to a icon
// 						value  : 0 - 100
//						clear  : 1 = clear icon first, 0 = don't clear icon first
// returns
// 						Failure: 0
//						Success: Handle to a icon
//------------------------------------------------------------------------------------------------------------------

HICON replaceicon(HICON hIcon, int value, BOOL clear)
{
  ICONINFO  uInfo;
  INT       lRes;
  HDC       hMemDc;
  HGDIOBJ   hOldBMP;
  HICON     hNewIcon;
  RECT      rectDraw;
  BITMAP    uBitmap;
  LOGFONT   font;
  HBRUSH    hBrush1;
  HBRUSH    hBrush2;

  lRes = GetIconInfo(hIcon, &amp;uInfo);
  if(!lRes)
    return 0;

  hMemDc = CreateCompatibleDC(NULL);
  if(!hMemDc)
    return 0;

  if(!GetObject(uInfo.hbmColor , sizeof(BITMAP), &amp;uBitmap))
    return 0;

  rectDraw.left  =                   0 ; rectDraw.top                       = 0 ;
  rectDraw.right = uBitmap.bmWidth - 1 ; rectDraw.bottom = uBitmap.bmHeight - 1 ;

  hOldBMP = SelectObject(hMemDc, uInfo.hbmColor);

  // ---

  RECT		bar;

  bar.left      = rectDraw.left;
  bar.right     = rectDraw.right;
  bar.top       = rectDraw.bottom  - (value * ((rectDraw.bottom - rectDraw.top)) / 100);
  bar.bottom    = rectDraw.bottom;

  if(clear)
    FillRect(hMemDc,&amp;rectDraw,(HBRUSH) (hBrush1=CreateSolidBrush(RGB( 64,  0, 64 ))));

  FillRect(hMemDc,&amp;bar,     (HBRUSH) (hBrush2=CreateSolidBrush(RGB( 220,32,255 ))));

  if(hBrush1)
    DeleteObject(hBrush1);
  if(hBrush2)
    DeleteObject(hBrush2);

  // ---

  char string[8];

  font.lfHeight             = uBitmap.bmHeight;
  font.lfWidth              = uBitmap.bmWidth/4;
  font.lfEscapement         = 0;
  font.lfOrientation        = 0;
  font.lfWeight             = 0; //FW_BOLD;
  font.lfItalic             = 0;
  font.lfUnderline          = 0;
  font.lfStrikeOut          = 0;
  font.lfCharSet            = ANSI_CHARSET;
  font.lfOutPrecision       = OUT_DEFAULT_PRECIS;
  font.lfClipPrecision      = CLIP_DEFAULT_PRECIS;
  font.lfQuality            = ANTIALIASED_QUALITY; //DEFAULT_QUALITY;
  font.lfPitchAndFamily     = DEFAULT_PITCH;
  strcpy(font.lfFaceName,   &quot;Tahoma&quot;);

       SelectObject(hMemDc, CreateFontIndirect(&amp;font));
          SetBkMode(hMemDc, TRANSPARENT);
            SetROP2(hMemDc, R2_COPYPEN);
  SetStretchBltMode(hMemDc, COLORONCOLOR);
       SetTextColor(hMemDc, RGB(235,235,255));
            sprintf(string, &quot;%d&quot;,value);

  lRes = DrawText(hMemDc, string, strlen(string), &amp;rectDraw, DT_CENTER | DT_VCENTER | DT_SINGLELINE);

  // ---

  if(!lRes)
    return 0;

  if(NULL || HGDI_ERROR == SelectObject(hMemDc, hOldBMP))
    return 0;

  hNewIcon = CreateIconIndirect(&amp;uInfo);

  if(!hNewIcon)
    return 0;

  DestroyIcon(hIcon);
  hIcon = hNewIcon;

  if(hMemDc)
   DeleteDC(hMemDc);

  if(uInfo.hbmMask)
    DeleteObject(uInfo.hbmMask);

  if(uInfo.hbmColor)
    DeleteObject(uInfo.hbmColor);

  return hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Add, modify or removes the tray icon. A value of 0 means remove
//------------------------------------------------------------------------------------------------------------------

HICON settrayicon(HICON hIcon,int value)
{
  NOTIFYICONDATA   icon;
  static BOOL      firstrun=1;

  ZeroMemory(&amp;icon,sizeof(NOTIFYICONDATA));
  icon.cbSize               = sizeof(NOTIFYICONDATA);
  icon.uID                  = 0;
  icon.hWnd                 = GetDesktopWindow();
  icon.uFlags               = NIF_ICON | NIF_TIP | NIF_MESSAGE;
  icon.hIcon                = hIcon;
  sprintf(icon.szTip,&quot;Value = %d&quot;,value);

  icon.hIcon = replaceicon(icon.hIcon, value, 1); // Modify the icon

  if(!icon.hIcon)
    printf(&quot;***ERROR: replaceicon()\n&quot;), exit(0);

  Shell_NotifyIcon(value==0?NIM_DELETE:firstrun?NIM_ADD,firstrun=0:NIM_MODIFY,&amp;icon);
  Sleep(0);

  return icon.hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------

int main(void)
{
  HICON		icon;

  icon = LoadImage(0,&quot;c:\\Progs\\Developing\\lcc\\projects\\DriveGleam\\Icons\\Drives\\full_idle.ico&quot;
                    ,IMAGE_ICON,32,32,LR_LOADFROMFILE);

  for(int x=0; x&lt;100; x+=3)
  {
    icon = settrayicon(icon,x); // add/update the icon
    sleep(200);                 // Let us se what happens
  }

  settrayicon(icon,0); // remove the icon
  return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4221</id>
      <timestamp>2006-04-21T20:03:15Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <minor/>
      <comment>Changed a very long path to something more readable</comment>
      <text xml:space="preserve">{{develop}}

This code is an example of how to create a dynamic icon in the Windows system tray. It allows you to draw on top of a template icon or redraw it completely.

&lt;codeblock language=c&gt;
&lt;&lt;dynamic_tray_icon.c&gt;&gt;=

/*
**
** Dynamic tray icon example
**
*/

#include &lt;windows.h&gt;
#include &lt;shellapi.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// replaceicon() - draws stuff on top of a template icon. Destroys the input icon and returns a new one
//
// Inputs
// 						hIcon  : Handle to a icon
// 						value  : 0 - 100
//						clear  : 1 = clear icon first, 0 = don't clear icon first
// returns
// 						Failure: 0
//						Success: Handle to a icon
//------------------------------------------------------------------------------------------------------------------

HICON replaceicon(HICON hIcon, int value, BOOL clear)
{
  ICONINFO  uInfo;
  INT       lRes;
  HDC       hMemDc;
  HGDIOBJ   hOldBMP;
  HICON     hNewIcon;
  RECT      rectDraw;
  BITMAP    uBitmap;
  LOGFONT   font;
  HBRUSH    hBrush1;
  HBRUSH    hBrush2;

  lRes = GetIconInfo(hIcon, &amp;uInfo);
  if(!lRes)
    return 0;

  hMemDc = CreateCompatibleDC(NULL);
  if(!hMemDc)
    return 0;

  if(!GetObject(uInfo.hbmColor , sizeof(BITMAP), &amp;uBitmap))
    return 0;

  rectDraw.left  =                   0 ; rectDraw.top                       = 0 ;
  rectDraw.right = uBitmap.bmWidth - 1 ; rectDraw.bottom = uBitmap.bmHeight - 1 ;

  hOldBMP = SelectObject(hMemDc, uInfo.hbmColor);

  // ---

  RECT		bar;

  bar.left      = rectDraw.left;
  bar.right     = rectDraw.right;
  bar.top       = rectDraw.bottom  - (value * ((rectDraw.bottom - rectDraw.top)) / 100);
  bar.bottom    = rectDraw.bottom;

  if(clear)
    FillRect(hMemDc,&amp;rectDraw,(HBRUSH) (hBrush1=CreateSolidBrush(RGB( 64,  0, 64 ))));

  FillRect(hMemDc,&amp;bar,     (HBRUSH) (hBrush2=CreateSolidBrush(RGB( 220,32,255 ))));

  if(hBrush1)
    DeleteObject(hBrush1);
  if(hBrush2)
    DeleteObject(hBrush2);

  // ---

  char string[8];

  font.lfHeight             = uBitmap.bmHeight;
  font.lfWidth              = uBitmap.bmWidth/4;
  font.lfEscapement         = 0;
  font.lfOrientation        = 0;
  font.lfWeight             = 0; //FW_BOLD;
  font.lfItalic             = 0;
  font.lfUnderline          = 0;
  font.lfStrikeOut          = 0;
  font.lfCharSet            = ANSI_CHARSET;
  font.lfOutPrecision       = OUT_DEFAULT_PRECIS;
  font.lfClipPrecision      = CLIP_DEFAULT_PRECIS;
  font.lfQuality            = ANTIALIASED_QUALITY; //DEFAULT_QUALITY;
  font.lfPitchAndFamily     = DEFAULT_PITCH;
  strcpy(font.lfFaceName,   &quot;Tahoma&quot;);

       SelectObject(hMemDc, CreateFontIndirect(&amp;font));
          SetBkMode(hMemDc, TRANSPARENT);
            SetROP2(hMemDc, R2_COPYPEN);
  SetStretchBltMode(hMemDc, COLORONCOLOR);
       SetTextColor(hMemDc, RGB(235,235,255));
            sprintf(string, &quot;%d&quot;,value);

  lRes = DrawText(hMemDc, string, strlen(string), &amp;rectDraw, DT_CENTER | DT_VCENTER | DT_SINGLELINE);

  // ---

  if(!lRes)
    return 0;

  if(NULL || HGDI_ERROR == SelectObject(hMemDc, hOldBMP))
    return 0;

  hNewIcon = CreateIconIndirect(&amp;uInfo);

  if(!hNewIcon)
    return 0;

  DestroyIcon(hIcon);
  hIcon = hNewIcon;

  if(hMemDc)
   DeleteDC(hMemDc);

  if(uInfo.hbmMask)
    DeleteObject(uInfo.hbmMask);

  if(uInfo.hbmColor)
    DeleteObject(uInfo.hbmColor);

  return hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Add, modify or removes the tray icon. A value of 0 means remove
//------------------------------------------------------------------------------------------------------------------

HICON settrayicon(HICON hIcon,int value)
{
  NOTIFYICONDATA   icon;
  static BOOL      firstrun=1;

  ZeroMemory(&amp;icon,sizeof(NOTIFYICONDATA));
  icon.cbSize               = sizeof(NOTIFYICONDATA);
  icon.uID                  = 0;
  icon.hWnd                 = GetDesktopWindow();
  icon.uFlags               = NIF_ICON | NIF_TIP | NIF_MESSAGE;
  icon.hIcon                = hIcon;
  sprintf(icon.szTip,&quot;Value = %d&quot;,value);

  icon.hIcon = replaceicon(icon.hIcon, value, 1); // Modify the icon

  if(!icon.hIcon)
    printf(&quot;***ERROR: replaceicon()\n&quot;), exit(0);

  Shell_NotifyIcon(value==0?NIM_DELETE:firstrun?NIM_ADD,firstrun=0:NIM_MODIFY,&amp;icon);
  Sleep(0);

  return icon.hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------

int main(void)
{
  HICON		icon;

  icon = LoadImage(0,&quot;c:\\some_icon.ico&quot;,IMAGE_ICON,32,32,LR_LOADFROMFILE);

  for(int x=0; x&lt;100; x+=3)
  {
    icon = settrayicon(icon,x); // add/update the icon
    sleep(200);                 // Let us se what happens
  }

  settrayicon(icon,0); // remove the icon
  return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
    <revision>
      <id>4224</id>
      <timestamp>2006-04-21T20:58:47Z</timestamp>
      <contributor>
        <username>Waxhead</username>
        <id>32</id>
      </contributor>
      <comment>Added link with shell32.lib in comment</comment>
      <text xml:space="preserve">{{develop}}

This code is an example of how to create a dynamic icon in the Windows system tray. It allows you to draw on top of a template icon or redraw it completely.

&lt;codeblock language=c&gt;
&lt;&lt;dynamic_tray_icon.c&gt;&gt;=

/*
**
** Dynamic tray icon example
**
** Link with: shell32.lib
*/

#include &lt;windows.h&gt;
#include &lt;shellapi.h&gt;
#include &lt;stdio.h&gt;

//------------------------------------------------------------------------------------------------------------------
// replaceicon() - draws stuff on top of a template icon. Destroys the input icon and returns a new one
//
// Inputs
// 						hIcon  : Handle to a icon
// 						value  : 0 - 100
//						clear  : 1 = clear icon first, 0 = don't clear icon first
// returns
// 						Failure: 0
//						Success: Handle to a icon
//------------------------------------------------------------------------------------------------------------------

HICON replaceicon(HICON hIcon, int value, BOOL clear)
{
  ICONINFO  uInfo;
  INT       lRes;
  HDC       hMemDc;
  HGDIOBJ   hOldBMP;
  HICON     hNewIcon;
  RECT      rectDraw;
  BITMAP    uBitmap;
  LOGFONT   font;
  HBRUSH    hBrush1;
  HBRUSH    hBrush2;

  lRes = GetIconInfo(hIcon, &amp;uInfo);
  if(!lRes)
    return 0;

  hMemDc = CreateCompatibleDC(NULL);
  if(!hMemDc)
    return 0;

  if(!GetObject(uInfo.hbmColor , sizeof(BITMAP), &amp;uBitmap))
    return 0;

  rectDraw.left  =                   0 ; rectDraw.top                       = 0 ;
  rectDraw.right = uBitmap.bmWidth - 1 ; rectDraw.bottom = uBitmap.bmHeight - 1 ;

  hOldBMP = SelectObject(hMemDc, uInfo.hbmColor);

  // ---

  RECT		bar;

  bar.left      = rectDraw.left;
  bar.right     = rectDraw.right;
  bar.top       = rectDraw.bottom  - (value * ((rectDraw.bottom - rectDraw.top)) / 100);
  bar.bottom    = rectDraw.bottom;

  if(clear)
    FillRect(hMemDc,&amp;rectDraw,(HBRUSH) (hBrush1=CreateSolidBrush(RGB( 64,  0, 64 ))));

  FillRect(hMemDc,&amp;bar,     (HBRUSH) (hBrush2=CreateSolidBrush(RGB( 220,32,255 ))));

  if(hBrush1)
    DeleteObject(hBrush1);
  if(hBrush2)
    DeleteObject(hBrush2);

  // ---

  char string[8];

  font.lfHeight             = uBitmap.bmHeight;
  font.lfWidth              = uBitmap.bmWidth/4;
  font.lfEscapement         = 0;
  font.lfOrientation        = 0;
  font.lfWeight             = 0; //FW_BOLD;
  font.lfItalic             = 0;
  font.lfUnderline          = 0;
  font.lfStrikeOut          = 0;
  font.lfCharSet            = ANSI_CHARSET;
  font.lfOutPrecision       = OUT_DEFAULT_PRECIS;
  font.lfClipPrecision      = CLIP_DEFAULT_PRECIS;
  font.lfQuality            = ANTIALIASED_QUALITY; //DEFAULT_QUALITY;
  font.lfPitchAndFamily     = DEFAULT_PITCH;
  strcpy(font.lfFaceName,   &quot;Tahoma&quot;);

       SelectObject(hMemDc, CreateFontIndirect(&amp;font));
          SetBkMode(hMemDc, TRANSPARENT);
            SetROP2(hMemDc, R2_COPYPEN);
  SetStretchBltMode(hMemDc, COLORONCOLOR);
       SetTextColor(hMemDc, RGB(235,235,255));
            sprintf(string, &quot;%d&quot;,value);

  lRes = DrawText(hMemDc, string, strlen(string), &amp;rectDraw, DT_CENTER | DT_VCENTER | DT_SINGLELINE);

  // ---

  if(!lRes)
    return 0;

  if(NULL || HGDI_ERROR == SelectObject(hMemDc, hOldBMP))
    return 0;

  hNewIcon = CreateIconIndirect(&amp;uInfo);

  if(!hNewIcon)
    return 0;

  DestroyIcon(hIcon);
  hIcon = hNewIcon;

  if(hMemDc)
   DeleteDC(hMemDc);

  if(uInfo.hbmMask)
    DeleteObject(uInfo.hbmMask);

  if(uInfo.hbmColor)
    DeleteObject(uInfo.hbmColor);

  return hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Add, modify or removes the tray icon. A value of 0 means remove
//------------------------------------------------------------------------------------------------------------------

HICON settrayicon(HICON hIcon,int value)
{
  NOTIFYICONDATA   icon;
  static BOOL      firstrun=1;

  ZeroMemory(&amp;icon,sizeof(NOTIFYICONDATA));
  icon.cbSize               = sizeof(NOTIFYICONDATA);
  icon.uID                  = 0;
  icon.hWnd                 = GetDesktopWindow();
  icon.uFlags               = NIF_ICON | NIF_TIP | NIF_MESSAGE;
  icon.hIcon                = hIcon;
  sprintf(icon.szTip,&quot;Value = %d&quot;,value);

  icon.hIcon = replaceicon(icon.hIcon, value, 1); // Modify the icon

  if(!icon.hIcon)
    printf(&quot;***ERROR: replaceicon()\n&quot;), exit(0);

  Shell_NotifyIcon(value==0?NIM_DELETE:firstrun?NIM_ADD,firstrun=0:NIM_MODIFY,&amp;icon);
  Sleep(0);

  return icon.hIcon;
}

//------------------------------------------------------------------------------------------------------------------
// Entry point...
//------------------------------------------------------------------------------------------------------------------

int main(void)
{
  HICON		icon;

  icon = LoadImage(0,&quot;c:\\some_icon.ico&quot;,IMAGE_ICON,32,32,LR_LOADFROMFILE);

  for(int x=0; x&lt;100; x+=3)
  {
    icon = settrayicon(icon,x); // add/update the icon
    sleep(200);                 // Let us se what happens
  }

  settrayicon(icon,0); // remove the icon
  return 0;
}


&lt;/codeblock&gt;

[[Category:Programming language:C]]
[[Category:Environment:Windows]]</text>
    </revision>
  </page>
  <page>
    <title>Eight Queens puzzle (Haskell)</title>
    <id>3685</id>
    <revision>
      <id>15501</id>
      <timestamp>2008-11-28T03:55:09Z</timestamp>
      <contributor>
        <username>JamesReynolds</username>
        <id>1748</id>
      </contributor>
      <text xml:space="preserve">{{category:Eight Queens Puzzle}}
The n-Queens is the extension of the 8-Queens problem to an n by n chessboard. The challenge is to place n queens on an n by n chessboard such that no two queens are attacking each other.

We represent solutions by a list of integers, &lt;code&gt;[Int]&lt;/code&gt;. The list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; represents &lt;code&gt;n&lt;/code&gt; queens in the positions:
&lt;code&gt;[(1,r&lt;sub&gt;1&lt;/sub&gt;),...,(n,r&lt;sub&gt;n&lt;/sub&gt;)]&lt;/code&gt;.

== A safe set of queens ==

We start by defining a function &lt;code&gt;safeAddition&lt;/code&gt; that determines whether adding a queen at &lt;code&gt;(0,r&lt;sub&gt;0&lt;/sub&gt;)&lt;/code&gt; is safe. We do this by checking the list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; to determine if:
# r&lt;sub&gt;i&lt;/sub&gt; = r&lt;sub&gt;0&lt;/sub&gt; or
# &lt;code&gt;abs (r&lt;sub&gt;0&lt;/sub&gt; - r&lt;sub&gt;i&lt;/sub&gt;) = i&lt;/code&gt;
for any &lt;code&gt;i&lt;/code&gt; in &lt;code&gt;[1..n]&lt;/code&gt;.

The first condition determines whether two queens are in the same row. The corresponding condition for columns is satisfied as a result of our data-structure: a list of &lt;code&gt;n&lt;/code&gt; queens represents &lt;code&gt;n&lt;/code&gt; queens in '''adjacent''' columns. The final condition determines whether queen &lt;code&gt;0&lt;/code&gt; is attacking queen &lt;code&gt;i&lt;/code&gt; on the diagonal: their the horizontal separation, &lt;code&gt;i - 0&lt;/code&gt;, is equal to their vertical separation, &lt;code&gt;r&lt;sub&gt;i&lt;/sub&gt; - r&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt;. If either of these conditions is true the addition is not safe.

&lt;codeblock&gt;
&lt;&lt;safeAddition&gt;&gt;=
safeAddition :: [Int] -&gt; Int -&gt; Int -&gt; Bool
safeAddition [] _ _ = True
safeAddition (r:rows) row i =
   row /= r &amp;&amp;
   abs (row - r) /= i &amp;&amp;
   safeAddition rows row (i + 1)
&lt;/codeblock&gt;

This function is therefore called as &lt;code&gt;safeAddition currentRows newRow 1&lt;/code&gt; to determine whether the addition is safe.

== Finding solutions ==

We find solutions by placing queens on the board, one at a time, from right to left. In the following code, the body of the work is performed by &lt;code&gt;placeQueens&lt;/code&gt;. To place &lt;code&gt;k&lt;/code&gt; queens on the board we return all solutions that can be '''safely''' created by adding a queen in &lt;code&gt;row&lt;/code&gt; to &lt;code&gt;k - 1&lt;/code&gt; queens. This is performed using a simple list comprehension: 

&lt;codeblock&gt;
&lt;&lt;queens&gt;&gt;=
queens :: Int -&gt; [[Int]]
queens n =
    placeQueens n where
    placeQueens 0 = [[]]
    placeQueens k = 
      [row : rows | 
             row &lt;- [1..n], 
             rows &lt;- placeQueens (k - 1), 
             safeAddition rows row 1]
&lt;/codeblock&gt;

== Running ==

The code then performs as follows:
    *Main&gt; queens 8
    [[4,2,7,3,6,8,5,1],[5,2,4,7,3,8,6,1],
     [3,5,2,8,6,4,7,1],[3,6,4,2,8,5,7,1],
     [5,7,1,3,8,6,4,2],...]</text>
    </revision>
    <revision>
      <id>15507</id>
      <timestamp>2008-11-28T15:24:11Z</timestamp>
      <contributor>
        <ip>81.62.97.138</ip>
      </contributor>
      <comment>fix cat</comment>
      <text xml:space="preserve">[[category:Eight queens puzzle]]
The n-Queens is the extension of the 8-Queens problem to an n by n chessboard. The challenge is to place n queens on an n by n chessboard such that no two queens are attacking each other.

We represent solutions by a list of integers, &lt;code&gt;[Int]&lt;/code&gt;. The list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; represents &lt;code&gt;n&lt;/code&gt; queens in the positions:
&lt;code&gt;[(1,r&lt;sub&gt;1&lt;/sub&gt;),...,(n,r&lt;sub&gt;n&lt;/sub&gt;)]&lt;/code&gt;.

== A safe set of queens ==

We start by defining a function &lt;code&gt;safeAddition&lt;/code&gt; that determines whether adding a queen at &lt;code&gt;(0,r&lt;sub&gt;0&lt;/sub&gt;)&lt;/code&gt; is safe. We do this by checking the list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; to determine if:
# r&lt;sub&gt;i&lt;/sub&gt; = r&lt;sub&gt;0&lt;/sub&gt; or
# &lt;code&gt;abs (r&lt;sub&gt;0&lt;/sub&gt; - r&lt;sub&gt;i&lt;/sub&gt;) = i&lt;/code&gt;
for any &lt;code&gt;i&lt;/code&gt; in &lt;code&gt;[1..n]&lt;/code&gt;.

The first condition determines whether two queens are in the same row. The corresponding condition for columns is satisfied as a result of our data-structure: a list of &lt;code&gt;n&lt;/code&gt; queens represents &lt;code&gt;n&lt;/code&gt; queens in '''adjacent''' columns. The final condition determines whether queen &lt;code&gt;0&lt;/code&gt; is attacking queen &lt;code&gt;i&lt;/code&gt; on the diagonal: their the horizontal separation, &lt;code&gt;i - 0&lt;/code&gt;, is equal to their vertical separation, &lt;code&gt;r&lt;sub&gt;i&lt;/sub&gt; - r&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt;. If either of these conditions is true the addition is not safe.

&lt;codeblock&gt;
&lt;&lt;safeAddition&gt;&gt;=
safeAddition :: [Int] -&gt; Int -&gt; Int -&gt; Bool
safeAddition [] _ _ = True
safeAddition (r:rows) row i =
   row /= r &amp;&amp;
   abs (row - r) /= i &amp;&amp;
   safeAddition rows row (i + 1)
&lt;/codeblock&gt;

This function is therefore called as &lt;code&gt;safeAddition currentRows newRow 1&lt;/code&gt; to determine whether the addition is safe.

== Finding solutions ==

We find solutions by placing queens on the board, one at a time, from right to left. In the following code, the body of the work is performed by &lt;code&gt;placeQueens&lt;/code&gt;. To place &lt;code&gt;k&lt;/code&gt; queens on the board we return all solutions that can be '''safely''' created by adding a queen in &lt;code&gt;row&lt;/code&gt; to &lt;code&gt;k - 1&lt;/code&gt; queens. This is performed using a simple list comprehension: 

&lt;codeblock&gt;
&lt;&lt;queens&gt;&gt;=
queens :: Int -&gt; [[Int]]
queens n =
    placeQueens n where
    placeQueens 0 = [[]]
    placeQueens k = 
      [row : rows | 
             row &lt;- [1..n], 
             rows &lt;- placeQueens (k - 1), 
             safeAddition rows row 1]
&lt;/codeblock&gt;

== Running ==

The code then performs as follows:
    *Main&gt; queens 8
    [[4,2,7,3,6,8,5,1],[5,2,4,7,3,8,6,1],
     [3,5,2,8,6,4,7,1],[3,6,4,2,8,5,7,1],
     [5,7,1,3,8,6,4,2],...]</text>
    </revision>
    <revision>
      <id>15508</id>
      <timestamp>2008-11-29T16:25:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>+ [[Category:Programming language:Haskell]], ...</comment>
      <text xml:space="preserve">The n-Queens is the extension of the 8-Queens problem to an n by n chessboard. The challenge is to place n queens on an n by n chessboard such that no two queens are attacking each other.

We represent solutions by a list of integers, &lt;code&gt;[Int]&lt;/code&gt;. The list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; represents &lt;code&gt;n&lt;/code&gt; queens in the positions:
&lt;code&gt;[(1,r&lt;sub&gt;1&lt;/sub&gt;),...,(n,r&lt;sub&gt;n&lt;/sub&gt;)]&lt;/code&gt;.

== A safe set of queens ==

We start by defining a function &lt;code&gt;safeAddition&lt;/code&gt; that determines whether adding a queen at &lt;code&gt;(0,r&lt;sub&gt;0&lt;/sub&gt;)&lt;/code&gt; is safe. We do this by checking the list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; to determine if:
# r&lt;sub&gt;i&lt;/sub&gt; = r&lt;sub&gt;0&lt;/sub&gt; or
# &lt;code&gt;abs (r&lt;sub&gt;0&lt;/sub&gt; - r&lt;sub&gt;i&lt;/sub&gt;) = i&lt;/code&gt;
for any &lt;code&gt;i&lt;/code&gt; in &lt;code&gt;[1..n]&lt;/code&gt;.

The first condition determines whether two queens are in the same row. The corresponding condition for columns is satisfied as a result of our data-structure: a list of &lt;code&gt;n&lt;/code&gt; queens represents &lt;code&gt;n&lt;/code&gt; queens in '''adjacent''' columns. The final condition determines whether queen &lt;code&gt;0&lt;/code&gt; is attacking queen &lt;code&gt;i&lt;/code&gt; on the diagonal: their the horizontal separation, &lt;code&gt;i - 0&lt;/code&gt;, is equal to their vertical separation, &lt;code&gt;r&lt;sub&gt;i&lt;/sub&gt; - r&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt;. If either of these conditions is true the addition is not safe.

&lt;codeblock&gt;
&lt;&lt;safeAddition&gt;&gt;=
safeAddition :: [Int] -&gt; Int -&gt; Int -&gt; Bool
safeAddition [] _ _ = True
safeAddition (r:rows) row i =
   row /= r &amp;&amp;
   abs (row - r) /= i &amp;&amp;
   safeAddition rows row (i + 1)
&lt;/codeblock&gt;

This function is therefore called as &lt;code&gt;safeAddition currentRows newRow 1&lt;/code&gt; to determine whether the addition is safe.

== Finding solutions ==

We find solutions by placing queens on the board, one at a time, from right to left. In the following code, the body of the work is performed by &lt;code&gt;placeQueens&lt;/code&gt;. To place &lt;code&gt;k&lt;/code&gt; queens on the board we return all solutions that can be '''safely''' created by adding a queen in &lt;code&gt;row&lt;/code&gt; to &lt;code&gt;k - 1&lt;/code&gt; queens. This is performed using a simple list comprehension: 

&lt;codeblock&gt;
&lt;&lt;queens&gt;&gt;=
queens :: Int -&gt; [[Int]]
queens n =
    placeQueens n where
    placeQueens 0 = [[]]
    placeQueens k = 
      [row : rows | 
             row &lt;- [1..n], 
             rows &lt;- placeQueens (k - 1), 
             safeAddition rows row 1]
&lt;/codeblock&gt;

== Running ==

The code then performs as follows:
    *Main&gt; queens 8
    [[4,2,7,3,6,8,5,1],[5,2,4,7,3,8,6,1],
     [3,5,2,8,6,4,7,1],[3,6,4,2,8,5,7,1],
     [5,7,1,3,8,6,4,2],...]

[[Category:Eight queens puzzle|Haskell]]
[[Category:Programming language:Haskell]]</text>
    </revision>
    <revision>
      <id>15676</id>
      <timestamp>2008-12-24T11:46:58Z</timestamp>
      <contributor>
        <ip>71.141.107.171</ip>
      </contributor>
      <text xml:space="preserve">The n-Queens is the extension of the 8-Queens problem to an n by n chessboard. The challenge is to place n queens on an n by n chessboard such that no two queens are attacking each other.

We represent solutions by a list of integers, &lt;code&gt;[Int]&lt;/code&gt;. The list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; represents &lt;code&gt;n&lt;/code&gt; queens in the positions:
&lt;code&gt;[(1,r&lt;sub&gt;1&lt;/sub&gt;),...,(n,r&lt;sub&gt;n&lt;/sub&gt;)]&lt;/code&gt;.

== A safe set of queens ==

We start by defining a function &lt;code&gt;safeAddition&lt;/code&gt; that determines whether adding a queen at &lt;code&gt;(0,r&lt;sub&gt;0&lt;/sub&gt;)&lt;/code&gt; is safe. We do this by checking the list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; to determine if:
# r&lt;sub&gt;i&lt;/sub&gt; = r&lt;sub&gt;0&lt;/sub&gt; or
# &lt;code&gt;abs (r&lt;sub&gt;0&lt;/sub&gt; - r&lt;sub&gt;i&lt;/sub&gt;) = i&lt;/code&gt;
for any &lt;code&gt;i&lt;/code&gt; in &lt;code&gt;[1..n]&lt;/code&gt;.

The first condition determines whether two queens are in the same row. The corresponding condition for columns is satisfied as a result of our data-structure: a list of &lt;code&gt;n&lt;/code&gt; queens represents &lt;code&gt;n&lt;/code&gt; queens in '''adjacent''' columns. The final condition determines whether queen &lt;code&gt;0&lt;/code&gt; is attacking queen &lt;code&gt;i&lt;/code&gt; on the diagonal: their the horizontal separation, &lt;code&gt;i - 0&lt;/code&gt;, is equal to their vertical separation, &lt;code&gt;r&lt;sub&gt;i&lt;/sub&gt; - r&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt;. If either of these conditions is true the addition is not safe.

&lt;codeblock language=&quot;haskell&quot;&gt;
&lt;&lt;safeAddition&gt;&gt;=
safeAddition :: [Int] -&gt; Int -&gt; Int -&gt; Bool
safeAddition [] _ _ = True
safeAddition (r:rows) row i =
   row /= r &amp;&amp;
   abs (row - r) /= i &amp;&amp;
   safeAddition rows row (i + 1)
&lt;/codeblock&gt;

This function is therefore called as &lt;code&gt;safeAddition currentRows newRow 1&lt;/code&gt; to determine whether the addition is safe.

== Finding solutions ==

We find solutions by placing queens on the board, one at a time, from right to left. In the following code, we perform a fold over the number of queens from 1 to &lt;code&gt;n&lt;/code&gt;. At each step, the function &lt;code&gt;f&lt;/code&gt; returns all solutions that can be '''safely''' created by adding a queen in &lt;code&gt;row&lt;/code&gt; to a previous solution for &lt;code&gt;k - 1&lt;/code&gt; queens. This is performed using a simple list comprehension: 

&lt;codeblock language=&quot;haskell&quot;&gt;
&lt;&lt;queens&gt;&gt;=
queens :: Int -&gt; [[Int]]
queens n = foldM f [] [1..n] where
    f rows _ = [row : rows |
                row &lt;- [1..n],
                safeAddition rows row 1]
&lt;/codeblock&gt;

== Running ==

The code then performs as follows:
    *Main&gt; queens 8
    [[4,2,7,3,6,8,5,1],[5,2,4,7,3,8,6,1],
     [3,5,2,8,6,4,7,1],[3,6,4,2,8,5,7,1],
     [5,7,1,3,8,6,4,2],...]

[[Category:Eight queens puzzle|Haskell]]
[[Category:Programming language:Haskell]]</text>
    </revision>
    <revision>
      <id>16167</id>
      <timestamp>2009-02-07T21:09:19Z</timestamp>
      <contributor>
        <ip>18.138.5.244</ip>
      </contributor>
      <comment>confusing</comment>
      <text xml:space="preserve">The n-Queens is the extension of the 8-Queens problem to an n by n chessboard. The challenge is to place n queens on an n by n chessboard such that no two queens are attacking each other.

We represent solutions by a list of integers, &lt;code&gt;[Int]&lt;/code&gt;. The list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; represents &lt;code&gt;n&lt;/code&gt; queens in the positions:
&lt;code&gt;[(1,r&lt;sub&gt;1&lt;/sub&gt;),...,(n,r&lt;sub&gt;n&lt;/sub&gt;)]&lt;/code&gt;.

== A safe set of queens ==

We start by defining a function &lt;code&gt;safeAddition&lt;/code&gt; that determines whether adding a queen at &lt;code&gt;(0,r&lt;sub&gt;0&lt;/sub&gt;)&lt;/code&gt; is safe. We do this by checking the list &lt;code&gt;[r&lt;sub&gt;1&lt;/sub&gt;,...,r&lt;sub&gt;n&lt;/sub&gt;]&lt;/code&gt; to determine if:
# r&lt;sub&gt;i&lt;/sub&gt; = r&lt;sub&gt;0&lt;/sub&gt; or
# &lt;code&gt;abs (r&lt;sub&gt;0&lt;/sub&gt; - r&lt;sub&gt;i&lt;/sub&gt;) = i&lt;/code&gt;
for any &lt;code&gt;i&lt;/code&gt; in &lt;code&gt;[1..n]&lt;/code&gt;.

The first condition determines whether two queens are in the same row. The corresponding condition for columns is satisfied as a result of our data-structure: a list of &lt;code&gt;n&lt;/code&gt; queens represents &lt;code&gt;n&lt;/code&gt; queens in '''adjacent''' columns. The second condition determines whether queen &lt;code&gt;0&lt;/code&gt; is attacking queen &lt;code&gt;i&lt;/code&gt; on the diagonal: whether their horizontal separation, &lt;code&gt;i - 0&lt;/code&gt;, is equal to their vertical separation, &lt;code&gt;r&lt;sub&gt;i&lt;/sub&gt; - r&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt;. If either of these conditions is true the addition is not safe.

&lt;codeblock language=&quot;haskell&quot;&gt;
&lt;&lt;safeAddition&gt;&gt;=
safeAddition :: [Int] -&gt; Int -&gt; Int -&gt; Bool
safeAddition [] _ _ = True
safeAddition (r:rows) row i =
   row /= r &amp;&amp;
   abs (row - r) /= i &amp;&amp;
   safeAddition rows row (i + 1)
&lt;/codeblock&gt;

This function is therefore called as &lt;code&gt;safeAddition currentRows newRow 1&lt;/code&gt; to determine whether the addition is safe.

== Finding solutions ==

We find solutions by placing queens on the board, one at a time, from right to left. In the following code, we perform a fold over the number of queens from 1 to &lt;code&gt;n&lt;/code&gt;. At each step, the function &lt;code&gt;f&lt;/code&gt; returns all solutions that can be '''safely''' created by adding a queen in &lt;code&gt;row&lt;/code&gt; to a previous solution for &lt;code&gt;k - 1&lt;/code&gt; queens. This is performed using a simple list comprehension: 

&lt;codeblock language=&quot;haskell&quot;&gt;
&lt;&lt;queens&gt;&gt;=
queens :: Int -&gt; [[Int]]
queens n = foldM f [] [1..n] where
    f rows _ = [row : rows |
                row &lt;- [1..n],
                safeAddition rows row 1]
&lt;/codeblock&gt;

== Running ==

The code then performs as follows:
    *Main&gt; queens 8
    [[4,2,7,3,6,8,5,1],[5,2,4,7,3,8,6,1],
     [3,5,2,8,6,4,7,1],[3,6,4,2,8,5,7,1],
     [5,7,1,3,8,6,4,2],...]

[[Category:Eight queens puzzle|Haskell]]
[[Category:Programming language:Haskell]]</text>
    </revision>
  </page>
  <page>
    <title>Eight queens puzzle (C)</title>
    <id>2916</id>
    <revision>
      <id>8570</id>
      <timestamp>2007-01-16T08:48:51Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>First solution in C, based on brute force search</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    return;
}
&lt;/codeblock&gt;

Finally, we test the current position to see if it is valid by examining each pair of queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
              queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
            queen_rows[queen_num_2] - queen_rows[queen_num_1] ==
              queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
            )
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

Finally, to print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(void) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;move to next position&gt;&gt;
        &lt;&lt;verify current position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8571</id>
      <timestamp>2007-01-16T08:54:41Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    return;
}
&lt;/codeblock&gt;

Finally, we test the current position to see if it is valid by examining each pair of queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes down and to the right:

{|border=&quot;1&quot;
|Q|width=20|.|width=20|.|width=20|.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_2] - queen_rows[queen_num_1] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2]
&lt;/codeblock&gt;

Finally, to print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;move to next position&gt;&gt;
        &lt;&lt;verify current position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8572</id>
      <timestamp>2007-01-16T08:56:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Explain diagonals more</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    return;
}
&lt;/codeblock&gt;

Finally, we test the current position to see if it is valid by examining each pair of queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])
&lt;/codeblock&gt;

Finally, to print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;move to next position&gt;&gt;
        &lt;&lt;verify current position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8573</id>
      <timestamp>2007-01-16T08:58:56Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Deallocation</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Finally, we test the current position to see if it is valid by examining each pair of queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])
&lt;/codeblock&gt;

Finally, to print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;move to next position&gt;&gt;
        &lt;&lt;verify current position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8574</id>
      <timestamp>2007-01-16T09:00:25Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Move to next after verify instead of before</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])
&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8575</id>
      <timestamp>2007-01-16T09:13:57Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Oops, two queens being compared must be different queens</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_num_1 != queen_num_2 &amp;&amp;
            (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
             queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
             &lt;&lt;queens are on same diagonal&gt;&gt;))
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8576</id>
      <timestamp>2007-01-16T09:44:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>+ Combination brute force search</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_num_1 != queen_num_2 &amp;&amp;
            (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
             queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
             &lt;&lt;queens are on same diagonal&gt;&gt;))
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num)
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2 &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = queen_cols[0];
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4

&lt;/pre&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8577</id>
      <timestamp>2007-01-16T09:46:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Compiler errors</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=0; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_num_1 != queen_num_2 &amp;&amp;
            (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
             queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
             &lt;&lt;queens are on same diagonal&gt;&gt;))
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4

&lt;/pre&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8578</id>
      <timestamp>2007-01-16T09:49:29Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Slight optimization in visiting queen pairs</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_num_1 != queen_num_2 &amp;&amp;
            (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
             queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
             &lt;&lt;queens are on same diagonal&gt;&gt;))
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4

&lt;/pre&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8579</id>
      <timestamp>2007-01-16T09:50:01Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>No longer need to test queens are different after loop change</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4

&lt;/pre&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8580</id>
      <timestamp>2007-01-16T09:56:21Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Combination brute force search */ Fix two problems causing infinite loop, add example output</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8581</id>
      <timestamp>2007-01-16T10:10:35Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add one queen per row</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only ___ seconds to find all 92 solutions to the 8 queens problem.

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8582</id>
      <timestamp>2007-01-16T10:12:52Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Measurement</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8583</id>
      <timestamp>2007-01-16T10:35:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Permutations</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8584</id>
      <timestamp>2007-01-16T10:40:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Permutation: Position remaining queens in free columns</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));
int col_num;

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8587</id>
      <timestamp>2007-01-16T11:43:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add backtracking search</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));
int col_num;

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        if (queen_cols[current_queen] &gt;= n) {
            /* Went off right side */
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (queen_cols[current_queen] &lt; n) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            /* We have a solution */
            &lt;&lt;print out current position&gt;&gt;
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8588</id>
      <timestamp>2007-01-16T11:44:32Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix chunks</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        if (queen_cols[current_queen] &gt;= n) {
            /* Went off right side */
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (queen_cols[current_queen] &lt; n) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            /* We have a solution */
            &lt;&lt;print out current position&gt;&gt;
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8589</id>
      <timestamp>2007-01-16T12:35:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Number of solutions, symmetry in final solution</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\floor{n/2}&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\floor{n/2}&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\ceil{n/2}&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8590</id>
      <timestamp>2007-01-16T12:52:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Single solutions, perf, etc.</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\floor{n/2}&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\floor{n/2}&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\ceil{n/2}&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

This is considerably faster than the simple permutation algorithm. On the same software and hardware, the basic permutation solution requires 77 seconds to solve the 12 queens problem, whereas backtracking search needs only 0.1 seconds, and can enumerate all solutions to the 15 queens problem in 30 seconds, confirming the known result that it has 2&amp;nbsp;279&amp;nbsp;184 solutions. Moreover, it can find a single solution to the 29 queen problem in 1 second.

== Single solutions ==

Although the above backtracking search technique does well at enumerating all solutions, there are techniques for finding single solutions that scale well to much larger ''n''. One successful technique, called the ''minimum-conflicts heuristic'', works by beginning with a partial solution where queens are attacking one another and attempting to eliminate them by moving queens. Here's how one such solution might work:

&lt;codeblock language=c&gt;
&lt;&lt;find single solution&gt;&gt;=
void find_single_solution() {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;

    for(queen_num = 0; queen_num &lt; n; queen_num++) {
        &lt;&lt;place queen in the column with the least conflicts&gt;&gt;
    }

    while(1) {
        &lt;&lt;find queen with the most conflicts&gt;&gt;
        &lt;&lt;move it to the column with the least conflicts&gt;&gt;
    }
    
    &lt;&lt;print out current position&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8591</id>
      <timestamp>2007-01-16T12:54:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fix math</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\lceil{n/2}\rceil&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

This is considerably faster than the simple permutation algorithm. On the same software and hardware, the basic permutation solution requires 77 seconds to solve the 12 queens problem, whereas backtracking search needs only 0.1 seconds, and can enumerate all solutions to the 15 queens problem in 30 seconds, confirming the known result that it has 2&amp;nbsp;279&amp;nbsp;184 solutions. Moreover, it can find a single solution to the 29 queen problem in 1 second.

== Single solutions ==

Although the above backtracking search technique does well at enumerating all solutions, there are techniques for finding single solutions that scale well to much larger ''n''. One successful technique, called the ''minimum-conflicts heuristic'', works by beginning with a partial solution where queens are attacking one another and attempting to eliminate them by moving queens. Here's how one such solution might work:

&lt;codeblock language=c&gt;
&lt;&lt;find single solution&gt;&gt;=
void find_single_solution() {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;

    for(queen_num = 0; queen_num &lt; n; queen_num++) {
        &lt;&lt;place queen in the column with the least conflicts&gt;&gt;
    }

    while(1) {
        &lt;&lt;find queen with the most conflicts&gt;&gt;
        &lt;&lt;move it to the column with the least conflicts&gt;&gt;
    }
    
    &lt;&lt;print out current position&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11641</id>
      <timestamp>2007-11-19T20:23:57Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\lceil{n/2}\rceil&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

This is considerably faster than the simple permutation algorithm. On the same software and hardware, the basic permutation solution requires 77 seconds to solve the 12 queens problem, whereas backtracking search needs only 0.1 seconds, and can enumerate all solutions to the 15 queens problem in 30 seconds, confirming the known result that it has 2&amp;nbsp;279&amp;nbsp;184 solutions. Moreover, it can find a single solution to the 29 queen problem in 1 second.

== Single solutions ==

Although the above backtracking search technique does well at enumerating all solutions, there are techniques for finding single solutions that scale well to much larger ''n''. One successful technique, called the ''minimum-conflicts heuristic'', works by beginning with a partial solution where queens are attacking one another and attempting to eliminate them by moving queens. Here's how one such solution might work:

&lt;codeblock language=c&gt;
&lt;&lt;find single solution&gt;&gt;=
void find_single_solution() {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;

    for(queen_num = 0; queen_num &lt; n; queen_num++) {
        &lt;&lt;place queen in the column with the least conflicts&gt;&gt;
    }

    while(1) {
        &lt;&lt;find queen with the most conflicts&gt;&gt;
        &lt;&lt;move it to the column with the least conflicts&gt;&gt;
    }
    
    &lt;&lt;print out current position&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15658</id>
      <timestamp>2008-12-18T11:55:48Z</timestamp>
      <contributor>
        <ip>194.69.32.50</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

FIELD_MESSAGE_erererlinoco

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\lceil{n/2}\rceil&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

This is considerably faster than the simple permutation algorithm. On the same software and hardware, the basic permutation solution requires 77 seconds to solve the 12 queens problem, whereas backtracking search needs only 0.1 seconds, and can enumerate all solutions to the 15 queens problem in 30 seconds, confirming the known result that it has 2&amp;nbsp;279&amp;nbsp;184 solutions. Moreover, it can find a single solution to the 29 queen problem in 1 second.

== Single solutions ==

Although the above backtracking search technique does well at enumerating all solutions, there are techniques for finding single solutions that scale well to much larger ''n''. One successful technique, called the ''minimum-conflicts heuristic'', works by beginning with a partial solution where queens are attacking one another and attempting to eliminate them by moving queens. Here's how one such solution might work:

&lt;codeblock language=c&gt;
&lt;&lt;find single solution&gt;&gt;=
void find_single_solution() {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;

    for(queen_num = 0; queen_num &lt; n; queen_num++) {
        &lt;&lt;place queen in the column with the least conflicts&gt;&gt;
    }

    while(1) {
        &lt;&lt;find queen with the most conflicts&gt;&gt;
        &lt;&lt;move it to the column with the least conflicts&gt;&gt;
    }
    
    &lt;&lt;print out current position&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15660</id>
      <timestamp>2008-12-18T12:18:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We present a few different solutions to the general ''n'' queens puzzle in C.

== Brute force search ==

In this obvious but very slow solution, we simply consider all possible places on the board where the ''n'' queens could go, rejecting any that don't satisfy the conditions, including the implicit condition that no two queens occupy the same square. For eight queens, this solution considers &lt;math&gt;64^8&lt;/math&gt; or 281&amp;nbsp;474&amp;nbsp;976&amp;nbsp;710&amp;nbsp;656 different solutions, of which only 92 are valid.

Rather than represent the board explicitly, we store the row and column number of each queen, between 0 and &lt;math&gt;n-1&lt;/math&gt;, in two arrays:

&lt;codeblock language=c&gt;
&lt;&lt;allocate data structures&gt;&gt;=
int* queen_rows = (int*)calloc(n, sizeof(int));
int* queen_cols = (int*)calloc(n, sizeof(int));

&lt;&lt;deallocate data structures&gt;&gt;=
free(queen_rows);
free(queen_cols);
&lt;/codeblock&gt;

Because we use &lt;code&gt;calloc()&lt;/code&gt;, all queens start at row 0, column 0, or the upper-left corner of the board. The call to &lt;code&gt;calloc()&lt;/code&gt; requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdlib.h&gt;   /* calloc() */
&lt;/codeblock&gt;

We can test the current position to see if it is valid by examining each pair of two different queens and making sure they are in different places and do not attack one another (the inner counter starts at &lt;code&gt;queen_num_1 + 1&lt;/code&gt; to ensure each pair of queens is visited only once):

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num_1, queen_num_2;
int is_valid;

&lt;&lt;verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_rows[queen_num_1] == queen_rows[queen_num_2] ||
            queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

There are two ways two queens could be on the same diagonal: in the first, the difference of their rows equals the difference of their columns, and the diagonal goes from upper-left to lower-right:

{|border=&quot;1&quot;
|Q||.||.||.
|-
|.||.||.||.
|-
|.||.||Q||.
|-
|.||.||.||.
|}

The other is that the difference of the rows is the negative of the difference of the columns, and the diagonal goes from upper-right to lower-left:

{|border=&quot;1&quot;
|.||.||Q||.
|-
|.||.||.||.
|-
|Q||.||.||.
|-
|.||.||.||.
|}

&lt;codeblock language=c&gt;
&lt;&lt;queens are on same diagonal&gt;&gt;=
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  queen_cols[queen_num_1] - queen_cols[queen_num_2] ||
queen_rows[queen_num_1] - queen_rows[queen_num_2] ==
  -(queen_cols[queen_num_1] - queen_cols[queen_num_2])&lt;/codeblock&gt;

To print out a position, we simply print the position of each queen:

&lt;codeblock language=c&gt;
&lt;&lt;variable declarations&gt;&gt;=
int queen_num;
&lt;&lt;print out current position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    printf(&quot;(%d,%d) &quot;, queen_rows[queen_num], queen_cols[queen_num]);
}
printf(&quot;\n&quot;);
&lt;/codeblock&gt;

I/O requires a header file:

&lt;codeblock language=c&gt;
&lt;&lt;header files&gt;&gt;=
#include &lt;stdio.h&gt;
&lt;/codeblock&gt;

To iterate through all the permutations, we move the very last queen one column to the right. If this puts it off the right side, we bring it down to the first column of the next row. If this puts it off the bottom side, we put it back in the top-left corner and move the previous queen forward one in the same manner. Finally, if the first queen moves off the board, we're done:

&lt;codeblock language=c&gt;
&lt;&lt;move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    if (queen_rows[queen_num] &gt;= n) {
        queen_rows[queen_num] = queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

We put it all together with a simple test driver taking ''n'' on the command line to get our first implementation:

&lt;codeblock language=c&gt;
&lt;&lt;brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

The program produces many outputs for each possible solution, each placing the queens in a different order, although order is irrelevant. For example, here is the output for the 4 queens problem, showing 24 ways of arranging each of the 2 possible solutions:

&lt;pre&gt;
(0,1) (1,3) (2,0) (3,2) &lt;-- solution 1
(0,1) (1,3) (3,2) (2,0)
(0,1) (2,0) (1,3) (3,2)
(0,1) (2,0) (3,2) (1,3)
(0,1) (3,2) (1,3) (2,0)
(0,1) (3,2) (2,0) (1,3)
(0,2) (1,0) (2,3) (3,1) &lt;-- solution 2
(0,2) (1,0) (3,1) (2,3)
(0,2) (2,3) (1,0) (3,1)
(0,2) (2,3) (3,1) (1,0)
(0,2) (3,1) (1,0) (2,3)
(0,2) (3,1) (2,3) (1,0)
(1,0) (0,2) (2,3) (3,1)
(1,0) (0,2) (3,1) (2,3)
(1,0) (2,3) (0,2) (3,1)
(1,0) (2,3) (3,1) (0,2)
(1,0) (3,1) (0,2) (2,3)
(1,0) (3,1) (2,3) (0,2)
(1,3) (0,1) (2,0) (3,2)
(1,3) (0,1) (3,2) (2,0)
(1,3) (2,0) (0,1) (3,2)
(1,3) (2,0) (3,2) (0,1)
(1,3) (3,2) (0,1) (2,0)
(1,3) (3,2) (2,0) (0,1)
(2,0) (0,1) (1,3) (3,2)
(2,0) (0,1) (3,2) (1,3)
(2,0) (1,3) (0,1) (3,2)
(2,0) (1,3) (3,2) (0,1)
(2,0) (3,2) (0,1) (1,3)
(2,0) (3,2) (1,3) (0,1)
(2,3) (0,2) (1,0) (3,1)
(2,3) (0,2) (3,1) (1,0)
(2,3) (1,0) (0,2) (3,1)
(2,3) (1,0) (3,1) (0,2)
(2,3) (3,1) (0,2) (1,0)
(2,3) (3,1) (1,0) (0,2)
(3,1) (0,2) (1,0) (2,3)
(3,1) (0,2) (2,3) (1,0)
(3,1) (1,0) (0,2) (2,3)
(3,1) (1,0) (2,3) (0,2)
(3,1) (2,3) (0,2) (1,0)
(3,1) (2,3) (1,0) (0,2)
(3,2) (0,1) (1,3) (2,0)
(3,2) (0,1) (2,0) (1,3)
(3,2) (1,3) (0,1) (2,0)
(3,2) (1,3) (2,0) (0,1)
(3,2) (2,0) (0,1) (1,3)
(3,2) (2,0) (1,3) (0,1)
&lt;/pre&gt;

== Combination brute force search ==

A number of improvements can be made to this very simple search. The simplest is that we can change our iteration step so that the queens never occupy the same square and are always in order from left to right and top to bottom. Since the order of the queens doesn't matter, this still covers all possibilities but avoids duplicated effort. To do this, we start with the ''n'' queens occupying the ''n'' distinct columns of the first row:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = 0;
    queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

When resetting a queen that has passed off the bottom of the board, it is placed in the position after the previous queen, after the previous queen has itself been moved. This ensures that the queens remain in order:

&lt;codeblock language=c&gt;
&lt;&lt;combinations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
        queen_rows[queen_num]++;
    }
    /* This condition makes sure there is room for all following queens */
    if (queen_rows[queen_num] &lt; n - 1 ||
        (queen_rows[queen_num] == n - 1 &amp;&amp; queen_cols[queen_num] &lt;= queen_num))
    {
        for(queen_num_2 = queen_num + 1; queen_num_2 &lt; n; queen_num_2++) {
            queen_cols[queen_num_2] = queen_cols[queen_num_2 - 1] + 1;
            if (queen_cols[queen_num_2] &lt; n) {
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1];
            } else {
                queen_cols[queen_num_2] = 0;
                queen_rows[queen_num_2] = queen_rows[queen_num_2 - 1] + 1;
            }
        }
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

The result of this normalization is that in the 8 queen case, we only examine &lt;math&gt;{}_{64}C_8&lt;/math&gt; or 4&amp;nbsp;426&amp;nbsp;165&amp;nbsp;368 solutions, about 63&amp;nbsp;000 times less, and moreover the output shows only different solutions, not reorderings (although it still separately shows solutions which are reflections or rotations of one another). Here is our new test main and example output:

&lt;codeblock language=c&gt;
&lt;&lt;combination_brute_force_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;combinations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;verify current position&gt;&gt;
        &lt;&lt;combinations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

Sample output for 4 and 5 queens:

&lt;pre&gt;
$ ./combination_brute_force_search_queens 4
(0,1) (1,3) (2,0) (3,2)
(0,2) (1,0) (2,3) (3,1)

$ ./combination_brute_force_search_queens 5
(0,0) (1,2) (2,4) (3,1) (4,3)
(0,0) (1,3) (2,1) (3,4) (4,2)
(0,1) (1,3) (2,0) (3,2) (4,4)
(0,1) (1,4) (2,2) (3,0) (4,3)
(0,2) (1,0) (2,3) (3,1) (4,4)
(0,2) (1,4) (2,1) (3,3) (4,0)
(0,3) (1,0) (2,2) (3,4) (4,1)
(0,3) (1,1) (2,4) (3,2) (4,0)
(0,4) (1,1) (2,3) (3,0) (4,2)
(0,4) (1,2) (2,0) (3,3) (4,1)
&lt;/pre&gt;

== One queen per row ==

The above search based on combinations is much faster than the initial brute force solution: when compiled with &quot;gcc -O3&quot; under Ubuntu Linux on a 2.4 GHz CPU, it finds all 92 solutions to the 8 queens problem in 2 minutes and 8 seconds. However, we can do much better by observing that it's possible to avoid even examining the solutions in which queens appear in the same row. The ''n''th queen must appear in the ''n''th row, since there are only ''n'' rows and none can contain more than one queen. We start each queen at the beginning of its row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = 0;
}
&lt;/codeblock&gt;

Iteration is particular simple. We move the queen to the right along its row, and if it moves off the end we reset it to the left side and do the same for the queen on the previous row:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    queen_cols[queen_num]++;
    if (queen_cols[queen_num] &gt;= n) {
        queen_cols[queen_num] = 0;
    } else {
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
&lt;/codeblock&gt;

Because it's no longer possible to have two queens in the same row, we need not test for this anymore either:

&lt;codeblock language=c&gt;
&lt;&lt;one queen per row: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (queen_cols[queen_num_1] == queen_cols[queen_num_2] ||
            &lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;one_queen_per_row_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;one queen per row: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;one queen per row: verify current position&gt;&gt;
        &lt;&lt;one queen per row: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

For the 8 queen problem, this searches through &lt;math&gt;8^8&lt;/math&gt; or 16&amp;nbsp;777&amp;nbsp;216 positions, about 260 times less than the previous one. On the same hardware and software, it requires only half a second to find all 92 solutions to the 8 queens problem.

== Permutations ==

The natural next question is, if we can avoid ever placing two queens in the same row, can we avoid ever placing them in the same column as well? The answer is that a set of queens with no two in the same row or column correspond to the mathematical concept of a [http://en.wikipedia.org/wiki/Permutation permutation] or reordering of the first ''n'' integers. For example, if the queens on rows 0 through 7 fall in columns 3, 6, 2, 7, 1, 4, 0, and 5 respectively, this corresponds to the reordering of the numbers 0, 1, 2, 3, 4, 5, 6, 7 into the order 3, 6, 2, 7, 1, 4, 0, 5. There are 8! = 40&amp;nbsp;320 such reorderings, corresponding to about 416 times less positions than in the previous implementation. We only need to check for diagonals:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: verify current position&gt;&gt;=
is_valid = 1; /* Assume initially is valid, search for disproof */
for(queen_num_1=0; is_valid &amp;&amp; queen_num_1 &lt; n; queen_num_1++) {
    for(queen_num_2=queen_num_1 + 1; is_valid &amp;&amp; queen_num_2 &lt; n; queen_num_2++) {
        if (&lt;&lt;queens are on same diagonal&gt;&gt;)
        {
            is_valid = 0;
        }
    }
}
if (is_valid) {
    &lt;&lt;print out current position&gt;&gt;
}
&lt;/codeblock&gt;

In the initial position, the queens are along the main diagonal, representing the identity permutation that does not change the order:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_cols[queen_num] = queen_num;
}
&lt;/codeblock&gt;

To iterate through the permutations, we ensure that we never place a queen in the same column as one of the ''previous'' queens by using an auxilary flag array that tracks which columns are &quot;in use&quot;, with a sentinel value at the end indicating that the &quot;''n''+1&quot;th column is never in use, whereas all the others initially are:

&lt;codeblock language=c&gt;
&lt;&lt;permutations: variable declarations&gt;&gt;=
int col_num;

&lt;&lt;permutations: allocate additional data structures&gt;&gt;=
int* col_in_use = (int*)calloc(n + 1, sizeof(int));

&lt;&lt;permutations: deallocate additional data structures&gt;&gt;=
free(col_in_use);

&lt;&lt;permutations: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    col_in_use[queen_num] = 1;
}

&lt;&lt;permutations: move to next position&gt;&gt;=
for(queen_num = n-1; queen_num &gt;= 0; queen_num--) {
    col_in_use[queen_cols[queen_num]] = 0;
    do {
        queen_cols[queen_num]++;
    } while(col_in_use[queen_cols[queen_num]]);
    if (queen_cols[queen_num] &lt; n) {
        col_in_use[queen_cols[queen_num]] = 1;
        break;
    }
}
if (queen_num &lt; 0) {
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
    return;
}
/* Put the remaining queens in the remaining free columns in order */
queen_num++;
for(col_num = 0; queen_num &lt; n &amp;&amp; col_num &lt; n; col_num++) {
    if (col_in_use[col_num] == 0) {
        col_in_use[col_num] = 1;
        queen_cols[queen_num] = col_num;
        queen_num++;
    }
}
&lt;/codeblock&gt;

The test main is similar:

&lt;codeblock language=c&gt;
&lt;&lt;permutation_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;permutations: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;permutations: set up initial queens position&gt;&gt;
    while(1) {
        &lt;&lt;permutations: verify current position&gt;&gt;
        &lt;&lt;permutations: move to next position&gt;&gt;
    }
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

On the same software and hardware, this solves the 8 queen problem in negligible time (&lt;0.01s). Whereas the one queen per row approach took nearly 6 minutes and examined 10 billion positions to solve the 10 queen problem, the permutation approach solved it in half a second and examined only 3&amp;nbsp;628&amp;nbsp;800 positions.

== Backtracking search ==

We can improve the permutation approach by noting that currently, even if a diagonal conflict occurs among the first ''k'' queens, we still iterate through all possible positions involving the rest of the queens and discard them all for the same reason. This is wasteful. Instead, we should immediately advance a queen if it ever enters the diagonal of a preceding queen. With this change our &quot;move to next position&quot; and &quot;verify current position&quot; blocks collapse into one, and we iterate only over valid solutions; this is effectively a backtracking search over the solution space.

We can no longer set up a valid initial position, since this would amount to finding a solution. Instead, we have only the first ''k'' queens on the board at any one time, and we advance the last one until it reaches a valid position before adding another one. We use the column &lt;code&gt;-1&lt;/code&gt; to indicate a queen that has yet to be placed.

Because this implementation handles problems with a very large number of solutions, printing time becomes significant, so we modify it to only print the first solution and count the rest.

&lt;codeblock language=c&gt;
&lt;&lt;backtracking: variable declarations&gt;&gt;=
int current_queen = 0;
int num_solutions = 0;
int went_off_right_side;

&lt;&lt;backtracking: set up initial queens position&gt;&gt;=
for(queen_num=0; queen_num &lt; n; queen_num++) {
    queen_rows[queen_num] = queen_num;
    queen_cols[queen_num] = -1;
}

&lt;&lt;backtracking: search for solutions&gt;&gt;=
while(current_queen &gt;= 0) {
    if (queen_cols[current_queen] != -1) {
        col_in_use[queen_cols[current_queen]] = 0;
    }
    do {
        /* Find next open column */
        do {
            queen_cols[current_queen]++;
        } while(col_in_use[queen_cols[current_queen]]);

        went_off_right_side = (queen_cols[current_queen] &gt;= n) ||
                              (current_queen == 0 &amp;&amp; queen_cols[0] &gt; (n-1)/2);
        if (went_off_right_side) {
            break;
        }

        /* Check for diagonals */
        is_valid = 1;
        queen_num_1 = current_queen;
        for(queen_num_2 = 0; queen_num_2 &lt; queen_num_1; queen_num_2++) {
            if (&lt;&lt;queens are on same diagonal&gt;&gt;) {
                is_valid = 0;
                break;
            }
        }
    } while(!is_valid);

    if (!went_off_right_side) {
        col_in_use[queen_cols[current_queen]] = 1;
        if (current_queen + 1 &lt; n) {
            current_queen++;
            queen_cols[current_queen] = -1;
        } else {
            if (num_solutions == 0) {
                &lt;&lt;print out current position&gt;&gt;
            }
            num_solutions++;
            if (queen_cols[0] &lt; n/2) {                
                num_solutions++; /* Add mirrored solution */
            }
        }
    } else {
        /* Backtrack */
        queen_cols[current_queen] = -1;
        current_queen--;
    }
}
&lt;/codeblock&gt;

We achieve an additional speedup by exploting symmetry. There is a one-to-one correspondence between solutions with the first queen in the first &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt; of the columns and the mirrored solutions with it in the last &lt;math&gt;\lfloor{n/2}\rfloor&lt;/math&gt;. Thus, we count these solutions twice and only allow the first queen to go up through &lt;math&gt;\lceil{n/2}\rceil&lt;/math&gt;. If the board has an odd size, solutions with the first queen in the middle column are only counted once.

The test driver is as usual:

&lt;codeblock language=c&gt;
&lt;&lt;backtracking_search_queens.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;

void search_for_queens_solutions(int n) {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;backtracking: variable declarations&gt;&gt;

    &lt;&lt;allocate data structures&gt;&gt;
    &lt;&lt;permutations: allocate additional data structures&gt;&gt;
    &lt;&lt;backtracking: set up initial queens position&gt;&gt;
    &lt;&lt;backtracking: search for solutions&gt;&gt;
    &lt;&lt;permutations: deallocate additional data structures&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;

    printf(&quot;Number of solutions: %d\n&quot;, num_solutions);
}

int main(int argc, char* argv[]) {
    search_for_queens_solutions(atoi(argv[1]));
    return 0;
}
&lt;/codeblock&gt;

This is considerably faster than the simple permutation algorithm. On the same software and hardware, the basic permutation solution requires 77 seconds to solve the 12 queens problem, whereas backtracking search needs only 0.1 seconds, and can enumerate all solutions to the 15 queens problem in 30 seconds, confirming the known result that it has 2&amp;nbsp;279&amp;nbsp;184 solutions. Moreover, it can find a single solution to the 29 queen problem in 1 second.

== Single solutions ==

Although the above backtracking search technique does well at enumerating all solutions, there are techniques for finding single solutions that scale well to much larger ''n''. One successful technique, called the ''minimum-conflicts heuristic'', works by beginning with a partial solution where queens are attacking one another and attempting to eliminate them by moving queens. Here's how one such solution might work:

&lt;codeblock language=c&gt;
&lt;&lt;find single solution&gt;&gt;=
void find_single_solution() {
    &lt;&lt;variable declarations&gt;&gt;
    &lt;&lt;allocate data structures&gt;&gt;

    for(queen_num = 0; queen_num &lt; n; queen_num++) {
        &lt;&lt;place queen in the column with the least conflicts&gt;&gt;
    }

    while(1) {
        &lt;&lt;find queen with the most conflicts&gt;&gt;
        &lt;&lt;move it to the column with the least conflicts&gt;&gt;
    }
    
    &lt;&lt;print out current position&gt;&gt;
    &lt;&lt;deallocate data structures&gt;&gt;
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Eight queens puzzle (Erlang)</title>
    <id>3087</id>
    <revision>
      <id>9663</id>
      <timestamp>2007-04-05T01:02:17Z</timestamp>
      <contributor>
        <ip>68.228.231.24</ip>
      </contributor>
      <comment>started page, need to fill in and debug</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens1).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>9664</id>
      <timestamp>2007-04-05T01:26:17Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <comment>added a bit of explanation</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We start by creating a function which given an integer N will return the number of ways to place N queens on an NxN board. This calls another method which keeps track of the board size, the number of queens left to place and a list of queens that have already been placed. This list contains the row of each queen. Each call this checks the state of the already placed queens.
&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

This function trys to place a queen in every row recursively calling count and decreasing the number of queens left to place.
&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

A state is good if it is an empty list or if every queen is in a different row and diagonal.
&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

All the queens are in different rows if there is only one queen or if the row of the first queen is not in the rest of the list and the rest of the queens are all in different rows.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

This function fans out from each queen checking that no other queen lies in its path.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

Putting this together we have a solution:
&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens1).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>9665</id>
      <timestamp>2007-04-05T01:29:24Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <minor/>
      <comment>little mistake fix</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

We start by creating a function which given an integer N will return the number of ways to place N queens on an NxN board. This calls another method which keeps track of the board size, the number of queens left to place and a list of queens that have already been placed. This list contains the row of each queen. Each call this checks the state of the already placed queens.
&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

This function trys to place a queen in every row recursively calling count and decreasing the number of queens left to place.
&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

A state is good if it is an empty list or if every queen is in a different row and diagonal.
&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

All the queens are in different rows if there is only one queen or if the row of the first queen is not in the rest of the list and the rest of the queens are all in different rows.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

This function fans out from each queen checking that no other queen lies in its path.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

Putting this together we have a solution:
&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>9667</id>
      <timestamp>2007-04-05T03:04:27Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

==Implementation==
We start by creating a function which given an integer N will return the number of ways to place N queens on an NxN board. This calls another method which keeps track of the board size, the number of queens left to place and a list of queens that have already been placed. This list contains the row of each queen. Each call this checks the state of the already placed queens.
&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

This function trys to place a queen in every row recursively calling count and decreasing the number of queens left to place.
&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

A state is good if it is an empty list or if every queen is in a different row and diagonal.
&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

All the queens are in different rows if there is only one queen or if the row of the first queen is not in the rest of the list and the rest of the queens are all in different rows.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

This function fans out from each queen checking that no other queen lies in its path.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

Putting this together we have a solution:
&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

==Testing==
&lt;codeblock language=erlang&gt;
&lt;&lt;test_queens.erl&gt;&gt;=
-module(queens_test).
-export([start/0]).

start() -&gt;
    io:format(&quot;Testing queens...~n&quot;),
    Inputs = [1,2,3,4,5,6,7,8,9,10],
    Outputs = [1,0,0,3,10,4,40,92,352,724],
    test_queens({queens,count},Inputs,Outputs),
    halt().

test_queens(_,[],[]) -&gt;
    true;
test_queens({Mod,Fun},[InCurr|Inputs],[OutCurr|Outputs]) -&gt;
    ModName = erlang:atom_to_list(Mod),
    FunName = erlang:atom_to_list(Fun),
    %Actual = ModName:FunName(InCurr),
    Actual = erlang:apply(Mod,Fun,[InCurr]),
    if
        Actual == OutCurr -&gt;
            io:format(&quot;~s:~s - passed - input: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, Actual]);
        true -&gt;
            io:format(&quot;~s:~s - failed - input: ~B, expected: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, OutCurr, Actual])
    end,
    test_queens({Mod,Fun},Inputs,Outputs).
&lt;/codeblock&gt;

This can be run by doing the following from a shell:
 &gt; erlc queens.erl 
 &gt; erlc queens_test.erl
 &gt; erl -run queens_test

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>11642</id>
      <timestamp>2007-11-19T20:24:29Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

==Implementation==
We start by creating a function which given an integer N will return the number of ways to place N queens on an NxN board. This calls another method which keeps track of the board size, the number of queens left to place and a list of queens that have already been placed. This list contains the row of each queen. Each call this checks the state of the already placed queens.
&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

This function trys to place a queen in every row recursively calling count and decreasing the number of queens left to place.
&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

A state is good if it is an empty list or if every queen is in a different row and diagonal.
&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

All the queens are in different rows if there is only one queen or if the row of the first queen is not in the rest of the list and the rest of the queens are all in different rows.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

This function fans out from each queen checking that no other queen lies in its path.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

Putting this together we have a solution:
&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

==Testing==
&lt;codeblock language=erlang&gt;
&lt;&lt;test_queens.erl&gt;&gt;=
-module(queens_test).
-export([start/0]).

start() -&gt;
    io:format(&quot;Testing queens...~n&quot;),
    Inputs = [1,2,3,4,5,6,7,8,9,10],
    Outputs = [1,0,0,3,10,4,40,92,352,724],
    test_queens({queens,count},Inputs,Outputs),
    halt().

test_queens(_,[],[]) -&gt;
    true;
test_queens({Mod,Fun},[InCurr|Inputs],[OutCurr|Outputs]) -&gt;
    ModName = erlang:atom_to_list(Mod),
    FunName = erlang:atom_to_list(Fun),
    %Actual = ModName:FunName(InCurr),
    Actual = erlang:apply(Mod,Fun,[InCurr]),
    if
        Actual == OutCurr -&gt;
            io:format(&quot;~s:~s - passed - input: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, Actual]);
        true -&gt;
            io:format(&quot;~s:~s - failed - input: ~B, expected: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, OutCurr, Actual])
    end,
    test_queens({Mod,Fun},Inputs,Outputs).
&lt;/codeblock&gt;

This can be run by doing the following from a shell:
 &gt; erlc queens.erl 
 &gt; erlc queens_test.erl
 &gt; erl -run queens_test

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle|Erlang]]</text>
    </revision>
    <revision>
      <id>13896</id>
      <timestamp>2008-07-07T22:28:51Z</timestamp>
      <contributor>
        <ip>81.245.11.32</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

==Implementation==
We start by creating a function which given an integer N will return the number of ways to place N queens on an NxN board. This calls another method which keeps track of the board size, the number of queens left to place and a list of queens that have already been placed. This list contains the row of each queen. Each call this checks the state of the already placed queens.
&lt;codeblock language=erlang&gt;
&lt;&lt;count&gt;&gt;=
count(N) -&gt;
    count(N,N,[]).

count(_,0,List) -&gt;
    case checkState(List) of
        true -&gt; 1;
        false -&gt; 0
    end;
count(N,Depth,List) -&gt;
    case checkState(List) of
        true -&gt;
            tryAllRows(N,Depth,N,List);
        false -&gt; 0
    end.
&lt;/codeblock&gt;

This function tries to place a queen in every row recursively calling count and decreasing the number of queens left to place.
&lt;codeblock language=erlang&gt;
&lt;&lt;tryAllRows&gt;&gt;=
tryAllRows(_,_,0,_) -&gt;
    0;
tryAllRows(N,Depth,Row,List) -&gt;
    count(N,Depth-1,List ++ [Row]) + tryAllRows(N,Depth,Row-1,List).
&lt;/codeblock&gt;

A state is good if it is an empty list or if every queen is in a different row and diagonal.
&lt;codeblock language=erlang&gt;
&lt;&lt;checkState&gt;&gt;=
checkState([]) -&gt;
    true;
checkState(List) -&gt;
    differentRows(List) and differentDiagonals(List).
&lt;/codeblock&gt;

All the queens are in different rows if there is only one queen or if the row of the first queen is not in the rest of the list and the rest of the queens are all in different rows.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentRows&gt;&gt;=
differentRows([_]) -&gt;
    true;
differentRows([First|Rest]) -&gt;
    not lists:member(First, Rest) and differentRows(Rest).
&lt;/codeblock&gt;

This function fans out from each queen checking that no other queen lies in its path.
&lt;codeblock language=erlang&gt;
&lt;&lt;differentDiagonals&gt;&gt;=
differentDiagonals([_]) -&gt;
    true;
differentDiagonals([First|Rest]) -&gt;
    differentDiagonals(Rest, First+1, First-1) and differentDiagonals(Rest).

differentDiagonals([], _, _) -&gt;
    true;
differentDiagonals([First|_], First, _) -&gt;
    false;
differentDiagonals([First|_], _, First) -&gt;
    false;
differentDiagonals([_|Rest], Up, Down) -&gt;
    differentDiagonals(Rest, Up+1, Down-1).
&lt;/codeblock&gt;

Putting this together we have a solution:
&lt;codeblock language=erlang&gt;
&lt;&lt;queens.erl&gt;&gt;=
-module(queens).
-export([count/1]).

&lt;&lt;count&gt;&gt;
&lt;&lt;tryAllRows&gt;&gt;
&lt;&lt;checkState&gt;&gt;
&lt;&lt;differentRows&gt;&gt;
&lt;&lt;differentDiagonals&gt;&gt;
&lt;/codeblock&gt;

==Testing==
&lt;codeblock language=erlang&gt;
&lt;&lt;test_queens.erl&gt;&gt;=
-module(queens_test).
-export([start/0]).

start() -&gt;
    io:format(&quot;Testing queens...~n&quot;),
    Inputs = [1,2,3,4,5,6,7,8,9,10],
    Outputs = [1,0,0,3,10,4,40,92,352,724],
    test_queens({queens,count},Inputs,Outputs),
    halt().

test_queens(_,[],[]) -&gt;
    true;
test_queens({Mod,Fun},[InCurr|Inputs],[OutCurr|Outputs]) -&gt;
    ModName = erlang:atom_to_list(Mod),
    FunName = erlang:atom_to_list(Fun),
    %Actual = ModName:FunName(InCurr),
    Actual = erlang:apply(Mod,Fun,[InCurr]),
    if
        Actual == OutCurr -&gt;
            io:format(&quot;~s:~s - passed - input: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, Actual]);
        true -&gt;
            io:format(&quot;~s:~s - failed - input: ~B, expected: ~B, actual: ~B~n&quot;, [ModName, FunName, InCurr, OutCurr, Actual])
    end,
    test_queens({Mod,Fun},Inputs,Outputs).
&lt;/codeblock&gt;

This can be run by doing the following from a shell:
 &gt; erlc queens.erl 
 &gt; erlc queens_test.erl
 &gt; erl -run queens_test

[[Category:Programming language:Erlang]]
[[Category:Eight queens puzzle|Erlang]]</text>
    </revision>
  </page>
  <page>
    <title>Eight queens puzzle (Forth)</title>
    <id>3778</id>
    <revision>
      <id>10013</id>
      <timestamp>2007-05-12T00:27:14Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This means of solving the N-queens puzzle uses bitmasks to represent attacks along files and diagonals. Thus, boards up to 32x32 can be represented using standard Forth cells.

==Bit utilities==
'''bits''' takes the board dimensions and generates a mask containing that many bits. For example, &lt;code&gt;8 bits&lt;/code&gt; generates 255. This is used for the initial set of unused rows.

'''lowBit''' takes a mask and returns the lowest bit. '''lowBit-''' takes that mask and removes the lowest bit. These are used to iterate through all the unused rows.

'''third''' is a common name for a stack operator that returns the third item on the stack. It is similar to '''over''', but going one item deeper.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
 : bits ( bits -- mask ) 1 swap lshift 1- ;
 : lowBit  ( mask -- bit ) dup negate and ;
 : lowBit- ( mask -- mask ) dup 1- and ;
 : third ( a b c -- a b c a ) 2 pick ;
&lt;/codeblock&gt;

==Recursive routine==

'''poss''' returns a mask representing the possible rows on which a queen can stand. It is calculated by ANDing together the available diagonals and rows.

'''next3''' takes the single-bit mask for the queen under consideration, and removes it from the next diagonals and row to consider for subsequent levels of recursion.

'''try''' is the recursive routine

&lt;codeblock language=Forth&gt;
&lt;&lt;recursion&gt;&gt;=
 variable solutions
 variable nodes
 : poss ( a b c -- a b c a&amp;b&amp;c ) dup 2over and and ;

 : next3 ( dl dr f Qfilebit -- dl dr f dl' dr' f' )
   invert &gt;r
   third r@ and 2* 1+
   third r@ and 2/
   third r&gt; and ;

 : try ( dl dr f -- )             \ bitmasks for unused diagonals and files
   dup if 1 nodes +!  poss
     begin ?dup while
       dup &gt;r lowBit next3 recurse r&gt; lowBit-
     repeat
   else ( .sol) 1 solutions +! then
   drop drop drop ;
&lt;/codeblock&gt;

==Main program==

'''queens''' takes a board size, calculates how many solutions there for that board, and prints the solution (along with the number for nodes visited to find the solution).

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;
&lt;&lt;recursion&gt;&gt;
 0 value N
 : queens ( n -- ) to N
   0 solutions ! 0 nodes !
   -1 dup N bits try
   N . .&quot; queens: &quot; solutions @ . .&quot; solutions, &quot; nodes @ . .&quot; nodes&quot; ;
&lt;/codeblock&gt;

[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10014</id>
      <timestamp>2007-05-12T00:32:28Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This means of solving the N-queens puzzle uses bitmasks to represent attacks along files and diagonals. Thus, boards up to 32x32 can be represented using standard Forth cells.

==Bit utilities==
'''bits''' takes the board dimensions and generates a mask containing that many bits. For example, &lt;code&gt;8 bits&lt;/code&gt; generates 255. This is used for the initial set of unused rows.

'''lowBit''' takes a mask and returns the lowest bit. '''lowBit-''' takes that mask and removes the lowest bit. These are used to iterate through all the unused rows.

'''third''' is a common name for a stack operator that returns the third item on the stack. It is similar to '''over''', but going one item deeper.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
 : bits ( bits -- mask ) 1 swap lshift 1- ;
 : lowBit  ( mask -- bit ) dup negate and ;
 : lowBit- ( mask -- mask ) dup 1- and ;
 : third ( a b c -- a b c a ) 2 pick ;
&lt;/codeblock&gt;

==Recursive routine==

'''poss''' returns a mask representing the possible rows on which a queen can stand. It is calculated by ANDing together the available diagonals and rows.

'''next3''' takes the single-bit mask for the queen under consideration, and removes it from the next diagonals and row to consider for subsequent levels of recursion.

'''try''' is the recursive routine

&lt;codeblock language=Forth&gt;
&lt;&lt;recursion&gt;&gt;=
 variable solutions
 variable nodes
 : poss ( a b c -- a b c a&amp;b&amp;c ) dup 2over and and ;

 : next3 ( dl dr f Qfilebit -- dl dr f dl' dr' f' )
   invert &gt;r
   third r@ and 2* 1+
   third r@ and 2/
   third r&gt; and ;

 : try ( dl dr f -- )             \ bitmasks for unused diagonals and files
   dup if 1 nodes +!  poss
     begin ?dup while
       dup &gt;r lowBit next3 recurse r&gt; lowBit-
     repeat
   else ( .sol) 1 solutions +! then
   drop drop drop ;
&lt;/codeblock&gt;

==Main program==

'''queens''' takes a board size, calculates how many solutions there for that board, and prints the solution (along with the number for nodes visited to find the solution).

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;
&lt;&lt;recursion&gt;&gt;
 0 value N
 : queens ( n -- ) to N
   0 solutions ! 0 nodes !
   -1 dup N bits try
   N . .&quot; queens: &quot; solutions @ . .&quot; solutions, &quot; nodes @ . .&quot; nodes&quot; ;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10015</id>
      <timestamp>2007-05-12T02:59:43Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Add missing file tag</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This means of solving the N-queens puzzle uses bitmasks to represent attacks along files and diagonals. Thus, boards up to 32x32 can be represented using standard Forth cells.

==Bit utilities==
'''bits''' takes the board dimensions and generates a mask containing that many bits. For example, &lt;code&gt;8 bits&lt;/code&gt; generates 255. This is used for the initial set of unused rows.

'''lowBit''' takes a mask and returns the lowest bit. '''lowBit-''' takes that mask and removes the lowest bit. These are used to iterate through all the unused rows.

'''third''' is a common name for a stack operator that returns the third item on the stack. It is similar to '''over''', but going one item deeper.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
 : bits ( bits -- mask ) 1 swap lshift 1- ;
 : lowBit  ( mask -- bit ) dup negate and ;
 : lowBit- ( mask -- mask ) dup 1- and ;
 : third ( a b c -- a b c a ) 2 pick ;
&lt;/codeblock&gt;

==Recursive routine==

'''poss''' returns a mask representing the possible rows on which a queen can stand. It is calculated by ANDing together the available diagonals and rows.

'''next3''' takes the single-bit mask for the queen under consideration, and removes it from the next diagonals and row to consider for subsequent levels of recursion.

'''try''' is the recursive routine

&lt;codeblock language=Forth&gt;
&lt;&lt;recursion&gt;&gt;=
 variable solutions
 variable nodes
 : poss ( a b c -- a b c a&amp;b&amp;c ) dup 2over and and ;

 : next3 ( dl dr f Qfilebit -- dl dr f dl' dr' f' )
   invert &gt;r
   third r@ and 2* 1+
   third r@ and 2/
   third r&gt; and ;

 : try ( dl dr f -- )             \ bitmasks for unused diagonals and files
   dup if 1 nodes +!  poss
     begin ?dup while
       dup &gt;r lowBit next3 recurse r&gt; lowBit-
     repeat
   else ( .sol) 1 solutions +! then
   drop drop drop ;
&lt;/codeblock&gt;

==Main program==

'''queens''' takes a board size, calculates how many solutions there for that board, and prints the solution (along with the number for nodes visited to find the solution).

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.4th&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;recursion&gt;&gt;
 0 value N
 : queens ( n -- ) to N
   0 solutions ! 0 nodes !
   -1 dup N bits try
   N . .&quot; queens: &quot; solutions @ . .&quot; solutions, &quot; nodes @ . .&quot; nodes&quot; ;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11643</id>
      <timestamp>2007-11-19T20:24:54Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This means of solving the N-queens puzzle uses bitmasks to represent attacks along files and diagonals. Thus, boards up to 32x32 can be represented using standard Forth cells.

==Bit utilities==
'''bits''' takes the board dimensions and generates a mask containing that many bits. For example, &lt;code&gt;8 bits&lt;/code&gt; generates 255. This is used for the initial set of unused rows.

'''lowBit''' takes a mask and returns the lowest bit. '''lowBit-''' takes that mask and removes the lowest bit. These are used to iterate through all the unused rows.

'''third''' is a common name for a stack operator that returns the third item on the stack. It is similar to '''over''', but going one item deeper.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
 : bits ( bits -- mask ) 1 swap lshift 1- ;
 : lowBit  ( mask -- bit ) dup negate and ;
 : lowBit- ( mask -- mask ) dup 1- and ;
 : third ( a b c -- a b c a ) 2 pick ;
&lt;/codeblock&gt;

==Recursive routine==

'''poss''' returns a mask representing the possible rows on which a queen can stand. It is calculated by ANDing together the available diagonals and rows.

'''next3''' takes the single-bit mask for the queen under consideration, and removes it from the next diagonals and row to consider for subsequent levels of recursion.

'''try''' is the recursive routine

&lt;codeblock language=Forth&gt;
&lt;&lt;recursion&gt;&gt;=
 variable solutions
 variable nodes
 : poss ( a b c -- a b c a&amp;b&amp;c ) dup 2over and and ;

 : next3 ( dl dr f Qfilebit -- dl dr f dl' dr' f' )
   invert &gt;r
   third r@ and 2* 1+
   third r@ and 2/
   third r&gt; and ;

 : try ( dl dr f -- )             \ bitmasks for unused diagonals and files
   dup if 1 nodes +!  poss
     begin ?dup while
       dup &gt;r lowBit next3 recurse r&gt; lowBit-
     repeat
   else ( .sol) 1 solutions +! then
   drop drop drop ;
&lt;/codeblock&gt;

==Main program==

'''queens''' takes a board size, calculates how many solutions there for that board, and prints the solution (along with the number for nodes visited to find the solution).

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.4th&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;recursion&gt;&gt;
 0 value N
 : queens ( n -- ) to N
   0 solutions ! 0 nodes !
   -1 dup N bits try
   N . .&quot; queens: &quot; solutions @ . .&quot; solutions, &quot; nodes @ . .&quot; nodes&quot; ;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12869</id>
      <timestamp>2008-03-19T23:35:51Z</timestamp>
      <contributor>
        <ip>216.227.90.175</ip>
      </contributor>
      <comment>Was code dump, now literate.</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
 \ board is left-diagonal, right-diagonal, and vertical attacks.
 : board ( n -- l r v )
   &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
 : safe-files ( l r v -- l r v  files )  3dup and and ;
 : first ( files -- first-file )  dup negate and ;
 : rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
 : place-queen ( l r v  file -- l r v  l' r' v' )
   invert &gt;r
   2 pick r@ and 2* 1+
   2 pick r@ and 2/
   2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
 : try ( l r v -- )
   dup 0= if &lt;&lt;count solution&gt;&gt;
   else      &lt;&lt;count position&gt;&gt;
     safe-files begin ?dup while
       dup &gt;r  first place-queen recurse  r&gt;
     rest repeat
   then
   drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
 : queens ( n -- )
   &lt;&lt;clear counts&gt;&gt;
   dup board try  . .&quot; queens: &quot; 
   &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
 variable positions
 variable solutions

&lt;&lt;count solution&gt;&gt;=
 1 solutions +!

&lt;&lt;count position&gt;&gt;=
 1 positions +!

&lt;&lt;clear counts&gt;&gt;=
 0 solutions !  0 positions !
 
&lt;&lt;show counts&gt;&gt;=
 solutions @ . .&quot; solutions (tried &quot;
 positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;
       
     
==Miscellany==

'''safe-files''' needs to duplicate the top three items; this isn't a
standard Forth stack operator.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
 : 3dup ( a b c -- a b c  a b c )  dup 2over ;
&lt;/codeblock&gt;

Also, Forth requires words to be defined before they can be used, so we
have to output everything in the right order.

&lt;codeblock&gt;
&lt;&lt;queens.fs&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>12870</id>
      <timestamp>2008-03-19T23:40:28Z</timestamp>
      <contributor>
        <ip>216.227.90.175</ip>
      </contributor>
      <comment>fixed spacing in downloaded code (I think)</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
\ board is left-diagonal, right-diagonal, and vertical attacks.
: board ( n -- l r v )
  &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: safe-files ( l r v -- l r v  files )  3dup and and ;
: first ( files -- first-file )  dup negate and ;
: rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: place-queen ( l r v  file -- l r v  l' r' v' )
  invert &gt;r
  2 pick r@ and 2* 1+
  2 pick r@ and 2/
  2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: try ( l r v -- )
  dup 0= if &lt;&lt;count solution&gt;&gt;
  else      &lt;&lt;count position&gt;&gt;
    safe-files begin ?dup while
      dup &gt;r  first place-queen recurse  r&gt;
    rest repeat
  then
  drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: queens ( n -- )
  &lt;&lt;clear counts&gt;&gt;
  dup board try  . .&quot; queens: &quot; 
  &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
variable positions
variable solutions
&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count solution&gt;&gt;=
1 solutions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count position&gt;&gt;=
1 positions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;clear counts&gt;&gt;=
0 solutions !  0 positions !&lt;/codeblock&gt;
 
&lt;codeblock language=Forth&gt;
&lt;&lt;show counts&gt;&gt;=
solutions @ . .&quot; solutions (tried &quot;
positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;


==Miscellany==

'''safe-files''' needs to duplicate the top three items; this isn't a
standard Forth stack operator.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
: 3dup ( a b c -- a b c  a b c )  dup 2over ;
&lt;/codeblock&gt;

Also, Forth requires words to be defined before they can be used, so we
have to output everything in the right order.

&lt;codeblock&gt;
&lt;&lt;queens.fs&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>12871</id>
      <timestamp>2008-03-19T23:42:34Z</timestamp>
      <contributor>
        <ip>216.227.90.175</ip>
      </contributor>
      <comment>Oops, missed language attribute.</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
\ board is left-diagonal, right-diagonal, and vertical attacks.
: board ( n -- l r v )
  &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: safe-files ( l r v -- l r v  files )  3dup and and ;
: first ( files -- first-file )  dup negate and ;
: rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: place-queen ( l r v  file -- l r v  l' r' v' )
  invert &gt;r
  2 pick r@ and 2* 1+
  2 pick r@ and 2/
  2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: try ( l r v -- )
  dup 0= if &lt;&lt;count solution&gt;&gt;
  else      &lt;&lt;count position&gt;&gt;
    safe-files begin ?dup while
      dup &gt;r  first place-queen recurse  r&gt;
    rest repeat
  then
  drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: queens ( n -- )
  &lt;&lt;clear counts&gt;&gt;
  dup board try  . .&quot; queens: &quot; 
  &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
variable positions
variable solutions
&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count solution&gt;&gt;=
1 solutions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count position&gt;&gt;=
1 positions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;clear counts&gt;&gt;=
0 solutions !  0 positions !&lt;/codeblock&gt;
 
&lt;codeblock language=Forth&gt;
&lt;&lt;show counts&gt;&gt;=
solutions @ . .&quot; solutions (tried &quot;
positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;


==Miscellany==

'''safe-files''' needs to duplicate the top three items; this isn't a
standard Forth stack operator.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
: 3dup ( a b c -- a b c  a b c )  dup 2over ;
&lt;/codeblock&gt;

Also, Forth requires words to be defined before they can be used, so we
have to output everything in the right order.

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.fs&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>12872</id>
      <timestamp>2008-03-19T23:44:30Z</timestamp>
      <contributor>
        <ip>216.227.90.175</ip>
      </contributor>
      <comment>grr...why does the header have the wrong comment type?</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
\ board is left-diagonal, right-diagonal, and vertical attacks.
: board ( n -- l r v )
  &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: safe-files ( l r v -- l r v  files )  3dup and and ;
: first ( files -- first-file )  dup negate and ;
: rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: place-queen ( l r v  file -- l r v  l' r' v' )
  invert &gt;r
  2 pick r@ and 2* 1+
  2 pick r@ and 2/
  2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: try ( l r v -- )
  dup 0= if &lt;&lt;count solution&gt;&gt;
  else      &lt;&lt;count position&gt;&gt;
    safe-files begin ?dup while
      dup &gt;r  first place-queen recurse  r&gt;
    rest repeat
  then
  drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: queens ( n -- )
  &lt;&lt;clear counts&gt;&gt;
  dup board try  . .&quot; queens: &quot; 
  &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
variable positions
variable solutions
&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count solution&gt;&gt;=
1 solutions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count position&gt;&gt;=
1 positions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;clear counts&gt;&gt;=
0 solutions !  0 positions !&lt;/codeblock&gt;
 
&lt;codeblock language=Forth&gt;
&lt;&lt;show counts&gt;&gt;=
solutions @ . .&quot; solutions (tried &quot;
positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;


==Miscellany==

'''safe-files''' needs to duplicate the top three items; this isn't a
standard Forth stack operator.

&lt;codeblock language=Forth&gt;
&lt;&lt;utilities&gt;&gt;=
: 3dup ( a b c -- a b c  a b c )  dup 2over ;
&lt;/codeblock&gt;

Also, Forth requires words to be defined before they can be used, so we
have to output everything in the right order.

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.4th&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13430</id>
      <timestamp>2008-05-21T19:59:31Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <comment>elide incorrect definition</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
\ board is left-diagonal, right-diagonal, and vertical attacks.
: board ( n -- l r v )
  &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: safe-files ( l r v -- l r v  files )  dup 2over and and ;
: first ( files -- first-file )  dup negate and ;
: rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: place-queen ( l r v  file -- l r v  l' r' v' )
  invert &gt;r
  2 pick r@ and 2* 1+
  2 pick r@ and 2/
  2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: try ( l r v -- )
  dup 0= if &lt;&lt;count solution&gt;&gt;
  else      &lt;&lt;count position&gt;&gt;
    safe-files begin ?dup while
      dup &gt;r  first place-queen recurse  r&gt;
    rest repeat
  then
  drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: queens ( n -- )
  &lt;&lt;clear counts&gt;&gt;
  dup board try  . .&quot; queens: &quot; 
  &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
variable positions
variable solutions
&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count solution&gt;&gt;=
1 solutions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count position&gt;&gt;=
1 positions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;clear counts&gt;&gt;=
0 solutions !  0 positions !&lt;/codeblock&gt;
 
&lt;codeblock language=Forth&gt;
&lt;&lt;show counts&gt;&gt;=
solutions @ . .&quot; solutions (tried &quot;
positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;


==Miscellany==

Forth requires words to be defined before they can be used, so we
have to declare everything in the right order.

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.4th&gt;&gt;=
&lt;&lt;utilities&gt;&gt;
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13431</id>
      <timestamp>2008-05-21T20:04:57Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This is a standard depth-first backtracking solution to the N queens
problem.  It uses bitmasks for the lists, thus it will only work for
values of N less than or equal to the cell size of your Forth (usually
32 bits).


==Board Representation==

We track the available files in the current rank with bitmasks in which
a '1' bit represents a safe file, and a '0' bit represents a file which
is under attack by one or more queens.  We use three bitmasks, one for
each of the three possible angles of attack.  One bitmask represents the
files which already contain a queen (and thus are under attack
vertically).  The other two bitmasks represent the files which are under
attack on a diagonal.  These two bitmasks are shifted over by one bit
when we move to the next rank.

Thus an empty board of size N consists of diagonals which are all clear
(all '1' bits for easier shifting), and N clear vertical files.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
\ board is left-diagonal, right-diagonal, and vertical attacks.
: board ( n -- l r v )
  &gt;r  -1 -1  1 r&gt; lshift 1- ;
&lt;/codeblock&gt;

To get the safe positions in the current rank, we simply use a bitwise
AND to keep only the files which are not under attack from any angle.
We also have two fancy bit-manipulation words (which depend on
twos-complement math) to get the first '1' bit (file) from the set, and
to clear the first '1' bit so we can move on to trying the next one.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: safe-files ( l r v -- l r v  files )  dup 2over and and ;
: first ( files -- first-file )  dup negate and ;
: rest ( files -- files' )  dup 1- and ;
&lt;/codeblock&gt;

When we recurse, we want to make a copy of the board (leaving the old
copy for backtracking), add a queen in the current rank, and move up to
the next rank.  So we take a bit representing the file in which to place
the new queen, clear that bit in all three bitmasks, and shift the
bitmasks representing diagonal attacks to get the bitmasks for the next
rank.

&lt;codeblock language=Forth&gt;
&lt;&lt;board manipulation&gt;&gt;=
: place-queen ( l r v  file -- l r v  l' r' v' )
  invert &gt;r
  2 pick r@ and 2* 1+
  2 pick r@ and 2/
  2 pick r&gt; and ;
&lt;/codeblock&gt;


==The Recursive Solver==

Now it's pretty straightforward to write the actual solver.  If all
files contain a queen (i.e. are under attack), we have a solution.
Otherwise, we recurse over all safe files.

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: try ( l r v -- )
  dup 0= if &lt;&lt;count solution&gt;&gt;
  else      &lt;&lt;count position&gt;&gt;
    safe-files begin ?dup while
      dup &gt;r  first place-queen recurse  r&gt;
    rest repeat
  then
  drop drop drop ;
&lt;/codeblock&gt;

Then we wrap the recursive part in a top-level loop:

&lt;codeblock language=Forth&gt;
&lt;&lt;solver&gt;&gt;=
: queens ( n -- )
  &lt;&lt;clear counts&gt;&gt;
  dup board try  . .&quot; queens: &quot; 
  &lt;&lt;show counts&gt;&gt; ; 
&lt;/codeblock&gt;


==Counting==

We use two variables to keep track of how many solutions are found and
how many partial positions we looked at to find them.
   
&lt;codeblock language=Forth&gt;
&lt;&lt;counters&gt;&gt;=
variable positions
variable solutions
&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count solution&gt;&gt;=
1 solutions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;count position&gt;&gt;=
1 positions +!&lt;/codeblock&gt;

&lt;codeblock language=Forth&gt;
&lt;&lt;clear counts&gt;&gt;=
0 solutions !  0 positions !&lt;/codeblock&gt;
 
&lt;codeblock language=Forth&gt;
&lt;&lt;show counts&gt;&gt;=
solutions @ . .&quot; solutions (tried &quot;
positions @ . .&quot; positions).&quot;&lt;/codeblock&gt;


==Miscellany==

Forth requires words to be defined before they can be used, so we
have to declare everything in the right order.

&lt;codeblock language=Forth&gt;
&lt;&lt;queens.4th&gt;&gt;=
&lt;&lt;board manipulation&gt;&gt;
&lt;&lt;counters&gt;&gt;
&lt;&lt;solver&gt;&gt;
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Eight queens puzzle (J)</title>
    <id>3104</id>
    <revision>
      <id>9837</id>
      <timestamp>2007-04-23T15:38:53Z</timestamp>
      <contributor>
        <ip>213.3.79.87</ip>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{codedump}}
{{Category:Eight queens puzzle}}
==theory==
The eight queens puzzle follows the ''hylomorphic'' pattern commonly known as &quot;generate and test&quot; &amp;mdash; we first unfold a set of possible solutions, and then fold over them to eliminate the ones with captures.
 
In theory, this can be expressed as a one-liner
&lt;codeblock language=&quot;j&quot;&gt;
(#~[:(0=&gt;./)[:,/[:([:}.([:i.#)=[:|(]-&quot;1{.))\.|:)(i.A.~[:i.!) 8
&lt;/codeblock&gt;
but in practice, we prefer to articulate the program.

==practice==
Our top level expression follows the generate and test paradigm:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8 queens&gt;&gt;=
(where good) sols 8&lt;/codeblock&gt;
where '''sols 8''' generates an array of possible solutions, and '''good''' tests for the actual solutions.

===generation===
A little thought suffices to realize that any solution must have one queen in each column, so we can represent each possible board position by listing the rows in which each queen is placed.  Furthermore, there will only be one queen in each row, so we can start by generating all the permutations of 8 rows.
* '''i.y''' generates the basic ordering, &quot;0 1 2 3 4 5 6 7&quot; &amp;mdash; all queens along the diagonal
* '''i.!y''' generates the indices ('''i.''') of the y! possible permutations
* '''A.''', or '''A'''nagram, then generates the y! permutations of the basic position.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
sols=: monad : '(i.!y) A. (i.y)'
&lt;/codeblock&gt;

Note that '''monad''' here only refers to the fact that we are defining a function that takes one argument, '''y''', as opposed to a dyadic function such as '''A.''' that takes both left and right arguments.

''Question: which Haskell-style monads '''are''' present in this program?  Can you find List, Maybe, and MaxPlus?''

===testing===
The good positions are those where no captures are possible:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
good=: monad : 'zero caps y'
&lt;/codeblock&gt;

To test for captures, we check each column for diagonal captures of its successors ('''diag\.'''), and refold the results by concatenating (''',/''').  (the initial transposition ('''|:''') is an isomorphism which is incidental to the theoretical process, but important in practice) 
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
caps=: monad : ',/diag\. |:y'
&lt;/codeblock&gt;

Two queens are on the same diagonal when their distance in rows
('''| diff''', where '''|''' is the absolute value)
is the same ('''=''') as their distance in columns
(generated here by counting up ('''i.''')
to the number of columns ('''#y''').
Because a queen is always diagonally coincident with itself,
we then apply '''}.''', or '''behead''', to remove the first result,
eliminating this reflexive case.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diag=: monad : '}. (i. #y)=(| diff y)'
&lt;/codeblock&gt;

Finding the distance in rows is simply a matter of subtracting
the position of the piece in the first column ('''{.'''),
thereby converting absolute to relative row positions.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diff=: monad : 'y -&quot;1 {.y'
&lt;/codeblock&gt;
The modified rank ('''-&quot;1''') for the subtraction, in conjunction with the earlier transposition,
is a technical detail allowing us to calculate the captures for all boards in parallel.

==wrapping up==
We must make two more small definitions:
* '''zero''' will test that the maximum of a list ('''&gt;./''') is equal to 0.
* '''where''' is the passive form (left and right arguments swapped) of repeat ('''#''') &amp;mdash; and a repeat with a boolean argument is a simply a projection.
These are both simple enough that we define them directly, in point-free style.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;ancillary defs&gt;&gt;=
where=: #~
zero=: 0=&gt;./
&lt;/codeblock&gt;

When we say &lt;code&gt;(where good) sols 8&lt;/code&gt;, [http://www.jsoftware.com/ J] treats the pair of functions ''where'' and ''good'' as a [http://www.jsoftware.com/help/primer/fork.htm fork] &amp;mdash; it shares the argument, executing an expression similar to &quot;''let'' v = sols 8 ''in'' v where (good v)&quot;.

Finally, we add some boilerplate to make a small script
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8queens.ijs&gt;&gt;=
&lt;&lt;ancillary defs&gt;&gt;
&lt;&lt;definitions&gt;&gt;
echo &lt;&lt;8 queens&gt;&gt;
exit ''
&lt;/codeblock&gt;
that prints the expected 92 solutions, of which the first few (with a queen at the origin) are:
&lt;pre&gt;
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
&lt;/pre&gt;

''Exercise: produce only the 12 unique solutions by eliminating symmetric duplicates''

''Exercise: add a command line argument to specify the board size''

[[Category:Programming language:J]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>9838</id>
      <timestamp>2007-04-23T15:42:39Z</timestamp>
      <contributor>
        <ip>213.3.79.87</ip>
      </contributor>
      <comment>-codedump</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}
==theory==
The eight queens puzzle follows the ''hylomorphic'' pattern commonly known as &quot;generate and test&quot; &amp;mdash; we first unfold a set of possible solutions, and then fold over them to eliminate the ones with captures.
 
In theory, this can be expressed as a one-liner
&lt;codeblock language=&quot;j&quot;&gt;
(#~[:(0=&gt;./)[:,/[:([:}.([:i.#)=[:|(]-&quot;1{.))\.|:)(i.A.~[:i.!) 8
&lt;/codeblock&gt;
but in practice, we prefer to articulate the program.

==practice==
Our top level expression follows the generate and test paradigm:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8 queens&gt;&gt;=
(where good) sols 8&lt;/codeblock&gt;
where '''sols 8''' generates an array of possible solutions, and '''good''' tests for the actual solutions.

===generation===
A little thought suffices to realize that any solution must have one queen in each column, so we can represent each possible board position by listing the rows in which each queen is placed.  Furthermore, there will only be one queen in each row, so we can start by generating all the permutations of 8 rows.
* '''i.y''' generates the basic ordering, &quot;0 1 2 3 4 5 6 7&quot; &amp;mdash; all queens along the diagonal
* '''i.!y''' generates the indices ('''i.''') of the y! possible permutations
* '''A.''', or '''A'''nagram, then generates the y! permutations of the basic position.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
sols=: monad : '(i.!y) A. (i.y)'&lt;/codeblock&gt;

Note that '''monad''' here only refers to the fact that we are defining a function that takes one argument, '''y''', as opposed to a dyadic function such as '''A.''' that takes both left and right arguments.

''Question: which Haskell-style monads '''are''' present in this program?  Can you find List, Maybe, and MaxPlus?''

===testing===
The good positions are those where no captures are possible:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
good=: monad : 'zero caps y'&lt;/codeblock&gt;

To test for captures, we check each column for diagonal captures of its successors ('''diag\.'''), and refold the results by concatenating (''',/''').  (the initial transposition ('''|:''') is an isomorphism which is incidental to the theoretical process, but important in practice) 
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
caps=: monad : ',/diag\. |:y'&lt;/codeblock&gt;

Two queens are on the same diagonal when their distance in rows
('''| diff''', where '''|''' is the absolute value)
is the same ('''=''') as their distance in columns
(generated here by counting up ('''i.''')
to the number of columns ('''#y''').
Because a queen is always diagonally coincident with itself,
we then apply '''}.''', or '''behead''', to remove the first result,
eliminating this reflexive case.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diag=: monad : '}. (i. #y)=(| diff y)'&lt;/codeblock&gt;

Finding the distance in rows is simply a matter of subtracting
the position of the piece in the first column ('''{.'''),
thereby converting absolute to relative row positions.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diff=: monad : 'y -&quot;1 {.y'&lt;/codeblock&gt;
The modified rank ('''-&quot;1''') for the subtraction, in conjunction with the earlier transposition,
is a technical detail allowing us to calculate the captures for all boards in parallel.

==wrapping up==
We must make two more small definitions:
* '''zero''' will test that the maximum of a list ('''&gt;./''') is equal to 0.
* '''where''' is the passive form (left and right arguments swapped) of repeat ('''#''') &amp;mdash; and a repeat with a boolean argument is a simply a projection.
These are both simple enough that we define them directly, in point-free style.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;ancillary defs&gt;&gt;=
where=: #~
zero=: 0=&gt;./&lt;/codeblock&gt;

When we say &lt;code&gt;(where good) sols 8&lt;/code&gt;, [http://www.jsoftware.com/ J] treats the pair of functions ''where'' and ''good'' as a [http://www.jsoftware.com/help/primer/fork.htm fork] &amp;mdash; it shares the argument, executing an expression similar to &quot;''let'' v = sols 8 ''in'' v where (good v)&quot;.

Finally, we add some boilerplate to make a small script
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8queens.ijs&gt;&gt;=
&lt;&lt;ancillary defs&gt;&gt;
&lt;&lt;definitions&gt;&gt;
echo &lt;&lt;8 queens&gt;&gt;
exit ''
&lt;/codeblock&gt;
that prints the expected 92 solutions, of which the first few (with a queen at the origin) are:
&lt;pre&gt;
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
&lt;/pre&gt;

''Exercise: produce only the 12 unique solutions by eliminating symmetric duplicates''

''Exercise: add a command line argument to specify the board size''

[[Category:Programming language:J]]
[[Category:Eight queens puzzle]]</text>
    </revision>
    <revision>
      <id>9840</id>
      <timestamp>2007-04-23T20:03:54Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>improve explanation</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}
==theory==
The eight queens puzzle follows the ''hylomorphic'' pattern commonly known as &quot;generate and test&quot; &amp;mdash; we first unfold a set of possible solutions, and then fold over them, retaining only the ones without captures.
 
In theory, the following one-line expression suffices to solve the puzzle
&lt;codeblock language=&quot;j&quot;&gt;
(#~[:(0=&gt;./)[:,/[:([:}.([:i.#)=[:|(]-&quot;1{.))\.|:)(i.A.~[:i.!) 8
&lt;/codeblock&gt;
but in practice, we prefer to articulate the program.

==practice==
Our top level expression follows the generate and test paradigm:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8 queens&gt;&gt;=
(where good) sols 8&lt;/codeblock&gt;
* '''sols 8''' generates a set of possible solutions for an 8x8 board
* '''good''' tests for actual solutions, satisfying the given constraints

===generation===
A little thought suffices to show that any solution must have one queen in each column, so we can represent each possible board position by listing the rows in which each queen is placed.  Furthermore, there must also be only one queen in each row, so we can start by generating all the permutations of 8 rows.
* '''i.y''' generates the basic ordering, &quot;0 1 2 3 4 5 6 7&quot; &amp;mdash; all queens along the diagonal
* '''i.!y''' generates the indices ('''i.''') of the y! possible permutations
* '''A.''', or '''A'''nagram, then generates the set of the y! permutations of the basic position.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
sols=: monad : '(i.!y) A. (i.y)'&lt;/codeblock&gt;

===attention!===
Note that '''monad''' here only refers to the fact that we are defining a function that takes one argument, called '''y''' &amp;mdash; as opposed to a dyadic function such as '''A.''' that takes both left and right arguments (which would be written in a definition as ''x'' and ''y'' respectively).  In the sequel we continue to define functions using this construct.

''Question: which Haskell-style monads '''are''' present in this program?  Can you find List, Maybe, and the MaxPlus monoid?''

===testing===
The '''good''' positions, the solutions of the puzzle, are those where no captures are possible:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
good=: monad : 'zero caps y'&lt;/codeblock&gt;

We have, by design, eliminated horizontal and vertical captures,
so we need only test for the existence of diagonal '''cap'''ture'''s'''.
Again, this is divided into a generating anamorphism and a testing catamorphism.
* ('''diag\.''') unfolds each board position into a series of tests for diagonal alignment between the queen in each column and those in the following columns
* (''',/''') then refolds the results, concatenating them into a single list (which ''zero'' will then fold down to a single boolean indicating the validity of the board position)
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
caps=: monad : ',/diag\. |:y'&lt;/codeblock&gt;
(the initial transposition ('''|:''') is an isomorphism &amp;mdash;
it's incidental to the theoretical process, but important in practice) 

Two queens are on the same '''diag'''onal when their distance in rows
('''| diff''', where '''|''' is the absolute value)
is the same as ('''=''') their distance in columns,
generated here by counting up ('''i.''')
to the number of columns ('''#y''').
A queen is always diagonally coincident with itself,
so we apply '''behead''' ('''}.''') to remove the first result,
eliminating this reflexive case.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diag=: monad : '}. (i. #y)=(| diff y)'&lt;/codeblock&gt;

Finding the '''diff'''erence in rows is
simply a matter of subtracting out
the position of the piece in the first column ('''{.y'''),
thereby converting a list of absolute to a list of relative row positions.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diff=: monad : 'y -&quot;1 {.y'&lt;/codeblock&gt;
The modified rank ('''-&quot;1''') for the subtraction, in conjunction with the earlier transposition,
is a technical detail which allows us to calculate the captures for all boards breadthwise, in parallel.

==wrapping up==
We must provide two more small definitions:
* '''zero''' tests that the maximum of a list ('''&gt;./''') is equal to 0.
* '''where''' is the passive form of repeat ('''#''') &amp;mdash; a repeat with a boolean argument is a simply a projection, and by using the passive adverb ('''~''') we are able to arrange that the right argument projects elements from the left, rather than vice versa.

These definitions are simple enough that we write them directly, in point-free style.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;ancillary defs&gt;&gt;=
where=: #~
zero=: 0=&gt;./&lt;/codeblock&gt;

When we say &lt;code&gt;(where good) sols 8&lt;/code&gt;, we take advantage of one of
[http://www.jsoftware.com/ J]'s unusual syntactic constructs.
The pair of functions ''where'' and ''good''
is treated as a [http://www.jsoftware.com/help/primer/fork.htm fork] &amp;mdash;
the argument is shared, resulting in an expression
which might be expressed in a different syntax
as &quot;''let'' v = sols 8 ''in'' v `where` (good v)&quot;.

''Question: what are the parallels between the phrase &lt;code&gt;(where good) sols 8&lt;/code&gt; and a list comprehension?''

Finally, we add some boilerplate to make a small script
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8queens.ijs&gt;&gt;=
&lt;&lt;ancillary defs&gt;&gt;
&lt;&lt;definitions&gt;&gt;
echo &lt;&lt;8 queens&gt;&gt;
exit ''
&lt;/codeblock&gt;
that prints the expected 92 solutions,
of which the first few (those with a queen at the origin) are:
&lt;pre&gt;
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
...
&lt;/pre&gt;

''Exercise: produce only the 12 unique solutions by eliminating symmetric duplicates''

''Exercise: add a command line argument to specify the board size''

[[Category:Programming language:J]]
[[Category:Eight queens puzzle]]
[[Category:Permutations]]</text>
    </revision>
    <revision>
      <id>9841</id>
      <timestamp>2007-04-23T20:09:31Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* generation */ link to Kth permutation</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}
==theory==
The eight queens puzzle follows the ''hylomorphic'' pattern commonly known as &quot;generate and test&quot; &amp;mdash; we first unfold a set of possible solutions, and then fold over them, retaining only the ones without captures.
 
In theory, the following one-line expression suffices to solve the puzzle
&lt;codeblock language=&quot;j&quot;&gt;
(#~[:(0=&gt;./)[:,/[:([:}.([:i.#)=[:|(]-&quot;1{.))\.|:)(i.A.~[:i.!) 8
&lt;/codeblock&gt;
but in practice, we prefer to articulate the program.

==practice==
Our top level expression follows the generate and test paradigm:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8 queens&gt;&gt;=
(where good) sols 8&lt;/codeblock&gt;
* '''sols 8''' generates a set of possible solutions for an 8x8 board
* '''good''' tests for actual solutions, satisfying the given constraints

===generation===
A little thought suffices to show that any solution must have one queen in each column, so we can represent each possible board position by listing the rows in which each queen is placed.  Furthermore, there must also be only one queen in each row, so we can start by generating all the permutations of 8 rows.
* '''i.y''' generates the basic ordering, &quot;0 1 2 3 4 5 6 7&quot; &amp;mdash; all queens along the diagonal
* '''i.!y''' generates the indices ('''i.''') of the y! possible permutations
* '''A.''', or '''A'''nagram, then generates the set of the y! [[Kth permutation (Python, functional)|permutations]] of the basic position.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
sols=: monad : '(i.!y) A. (i.y)'&lt;/codeblock&gt;

===attention!===
Note that '''monad''' here only refers to the fact that we are defining a function that takes one argument, called '''y''' &amp;mdash; as opposed to a dyadic function such as '''A.''' that takes both left and right arguments (which would be written in a definition as ''x'' and ''y'' respectively).  In the sequel we continue to define functions using this construct.

''Question: which Haskell-style monads '''are''' present in this program?  Can you find List, Maybe, and the MaxPlus monoid?''

===testing===
The '''good''' positions, the solutions of the puzzle, are those where no captures are possible:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
good=: monad : 'zero caps y'&lt;/codeblock&gt;

We have, by design, eliminated horizontal and vertical captures,
so we need only test for the existence of diagonal '''cap'''ture'''s'''.
Again, this is divided into a generating anamorphism and a testing catamorphism.
* ('''diag\.''') unfolds each board position into a series of tests for diagonal alignment between the queen in each column and those in the following columns
* (''',/''') then refolds the results, concatenating them into a single list (which ''zero'' will then fold down to a single boolean indicating the validity of the board position)
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
caps=: monad : ',/diag\. |:y'&lt;/codeblock&gt;
(the initial transposition ('''|:''') is an isomorphism &amp;mdash;
it's incidental to the theoretical process, but important in practice) 

Two queens are on the same '''diag'''onal when their distance in rows
('''| diff''', where '''|''' is the absolute value)
is the same as ('''=''') their distance in columns,
generated here by counting up ('''i.''')
to the number of columns ('''#y''').
A queen is always diagonally coincident with itself,
so we apply '''behead''' ('''}.''') to remove the first result,
eliminating this reflexive case.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diag=: monad : '}. (i. #y)=(| diff y)'&lt;/codeblock&gt;

Finding the '''diff'''erence in rows is
simply a matter of subtracting out
the position of the piece in the first column ('''{.y'''),
thereby converting a list of absolute to a list of relative row positions.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diff=: monad : 'y -&quot;1 {.y'&lt;/codeblock&gt;
The modified rank ('''-&quot;1''') for the subtraction, in conjunction with the earlier transposition,
is a technical detail which allows us to calculate the captures for all boards breadthwise, in parallel.

==wrapping up==
We must provide two more small definitions:
* '''zero''' tests that the maximum of a list ('''&gt;./''') is equal to 0.
* '''where''' is the passive form of repeat ('''#''') &amp;mdash; a repeat with a boolean argument is a simply a projection, and by using the passive adverb ('''~''') we are able to arrange that the right argument projects elements from the left, rather than vice versa.

These definitions are simple enough that we write them directly, in point-free style.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;ancillary defs&gt;&gt;=
where=: #~
zero=: 0=&gt;./&lt;/codeblock&gt;

When we say &lt;code&gt;(where good) sols 8&lt;/code&gt;, we take advantage of one of
[http://www.jsoftware.com/ J]'s unusual syntactic constructs.
The pair of functions ''where'' and ''good''
is treated as a [http://www.jsoftware.com/help/primer/fork.htm fork] &amp;mdash;
the argument is shared, resulting in an expression
which might be expressed in a different syntax
as &quot;''let'' v = sols 8 ''in'' v `where` (good v)&quot;.

''Question: what are the parallels between the phrase &lt;code&gt;(where good) sols 8&lt;/code&gt; and a list comprehension?''

Finally, we add some boilerplate to make a small script
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8queens.ijs&gt;&gt;=
&lt;&lt;ancillary defs&gt;&gt;
&lt;&lt;definitions&gt;&gt;
echo &lt;&lt;8 queens&gt;&gt;
exit ''
&lt;/codeblock&gt;
that prints the expected 92 solutions,
of which the first few (those with a queen at the origin) are:
&lt;pre&gt;
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
...
&lt;/pre&gt;

''Exercise: produce only the 12 unique solutions by eliminating symmetric duplicates''

''Exercise: add a command line argument to specify the board size''

[[Category:Programming language:J]]
[[Category:Eight queens puzzle]]
[[Category:Permutations]]</text>
    </revision>
    <revision>
      <id>11644</id>
      <timestamp>2007-11-19T20:25:13Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}
==theory==
The eight queens puzzle follows the ''hylomorphic'' pattern commonly known as &quot;generate and test&quot; &amp;mdash; we first unfold a set of possible solutions, and then fold over them, retaining only the ones without captures.
 
In theory, the following one-line expression suffices to solve the puzzle
&lt;codeblock language=&quot;j&quot;&gt;
(#~[:(0=&gt;./)[:,/[:([:}.([:i.#)=[:|(]-&quot;1{.))\.|:)(i.A.~[:i.!) 8
&lt;/codeblock&gt;
but in practice, we prefer to articulate the program.

==practice==
Our top level expression follows the generate and test paradigm:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8 queens&gt;&gt;=
(where good) sols 8&lt;/codeblock&gt;
* '''sols 8''' generates a set of possible solutions for an 8x8 board
* '''good''' tests for actual solutions, satisfying the given constraints

===generation===
A little thought suffices to show that any solution must have one queen in each column, so we can represent each possible board position by listing the rows in which each queen is placed.  Furthermore, there must also be only one queen in each row, so we can start by generating all the permutations of 8 rows.
* '''i.y''' generates the basic ordering, &quot;0 1 2 3 4 5 6 7&quot; &amp;mdash; all queens along the diagonal
* '''i.!y''' generates the indices ('''i.''') of the y! possible permutations
* '''A.''', or '''A'''nagram, then generates the set of the y! [[Kth permutation (Python, functional)|permutations]] of the basic position.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
sols=: monad : '(i.!y) A. (i.y)'&lt;/codeblock&gt;

===attention!===
Note that '''monad''' here only refers to the fact that we are defining a function that takes one argument, called '''y''' &amp;mdash; as opposed to a dyadic function such as '''A.''' that takes both left and right arguments (which would be written in a definition as ''x'' and ''y'' respectively).  In the sequel we continue to define functions using this construct.

''Question: which Haskell-style monads '''are''' present in this program?  Can you find List, Maybe, and the MaxPlus monoid?''

===testing===
The '''good''' positions, the solutions of the puzzle, are those where no captures are possible:
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
good=: monad : 'zero caps y'&lt;/codeblock&gt;

We have, by design, eliminated horizontal and vertical captures,
so we need only test for the existence of diagonal '''cap'''ture'''s'''.
Again, this is divided into a generating anamorphism and a testing catamorphism.
* ('''diag\.''') unfolds each board position into a series of tests for diagonal alignment between the queen in each column and those in the following columns
* (''',/''') then refolds the results, concatenating them into a single list (which ''zero'' will then fold down to a single boolean indicating the validity of the board position)
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
caps=: monad : ',/diag\. |:y'&lt;/codeblock&gt;
(the initial transposition ('''|:''') is an isomorphism &amp;mdash;
it's incidental to the theoretical process, but important in practice) 

Two queens are on the same '''diag'''onal when their distance in rows
('''| diff''', where '''|''' is the absolute value)
is the same as ('''=''') their distance in columns,
generated here by counting up ('''i.''')
to the number of columns ('''#y''').
A queen is always diagonally coincident with itself,
so we apply '''behead''' ('''}.''') to remove the first result,
eliminating this reflexive case.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diag=: monad : '}. (i. #y)=(| diff y)'&lt;/codeblock&gt;

Finding the '''diff'''erence in rows is
simply a matter of subtracting out
the position of the piece in the first column ('''{.y'''),
thereby converting a list of absolute to a list of relative row positions.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;definitions&gt;&gt;=
diff=: monad : 'y -&quot;1 {.y'&lt;/codeblock&gt;
The modified rank ('''-&quot;1''') for the subtraction, in conjunction with the earlier transposition,
is a technical detail which allows us to calculate the captures for all boards breadthwise, in parallel.

==wrapping up==
We must provide two more small definitions:
* '''zero''' tests that the maximum of a list ('''&gt;./''') is equal to 0.
* '''where''' is the passive form of repeat ('''#''') &amp;mdash; a repeat with a boolean argument is a simply a projection, and by using the passive adverb ('''~''') we are able to arrange that the right argument projects elements from the left, rather than vice versa.

These definitions are simple enough that we write them directly, in point-free style.
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;ancillary defs&gt;&gt;=
where=: #~
zero=: 0=&gt;./&lt;/codeblock&gt;

When we say &lt;code&gt;(where good) sols 8&lt;/code&gt;, we take advantage of one of
[http://www.jsoftware.com/ J]'s unusual syntactic constructs.
The pair of functions ''where'' and ''good''
is treated as a [http://www.jsoftware.com/help/primer/fork.htm fork] &amp;mdash;
the argument is shared, resulting in an expression
which might be expressed in a different syntax
as &quot;''let'' v = sols 8 ''in'' v `where` (good v)&quot;.

''Question: what are the parallels between the phrase &lt;code&gt;(where good) sols 8&lt;/code&gt; and a list comprehension?''

Finally, we add some boilerplate to make a small script
&lt;codeblock language=&quot;j&quot;&gt;
&lt;&lt;8queens.ijs&gt;&gt;=
&lt;&lt;ancillary defs&gt;&gt;
&lt;&lt;definitions&gt;&gt;
echo &lt;&lt;8 queens&gt;&gt;
exit ''
&lt;/codeblock&gt;
that prints the expected 92 solutions,
of which the first few (those with a queen at the origin) are:
&lt;pre&gt;
0 4 7 5 2 6 1 3
0 5 7 2 6 3 1 4
0 6 3 5 7 1 4 2
0 6 4 7 1 3 5 2
...
&lt;/pre&gt;

''Exercise: produce only the 12 unique solutions by eliminating symmetric duplicates''

''Exercise: add a command line argument to specify the board size''

[[Category:Programming language:J]]
[[Category:Eight queens puzzle|J]]
[[Category:Permutations]]</text>
    </revision>
  </page>
  <page>
    <title>Eight queens puzzle (Scala)</title>
    <id>3228</id>
    <revision>
      <id>10976</id>
      <timestamp>2007-09-27T16:37:08Z</timestamp>
      <contributor>
        <ip>212.113.123.22</ip>
      </contributor>
      <text xml:space="preserve">&lt;codeblock language=scala&gt;
object queens {

  def abs(x: Int) = if (x&gt;=0) x else -x

  def isSafe(col: Int, queens: List[Int], delta: Int): Boolean =
    queens.isEmpty || ((queens.head != col) &amp;&amp; (abs(queens.head - col) != delta) &amp;&amp; isSafe(col, queens.tail, delta+1))

  def queens(n: Int): List[List[Int]] = {
    def placeQueens(k: Int): List[List[Int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- List.range(1, n + 1)
                 if isSafe(column, queens, 1) } yield column :: queens
    placeQueens(n)
  }

}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10987</id>
      <timestamp>2007-09-30T04:15:13Z</timestamp>
      <contributor>
        <ip>81.222.208.204</ip>
      </contributor>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=scala&gt;
object queens {

  def abs(x: Int) = if (x&gt;=0) x else -x

  def isSafe(col: Int, queens: List[Int], delta: Int): Boolean =
    queens.isEmpty || ((queens.head != col) &amp;&amp; (abs(queens.head - col) != delta) &amp;&amp; isSafe(col, queens.tail, delta+1))

  def queens(n: Int): List[List[Int]] = {
    def placeQueens(k: Int): List[List[Int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- List.range(1, n + 1)
                 if isSafe(column, queens, 1) } yield column :: queens
    placeQueens(n)
  }

}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11645</id>
      <timestamp>2007-11-19T20:25:38Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=scala&gt;
object queens {

  def abs(x: Int) = if (x&gt;=0) x else -x

  def isSafe(col: Int, queens: List[Int], delta: Int): Boolean =
    queens.isEmpty || ((queens.head != col) &amp;&amp; (abs(queens.head - col) != delta) &amp;&amp; isSafe(col, queens.tail, delta+1))

  def queens(n: Int): List[List[Int]] = {
    def placeQueens(k: Int): List[List[Int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- List.range(1, n + 1)
                 if isSafe(column, queens, 1) } yield column :: queens
    placeQueens(n)
  }

}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12883</id>
      <timestamp>2008-03-22T07:51:21Z</timestamp>
      <contributor>
        <ip>61.213.69.15</ip>
      </contributor>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=scala&gt;
object EightQueens extends Application {
  def isSafe(col: int, queens: List[int], delta: int): boolean =
    queens.isEmpty || 
      (queens.head != col &amp;&amp; 
       Math.abs(queens.head - col) != delta &amp;&amp; 
       isSafe(col, queens.tail, delta + 1))

  def queens(n: int): List[List[int]] = {
    def placeQueens(k: int): List[List[int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- (1 to n)
                 if isSafe(column, queens, 1) } yield column :: queens
    placeQueens(n)
  }
  
  queens(8).foreach(println(_))
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12884</id>
      <timestamp>2008-03-22T08:31:13Z</timestamp>
      <contributor>
        <ip>61.213.69.15</ip>
      </contributor>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=scala&gt;
object EightQueens extends Application {
  def isSafe(queens: List[int], column: int, delta: int): boolean =
    queens.isEmpty || 
      (queens.head != column &amp;&amp; 
       Math.abs(queens.head - column) != delta &amp;&amp; 
       isSafe(queens.tail, column, delta + 1))
  def queens(n: int): List[List[int]] = {
    def placeQueens(k: int): List[List[int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- (1 to n)
                 if isSafe(queens, column, 1) } yield column :: queens
    placeQueens(n)
  }
  queens(8).foreach(println(_))
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13025</id>
      <timestamp>2008-04-10T14:09:47Z</timestamp>
      <contributor>
        <ip>91.121.102.64</ip>
      </contributor>
      <text xml:space="preserve">{{codedump}}

&lt;codeblock language=scala&gt;
object EightQueens extends Application {
  def isSafe(queens: List[Int], column: Int, delta: Int): Boolean =
    queens.isEmpty || 
      ((queens.head != column) &amp;&amp; 
      (Math.abs(queens.head - column) != delta) &amp;&amp;
      isSafe(queens.tail, column, delta+1))

  def queens(n: Int): List[List[Int]] = {
    def placeQueens(k: Int): List[List[Int]] =
      if (k == 0) List(List())
      else for { queens &lt;- placeQueens(k - 1)
                 column &lt;- (1 to n)
                 if isSafe(queens, column, 1) } yield column :: queens
    placeQueens(n)
  }
  queens(8).foreach(println(_))
}
&lt;/codeblock&gt;

{{TODO|Finish this solution}}

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16616</id>
      <timestamp>2010-01-08T12:21:09Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">To be able to solve the Eight Queens puzzle, we must first be able to add one queen to a partial solution (adding a queen to an empty solution is trivial).  Assume that our strategy is to place queens one row at a time, starting with the bottom row.  If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a list containing the column numbers of the queens that have already been placed and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
    val finder: ((Int, Int)) =&gt; Seq[Int] =
      { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'' for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
      (s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
  object UnsafeSet {

    &lt;&lt;Define finder function&gt;&gt;

    def apply (s: List[Int]) =

      &lt;&lt;Create set of unsafe squares&gt;&gt;
  }
&lt;/codeblock&gt;

If ''p'' is the list of solutions, we can get a partial solution to work on by picking it from that list.  At the same time, we can calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
        s &lt;- p
        u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range ''1 to n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
        x &lt;- 1 to n
        if !u(x)
&lt;/codeblock&gt;

The previous chunks are part of a &lt;tt&gt;for&lt;/tt&gt; comprehension that makes a new list of partial solutions by adding usable values of ''x'' to the existing solutions ''s''.  Note that the solution list is extended both in length and number of elements: if ''p'' had the element &lt;tt&gt;List(1, 7, 2, 6)&lt;/tt&gt;, it will be extended to have &lt;tt&gt;List(3, 1, 7, 2, 6)&lt;/tt&gt; and &lt;tt&gt;List(4, 1, 7, 2, 6)&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
      for {

        &lt;&lt;Get partial solution and unsafe set&gt;&gt;

        &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

      } yield x :: s
&lt;/codeblock&gt;

The process of adding the ''k''th queen therefore means 1) remove all partial solutions (''PS'') that can't have another queen added, 2) make all ''PS''s of length ''k-1'' into partial solutions of length ''k'', and 3) if a queen can be added to a ''PS'' in more than one way, add new ''PS''s.  The type alias &lt;tt&gt;LLI&lt;/tt&gt;, by the way, stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
  val add: (LLI, Int) =&gt; LLI =
    { (p, _) =&gt;

      &lt;&lt;Extend solution list&gt;&gt;

    }
&lt;/codeblock&gt;

Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a solution list using the &lt;tt&gt;add&lt;/tt&gt; method for operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
  def queens (start: LLI) =
    (start /: (1 to n))(add)
&lt;/codeblock&gt;

And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16617</id>
      <timestamp>2010-01-08T12:24:39Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>white space adjustment</comment>
      <text xml:space="preserve">To be able to solve the Eight Queens puzzle, we must first be able to add one queen to a partial solution (adding a queen to an empty solution is trivial).  Assume that our strategy is to place queens one row at a time, starting with the bottom row.  If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a list containing the column numbers of the queens that have already been placed and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
val finder: ((Int, Int)) =&gt; Seq[Int] =
  { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'' for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
(s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
object UnsafeSet {

  &lt;&lt;Define finder function&gt;&gt;

  def apply (s: List[Int]) =

    &lt;&lt;Create set of unsafe squares&gt;&gt;
}
&lt;/codeblock&gt;

If ''p'' is the list of solutions, we can get a partial solution to work on by picking it from that list.  At the same time, we can calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
s &lt;- p
u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range ''1 to n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
x &lt;- 1 to n
if !u(x)
&lt;/codeblock&gt;

The previous chunks are part of a &lt;tt&gt;for&lt;/tt&gt; comprehension that makes a new list of partial solutions by adding usable values of ''x'' to the existing solutions ''s''.  Note that the solution list is extended both in length and number of elements: if ''p'' had the element &lt;tt&gt;List(1, 7, 2, 6)&lt;/tt&gt;, it will be extended to have &lt;tt&gt;List(3, 1, 7, 2, 6)&lt;/tt&gt; and &lt;tt&gt;List(4, 1, 7, 2, 6)&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
for {

  &lt;&lt;Get partial solution and unsafe set&gt;&gt;

  &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

} yield x :: s
&lt;/codeblock&gt;

The process of adding the ''k''th queen therefore means 1) remove all partial solutions (''PS'') that can't have another queen added, 2) make all ''PS''s of length ''k-1'' into partial solutions of length ''k'', and 3) if a queen can be added to a ''PS'' in more than one way, add new ''PS''s.  The type alias &lt;tt&gt;LLI&lt;/tt&gt;, by the way, stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
val add: (LLI, Int) =&gt; LLI =
  { (p, _) =&gt;

    &lt;&lt;Extend solution list&gt;&gt;

  }
&lt;/codeblock&gt;

Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a solution list using the &lt;tt&gt;add&lt;/tt&gt; method for operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
def queens (start: LLI) =
  (start /: (1 to n))(add)
&lt;/codeblock&gt;

And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16618</id>
      <timestamp>2010-01-10T00:23:03Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

==Find a safe place==
To be able to solve the Eight Queens puzzle, we must first be able to add one queen to a partial solution (adding a queen to an empty solution is trivial).  Assume that our strategy is to place queens one row at a time, starting with the bottom row.  If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a list containing the column numbers of the queens that have already been placed and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
val finder: ((Int, Int)) =&gt; Seq[Int] =
  { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'' for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
(s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
object UnsafeSet {

  &lt;&lt;Define finder function&gt;&gt;

  def apply (s: List[Int]) =

    &lt;&lt;Create set of unsafe squares&gt;&gt;
}
&lt;/codeblock&gt;

==Define an add operator==
The unsafe set generator will help us define an operator that can take a collection ''p'' of (partial) solutions, each with ''k''-1 queens placed, and return a collection of solutions with ''k'' queens placed.

We pick a partial solution ''s'' from ''p'' and calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
s &lt;- p
u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range 1 to ''n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
x &lt;- 1 to n
if !u(x)
&lt;/codeblock&gt;

Every ''x''-value that passes the test is consed with the current ''s'' and collected by the &lt;tt&gt;for&lt;/tt&gt; comprehension.  Values of ''s'' that don't allow any ''x''-value to pass are discarded.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
for {

  &lt;&lt;Get partial solution and unsafe set&gt;&gt;

  &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

} yield x :: s
&lt;/codeblock&gt;

Now we can define the ''add'' operator:

''p&lt;sub&gt;k&lt;/sub&gt;'' &amp;larr; ''p&lt;sub&gt;k-1&lt;/sub&gt;'' '''add''' ''k''

It takes a list of partial solutions with ''k''-1 queens each and an integer value (which it ignores, since it doesn't need it) and returns a list of partial solutions with ''k'' queens each.  The type alias &lt;tt&gt;LLI&lt;/tt&gt; stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
val add: (LLI, Int) =&gt; LLI =
  { (p, _) =&gt;

    &lt;&lt;Extend solution list&gt;&gt;

  }
&lt;/codeblock&gt;

==Define a solution list builder==
Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a list of complete solutions step by step using the &lt;tt&gt;add&lt;/tt&gt; operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
def queens (start: LLI) =
  (start /: (1 to n))(add)
&lt;/codeblock&gt;

==The complete program==
And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16619</id>
      <timestamp>2010-01-10T00:28:49Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

==Find a safe place==
To be able to solve the Eight Queens puzzle, we must first be able to add one queen to a partial solution (adding a queen to an empty solution is trivial).  Assume that our strategy is to place queens one row at a time, starting with the bottom row.  If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a list containing the column numbers of the queens that have already been placed and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
val finder: ((Int, Int)) =&gt; Seq[Int] =
  { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'' for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
(s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
object UnsafeSet {

  &lt;&lt;Define finder function&gt;&gt;

  def apply (s: List[Int]) =

    &lt;&lt;Create set of unsafe squares&gt;&gt;
}
&lt;/codeblock&gt;

==Define an add operator==
The unsafe set generator will help us define an operator that can take a collection ''p'' of (partial) solutions, each with ''k''-1 queens placed, and return a collection of solutions with ''k'' queens placed.

We pick a partial solution ''s'' from ''p'' and calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
s &lt;- p
u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range 1 to ''n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
x &lt;- 1 to n
if !u(x)
&lt;/codeblock&gt;

Every ''x''-value that passes the test is consed with the current ''s'' and collected by the &lt;tt&gt;for&lt;/tt&gt; comprehension.  Values of ''s'' that don't allow any ''x''-value to pass are discarded.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
for {

  &lt;&lt;Get partial solution and unsafe set&gt;&gt;

  &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

} yield x :: s
&lt;/codeblock&gt;

Now we can define the ''add'' operator:

''p&lt;sup&gt;k&lt;/sup&gt;'' &amp;larr; ''p&lt;sup&gt;k-1&lt;/sup&gt;'' '''add''' ''k''

It takes a list of partial solutions with ''k''-1 queens each and an integer value (which it ignores, since it doesn't need it) and returns a list of partial solutions with ''k'' queens each.  The type alias &lt;tt&gt;LLI&lt;/tt&gt; stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
val add: (LLI, Int) =&gt; LLI =
  { (p, _) =&gt;

    &lt;&lt;Extend solution list&gt;&gt;

  }
&lt;/codeblock&gt;

==Define a solution list builder==
Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a list of complete solutions step by step using the &lt;tt&gt;add&lt;/tt&gt; operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
def queens (start: LLI) =
  (start /: (1 to n))(add)
&lt;/codeblock&gt;

==The complete program==
And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16620</id>
      <timestamp>2010-01-10T00:40:30Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This article describes a simple [http://en.wikipedia.org/wiki/Scala Scala] implementation of a solver for the Eight Queens puzzle.

==Representation==
The solver will create a list of solutions, where each solution is a list of integers.  Each of those integers represent a column in which one of the queens is placed.  The queens are in reverse order, i.e. the last queen to be placed is first in the solution.

==Strategy==
We will begin with an empty list of solutions and perform an '''add''' operation on it to get a list of partial solutions with one queen each.  The '''add''' operation will be repeated until we have a list of solutions with eight queens each.  We will need to define the '''add''' operator, and to be able to do that, we have to define a way to know, given a partial solution, which of the squares in the next row can be attacked by the already placed queens.

==Find a safe place==
If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a solution (a list containing the column numbers of the queens that have already been placed) and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
val finder: ((Int, Int)) =&gt; Seq[Int] =
  { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'', which stands for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
(s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
object UnsafeSet {

  &lt;&lt;Define finder function&gt;&gt;

  def apply (s: List[Int]) =

    &lt;&lt;Create set of unsafe squares&gt;&gt;
}
&lt;/codeblock&gt;

==Define an add operator==
The unsafe set generator will help us define an operator that can take a collection ''p'' of (partial) solutions, each with ''k''-1 queens placed, and return a collection of solutions with ''k'' queens placed.

We pick a partial solution ''s'' from ''p'' and calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
s &lt;- p
u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range 1 to ''n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
x &lt;- 1 to n
if !u(x)
&lt;/codeblock&gt;

Every ''x''-value that passes the test is consed with the current ''s'' and collected by the &lt;tt&gt;for&lt;/tt&gt; comprehension.  Values of ''s'' that don't allow any ''x''-value to pass are discarded.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
for {

  &lt;&lt;Get partial solution and unsafe set&gt;&gt;

  &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

} yield x :: s
&lt;/codeblock&gt;

Now we can define the ''add'' operator:

''p&lt;sup&gt;k&lt;/sup&gt;'' &amp;larr; ''p&lt;sup&gt;k-1&lt;/sup&gt;'' '''add''' ''k''

It takes a list of partial solutions with ''k''-1 queens each and an integer value (which it ignores, since it doesn't need it) and returns a list of partial solutions with ''k'' queens each.  The type alias &lt;tt&gt;LLI&lt;/tt&gt; stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
val add: (LLI, Int) =&gt; LLI =
  { (p, _) =&gt;

    &lt;&lt;Extend solution list&gt;&gt;

  }
&lt;/codeblock&gt;

==Define a solution list builder==
Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a list of complete solutions step by step using the &lt;tt&gt;add&lt;/tt&gt; operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
def queens (start: LLI) =
  (start /: (1 to n))(add)
&lt;/codeblock&gt;

==The complete program==
And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16621</id>
      <timestamp>2010-01-11T12:52:51Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>Fix to make it work outside of interactive shell.</comment>
      <text xml:space="preserve">{{Category:Eight queens puzzle}}

This article describes a simple [http://en.wikipedia.org/wiki/Scala Scala] implementation of a solver for the Eight Queens puzzle.

==Representation==
The solver will create a list of solutions, where each solution is a list of integers.  Each of those integers represent a column in which one of the queens is placed.  The queens are in reverse order, i.e. the last queen to be placed is first in the solution.

==Strategy==
We will begin with an empty list of solutions and perform an '''add''' operation on it to get a list of partial solutions with one queen each.  The '''add''' operation will be repeated until we have a list of solutions with eight queens each.  We will need to define the '''add''' operator, and to be able to do that, we have to define a way to know, given a partial solution, which of the squares in the next row can be attacked by the already placed queens.

==Find a safe place==
If we have already placed four queens on rows 1 - 4, the placement of the fifth queen is constrained by the earlier placements such that 1) we may not place the queen in the same column as any of the earlier queens, and 2) we may not place the queen in a square that is diagonally connected to any of the earlier queens.  The first constraint is easy to implement if ''s'' is a solution (a list containing the column numbers of the queens that have already been placed) and ''x'' is a candidate column number for the next queen:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
val unsafe = s toSet
if (unsafe(x))
  // no
else
  // ok
&lt;/codeblock&gt;

The second constraint is a little bit more complicated, since we need to calculate which squares are diagonally connected to the queens we already have.  For the queen in the previous row, those squares are 4 and 6, and for the queen before that, they are 5 and 9 (the first one is already taken, and the other is off the board, but never mind).  In general, if one of the queens in the partial solution is on column ''c'' and it is the ''r''th queen going backwards in the solution (starting from 1), squares ''c - r'', ''c'', and ''c + r'' are attacked by that queen.  This means that we can define a function for the calculation:

&lt;codeblock language=scala&gt;
&lt;&lt;Define finder function&gt;&gt;=
val finder: ((Int, Int)) =&gt; Seq[Int] =
  { case (c, r) =&gt; Seq(c - r, c, c + r) }
&lt;/codeblock&gt;

To use this function, we need values for ''c'' and ''r''.  The former comes directly from the partial solution, and the latter can be zipped in:

&lt;codeblock language=scala&gt;
val s = List(5, 7, 2, 6)
s zip (1 to 8) // yields List((5,1), (7,2), (2,3), (6,4))
&lt;/codeblock&gt;

Given the constant ''n'', which stands for 8, we can create the set of unsafe squares like this:

&lt;codeblock language=scala&gt;
&lt;&lt;Create set of unsafe squares&gt;&gt;=
(s zip (1 to n)) flatMap finder toSet
&lt;/codeblock&gt;

Let us put what we have so far in an object:

&lt;codeblock language=scala&gt;
&lt;&lt;Find unsafe set for s&gt;&gt;=
object UnsafeSet {

  &lt;&lt;Define finder function&gt;&gt;

  def apply (s: List[Int]) =

    &lt;&lt;Create set of unsafe squares&gt;&gt;
}
&lt;/codeblock&gt;

==Define an add operator==
The unsafe set generator will help us define an operator that can take a collection ''p'' of (partial) solutions, each with ''k''-1 queens placed, and return a collection of solutions with ''k'' queens placed.

We pick a partial solution ''s'' from ''p'' and calculate the unsafe set for that partial solution.

&lt;codeblock language=scala&gt;
&lt;&lt;Get partial solution and unsafe set&gt;&gt;=
s &lt;- p
u = UnsafeSet(s)
&lt;/codeblock&gt;

We can get a candidate column for placement by picking it from the range 1 to ''n''.  If it isn't in the unsafe set, we can use it.

&lt;codeblock language=scala&gt;
&lt;&lt;Get candidate column and check if it is safe&gt;&gt;=
x &lt;- 1 to n
if !u(x)
&lt;/codeblock&gt;

Every ''x''-value that passes the test is consed with the current ''s'' and collected by the &lt;tt&gt;for&lt;/tt&gt; comprehension.  Values of ''s'' that don't allow any ''x''-value to pass are discarded.

&lt;codeblock language=scala&gt;
&lt;&lt;Extend solution list&gt;&gt;=
for {

  &lt;&lt;Get partial solution and unsafe set&gt;&gt;

  &lt;&lt;Get candidate column and check if it is safe&gt;&gt;

} yield x :: s
&lt;/codeblock&gt;

Now we can define the ''add'' operator:

''p&lt;sup&gt;k&lt;/sup&gt;'' &amp;larr; ''p&lt;sup&gt;k-1&lt;/sup&gt;'' '''add''' ''k''

It takes a list of partial solutions with ''k''-1 queens each and an integer value (which it ignores, since it doesn't need it) and returns a list of partial solutions with ''k'' queens each.  The type alias &lt;tt&gt;LLI&lt;/tt&gt; stands for &lt;tt&gt;List[List[Int]]&lt;/tt&gt;.

&lt;codeblock language=scala&gt;
&lt;&lt;Add queen&gt;&gt;=
val add: (LLI, Int) =&gt; LLI =
  { (p, _) =&gt;

    &lt;&lt;Extend solution list&gt;&gt;

  }
&lt;/codeblock&gt;

==Define a solution list builder==
Using the shorthand form of &lt;tt&gt;foldLeft&lt;/tt&gt;, we can define a function that builds a list of complete solutions step by step using the &lt;tt&gt;add&lt;/tt&gt; operator.

&lt;codeblock language=scala&gt;
&lt;&lt;Define solution builder&gt;&gt;=
def queens (start: LLI) =
  (start /: (1 to n))(add)
&lt;/codeblock&gt;

==The complete program==
And here is the complete program.

&lt;codeblock language=scala&gt;
&lt;&lt;eightqueens.scala&gt;&gt;=
object EightQueens {
  val  n   = 8
  type LLI = List[List[Int]]

  &lt;&lt;Find unsafe set for s&gt;&gt;

  &lt;&lt;Add queen&gt;&gt;

  &lt;&lt;Define solution builder&gt;&gt;

  def main (args: Array[String]) {
    val solutions = queens(List(List()))
    solutions foreach println
    println(solutions.size)
  }
}
&lt;/codeblock&gt;

[[Category:Eight queens puzzle|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclid's Algorithm</title>
    <id>3948</id>
    <revision>
      <id>16768</id>
      <timestamp>2010-07-27T14:10:50Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>[[Euclid's Algorithm]] moved to [[Euclid's Algorithm (Java)]]: Programming language not stated in the original title.</comment>
      <text xml:space="preserve">#REDIRECT [[Euclid's Algorithm (Java)]]</text>
    </revision>
  </page>
  <page>
    <title>Euclid's Algorithm (Java)</title>
    <id>3951</id>
    <revision>
      <id>16776</id>
      <timestamp>2010-07-27T19:30:17Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>[[Euclid's Algorithm (Java)]] moved to [[Euclidean algorithm (Java, recursive)]]: I hope the title will work now...</comment>
      <text xml:space="preserve">#REDIRECT [[Euclidean algorithm (Java, recursive)]]</text>
    </revision>
  </page>
  <page>
    <title>Euclid's Algorithm (Scala)</title>
    <id>3952</id>
    <revision>
      <id>16780</id>
      <timestamp>2010-07-27T20:53:12Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>[[Euclid's Algorithm (Scala)]] moved to [[Euclidean algorithm (Scala)]]: Bring the page into the list of implementations for the category.</comment>
      <text xml:space="preserve">#REDIRECT [[Euclidean algorithm (Scala)]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean Algorithm (Java, recursive)</title>
    <id>3950</id>
    <revision>
      <id>16774</id>
      <timestamp>2010-07-27T19:24:02Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>[[Euclidean Algorithm (Java, recursive)]] moved to [[Euclid's Algorithm (Java)]]: Earlier rename used capitalization, which was apparently bad.</comment>
      <text xml:space="preserve">#REDIRECT [[Euclid's Algorithm (Java)]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (C)</title>
    <id>1980</id>
    <revision>
      <id>4590</id>
      <timestamp>2006-05-12T16:13:28Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Description, a couple impls, see also, cats</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
#include &lt;stdio.h&gt;

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2]));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4591</id>
      <timestamp>2006-05-12T16:14:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Chunk name</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2]));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4592</id>
      <timestamp>2006-05-12T16:15:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>headers</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;  /* printf */
#include &lt;stdlib.h&gt; /* atoi */

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2]));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4593</id>
      <timestamp>2006-05-12T16:15:38Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Paren</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;  /* printf */
#include &lt;stdlib.h&gt; /* atoi */

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2])));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4765</id>
      <timestamp>2006-05-15T03:02:54Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;  /* printf */
#include &lt;stdlib.h&gt; /* atoi */

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2])));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6838</id>
      <timestamp>2006-07-11T12:47:49Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Euclidean algorithm (C)]] moved to [[Euclidean algorithm (C) on Wheels]]</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;  /* printf */
#include &lt;stdlib.h&gt; /* atoi */

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2])));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6998</id>
      <timestamp>2006-07-11T14:29:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Euclidean algorithm (C) on Wheels]] moved to [[Euclidean algorithm (C)]]: revert</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in C using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' simultaneously until ''b'' becomes zero. This requires a temporary variable:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm main loop simple&gt;&gt;=
while (b != 0) {
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We need only ensure that at the start ''a'' &gt; ''b'' by swapping the inputs if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm simple&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) { int t = a; a = b; b = t; }
    &lt;&lt;Euclidean algorithm main loop simple&gt;&gt;
}
&lt;/codeblock&gt;

Another strategy that involves less copy operations is to unroll the loop to two iterations and alternate the roles of a and b each iteration:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm unrolled&gt;&gt;=
int euclidean_gcd(int a, int b) {
    if (b &gt; a) goto b_larger;
    while (1) {
        a = a % b;
        if (a == 0) return b;
b_larger:
        b = b % a;
        if (b == 0) return a;
    }
}
&lt;/codeblock&gt;

In the first part, a is always larger, while in the second part b is always larger. The label in the middle allows us to jump into the middle of the loop in the case where b is initially larger. We can try out our implementation with this simple test driver:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;euclidean_gcd.c&gt;&gt;=
#include &lt;stdio.h&gt;  /* printf */
#include &lt;stdlib.h&gt; /* atoi */

&lt;&lt;Euclidean algorithm unrolled&gt;&gt;

int main(int argc, char* argv[]) {
    printf(&quot;%d\n&quot;, euclidean_gcd(atoi(argv[1]), atoi(argv[2])));
    return 0;
}
&lt;/codeblock&gt;

== See also ==

* [[Binary Euclidean algorithm (C)]]

[[Category:Euclidean algorithm|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Erlang)</title>
    <id>3131</id>
    <revision>
      <id>10094</id>
      <timestamp>2007-05-15T21:07:00Z</timestamp>
      <contributor>
        <username>Goofyheadedpunk</username>
        <id>157</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in Erlang, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0. 

&lt;codeblock language=&quot;erlang&quot;&gt;
gcd(X, Y) -&gt;
    R = X rem Y,
    case R of
        0 -&gt;
            Y;
        _ -&gt;
            gcd(Y, R)
    end.

&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function (denoted gcd/2 as Erlang functions are named by atom and arity).

&lt;codeblock language=&quot;erlang&quot;&gt;
gcd([H|T]) -&gt;
    lists:foldl(fun gcd/2, H, T).
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10177</id>
      <timestamp>2007-05-16T18:23:11Z</timestamp>
      <contributor>
        <username>Goofyheadedpunk</username>
        <id>157</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in Erlang, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0. 

&lt;codeblock language=&quot;erlang&quot;&gt;
gcd(A, 0) -&gt; A;
gcd(A, B) -&gt; gcd(B, A rem B).
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function (denoted gcd/2 as Erlang functions are named by atom and arity).

&lt;codeblock language=&quot;erlang&quot;&gt;
gcd([H|T]) -&gt;
    lists:foldl(fun gcd/2, H, T).
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Forth)</title>
    <id>2861</id>
    <revision>
      <id>8320</id>
      <timestamp>2006-12-09T20:05:24Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean GCD algorithm is straightforward to describe in Forth using a loop that repeatedly replaces ''a'' by ''b'' and ''b'' by ''a'' mod ''b'' while ''b'' is not zero.

'''begin ?dup while ... repeat''' executes the loop while the top of the stack is non-zero.  '''?dup''' compared to '''dup''' does not duplicate the top item if it is zero. It is equivalent to the loop '''begin dup while ... repeat drop'''. 

'''tuck''' ( a b -- b a b ) copies the top item underneath the second item on the stack. It is equivalent to '''swap over'''.

'''mod''' ( a b -- a%b ) takes the modulus of the top two items on the stack.

Together, '''tuck mod''' does ( a b -- b a%b ).

&lt;codeblock language=forth&gt;
&lt;&lt;gcd.fs&gt;&gt;=
: gcd ( a b -- gcd )
  begin ?dup while tuck mod repeat ;

\ Some tests

cr  6 10 gcd .     \ 2
cr 10  6 gcd .     \ 2 (order doesn't matter)
cr 10 21 gcd .     \ 1 (no factors in common)
cr  3  0 gcd .     \ 3 (allow 0)
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Haskell)</title>
    <id>3620</id>
    <revision>
      <id>15002</id>
      <timestamp>2008-10-14T00:14:12Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>translated from erlang</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in Haskell, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0. Note that for practical purposes you should instead use the &quot;gcd&quot; function that is already provided in the Prelude, which also handles negative numbers and the case where both args are 0.

&lt;codeblock language=&quot;haskell&quot;&gt;
gcd a 0 = a
gcd a b = gcd b (a `mod` b)
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function. Note that 0 is an identity for gcd.

&lt;codeblock language=&quot;haskell&quot;&gt;
gcdList = foldl gcd 0
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15246</id>
      <timestamp>2008-10-23T19:08:09Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>translated from haskell</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in OCaml, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0.

&lt;codeblock language=&quot;ocaml&quot;&gt;
let rec gcd a = function
   0 -&gt; a
 | b -&gt; gcd b (a mod b)
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function. Note that 0 is an identity for gcd.

&lt;codeblock language=&quot;ocaml&quot;&gt;
let gcd_list = List.fold_left gcd 0
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15248</id>
      <timestamp>2008-10-23T19:09:13Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>oops revert</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in Haskell, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0. Note that for practical purposes you should instead use the &quot;gcd&quot; function that is already provided in the Prelude, which also handles negative numbers and the case where both args are 0.

&lt;codeblock language=&quot;haskell&quot;&gt;
gcd a 0 = a
gcd a b = gcd b (a `mod` b)
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function. Note that 0 is an identity for gcd.

&lt;codeblock language=&quot;haskell&quot;&gt;
gcdList = foldl gcd 0
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Java)</title>
    <id>3325</id>
    <revision>
      <id>12585</id>
      <timestamp>2008-02-23T01:19:02Z</timestamp>
      <contributor>
        <username>Djshaw</username>
        <id>1637</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">The Java implementation of the Euclidean algorithm is remarkably similar to the [[Euclidean algorithm (C)|C implementation]] of the Euclidean algorithm.

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclidean algorithm loop&gt;&gt;=
while (b != 0) 
{
    int m = a % b;
    a = b;
    b = m;
}
return a;
&lt;/codeblock&gt;

We only need to ensure that ''a'' &gt; ''b'' by swapping the inputs at the start of the function, if necessary:

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;Euclidean algorithm&gt;&gt;=
public static int gcd(int a, int b)
{
    if (b &gt; a)
    {
        int temp = a;
        a = b;
        b = temp;
    }

    &lt;&lt;Euclidean algorithm loop&gt;&gt;
}
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Java, recursive)</title>
    <id>3946</id>
    <revision>
      <id>16763</id>
      <timestamp>2010-07-21T16:20:47Z</timestamp>
      <contributor>
        <username>Kmandew</username>
        <id>2087</id>
      </contributor>
      <text xml:space="preserve">//Recursive method to return the greatest common divisor of 2 integers of type long using Euclid's algorithm.

public static long gcd( long b, long r)
{
    return r == 0 ? b : gcd( r, b % r);
}</text>
    </revision>
    <revision>
      <id>16764</id>
      <timestamp>2010-07-27T00:49:00Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclid's Algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

[[Category:Euclid's Algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16765</id>
      <timestamp>2010-07-27T01:00:44Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>Fixed Wikipedia link</comment>
      <text xml:space="preserve">{{Category:Euclid's Algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

[[Category:Euclid's Algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16767</id>
      <timestamp>2010-07-27T14:10:50Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>[[Euclid's Algorithm]] moved to [[Euclid's Algorithm (Java)]]: Programming language not stated in the original title.</comment>
      <text xml:space="preserve">{{Category:Euclid's Algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

[[Category:Euclid's Algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16769</id>
      <timestamp>2010-07-27T15:31:09Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>Added run demonstration.</comment>
      <text xml:space="preserve">{{Category:Euclid's Algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

== Implementation ==

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclid's Algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16770</id>
      <timestamp>2010-07-27T15:45:06Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>I searched for &quot;Euclid&quot; but still didn't find the correct category.  Bother.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

== Implementation ==

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16771</id>
      <timestamp>2010-07-27T15:46:09Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>[[Euclid's Algorithm (Java)]] moved to [[Euclidean Algorithm (Java, recursive)]]: The same algorithm has already been described on the wiki, but with another name.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

== Implementation ==

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16773</id>
      <timestamp>2010-07-27T19:24:02Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>[[Euclidean Algorithm (Java, recursive)]] moved to [[Euclid's Algorithm (Java)]]: Earlier rename used capitalization, which was apparently bad.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

== Implementation ==

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16775</id>
      <timestamp>2010-07-27T19:30:16Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>[[Euclid's Algorithm (Java)]] moved to [[Euclidean algorithm (Java, recursive)]]: I hope the title will work now...</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

== Implementation ==

These equations give us the general and base case of a recursive function

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
    if (b == 0) {
        return a;
    }
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
    else {
        return gcd(b, a % b);
    }
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long a = Long.parseLong(args[0]);
        long b = Long.parseLong(args[1]);

        System.out.println(gcd(a, b));
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16777</id>
      <timestamp>2010-07-27T20:00:47Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>Brought the text in line with the category text.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of the algorithm.

The ''gcd'' method requires that ''a'' and ''b'' are positive integers and that &lt;math&gt;a&gt;b&lt;/math&gt;.

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
    public static long gcd(long a, long b)
    {
        &lt;&lt;base case&gt;&gt;
        &lt;&lt;general case&gt;&gt;
    }
&lt;/codeblock&gt;

The base case applies when ''b'' is equal to 0:

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
        if (b == 0) return a;
&lt;/codeblock&gt;

Since &lt;math&gt;a&gt;b&lt;/math&gt;, the first identity can be used for the general case:

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
        else return gcd(b, a % b);
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long n0 = Long.parseLong(args[0]);
        long n1 = Long.parseLong(args[1]);

        long res;
        if (n0 &gt; n1)
            res = gcd(n0, n1);
        else if (n1 &gt; n0)
            res = gcd(n1, n0);
        else
            res = n0;

        System.out.println(res);
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16782</id>
      <timestamp>2010-07-27T21:08:42Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>Adjusted whitespace.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a recursive [http://en.wikipedia.org/wiki/Java_%28programming_language%29 Java] implementation of the algorithm.

The ''gcd'' method requires that ''a'' and ''b'' are positive integers and that &lt;math&gt;a&gt;b&lt;/math&gt;.

&lt;codeblock language=java&gt;
&lt;&lt;gcd method&gt;&gt;=
public static long gcd(long a, long b)
{
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

The base case applies when ''b'' is equal to 0:

&lt;codeblock language=java&gt;
&lt;&lt;base case&gt;&gt;=
if (b == 0) return a;
&lt;/codeblock&gt;

Since &lt;math&gt;a&gt;b&lt;/math&gt;, the first identity can be used for the general case:

&lt;codeblock language=java&gt;
&lt;&lt;general case&gt;&gt;=
else return gcd(b, a % b);
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;java&quot;&gt;
&lt;&lt;Euclid.java&gt;&gt;=

public class Euclid
{
    &lt;&lt;gcd method&gt;&gt;

    public static void main(String[] args)
    {
        long n0 = Long.parseLong(args[0]);
        long n1 = Long.parseLong(args[1]);

        long res;
        if (n0 &gt; n1)
            res = gcd(n0, n1);
        else if (n1 &gt; n0)
            res = gcd(n1, n0);
        else
            res = n0;

        System.out.println(res);
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
java Euclid 35 42
java Euclid 35 40
java Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (OCaml)</title>
    <id>3648</id>
    <revision>
      <id>15247</id>
      <timestamp>2008-10-23T19:08:55Z</timestamp>
      <contributor>
        <ip>71.106.183.17</ip>
      </contributor>
      <comment>translated from haskell</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in OCaml, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0.

&lt;codeblock language=&quot;ocaml&quot;&gt;
let rec gcd a = function
   0 -&gt; a
 | b -&gt; gcd b (a mod b)
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function. Note that 0 is an identity for gcd.

&lt;codeblock language=&quot;ocaml&quot;&gt;
let gcd_list = List.fold_left gcd 0
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Prolog)</title>
    <id>2397</id>
    <revision>
      <id>6606</id>
      <timestamp>2006-07-02T12:40:19Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This page explains how to implement the '''Euclidean algorithm''' in [http://en.wikipedia.org/wiki/Prolog Prolog]. The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] determines the greatest common divisor (gcd) of two integers without factoring. Although the Euclidean algorithm can be extended to compute the gcd of any [http://en.wikipedia.org/wiki/Euclidean_domain Euclidean domain] elements such as polynomials over a field, this article only deals with the case when the input is integer.

==Simple version==
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd_simple.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y - X,
  gcd(X, Y1, G).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

==Tricky version==
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y mod X,
  (Y1 = 0 -&gt; G = X; gcd(X, Y1, G)).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

==Execution result==
 crypto@crypto ~/gcd_prolog
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd.pl'].
 % gcd.pl compiled 0.00 sec, 1,040 bytes
 
 Yes
 ?- gcd(2048, 24, X).
 
 X = 8
 
 Yes

 

[[Category:Euclidean algorithm|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6614</id>
      <timestamp>2006-07-02T14:32:06Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <comment>/* Execution result */</comment>
      <text xml:space="preserve">This page explains how to implement the '''Euclidean algorithm''' in [http://en.wikipedia.org/wiki/Prolog Prolog]. The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] determines the greatest common divisor (gcd) of two integers without factoring. Although the Euclidean algorithm can be extended to compute the gcd of any [http://en.wikipedia.org/wiki/Euclidean_domain Euclidean domain] elements such as polynomials over a field, this article only deals with the case when the input is integer.

==Simple version==
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd_simple.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y - X,
  gcd(X, Y1, G).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

==Tricky version==
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y mod X,
  (Y1 = 0 -&gt; G = X; gcd(X, Y1, G)).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

==Execution result==
The simple version works well. However, it fails to compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; as it takes too many steps to reduce 19827345 to a small number by repeatedly subtracting 4.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd_simple.pl'].
 % gcd_simple.pl compiled 0.00 sec, 1,032 bytes
 
 Yes
 ?- gcd(4, 8, X).
 
 X = 4
 
 Yes
 ?- gcd(15, 120, X).
 
 X = 15
 
 Yes
 ?- gcd(4, 19827345, X).
 ERROR: Out of local stack
    Exception: (29,873) gcd(4, 19707881, _G19) ? abort
 % Execution Aborted
 ?-
The tricky version can easily compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; because it employs the modulo operator &lt;code&gt;mod&lt;/code&gt; without resorting to the repeated subtraction.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd.pl'].
 % gcd.pl compiled 0.00 sec, 1,040 bytes
 
 Yes
 ?- gcd(4, 19827345, X).
 
 X = 1
 
 Yes

[[Category:Euclidean algorithm|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6615</id>
      <timestamp>2006-07-02T14:45:31Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This page explains how to implement the '''Euclidean algorithm''' in [http://en.wikipedia.org/wiki/Prolog Prolog]. The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] determines the greatest common divisor (gcd) of two integers without factoring. Although the Euclidean algorithm can be extended to compute the gcd of any [http://en.wikipedia.org/wiki/Euclidean_domain Euclidean domain] elements such as polynomials over a field, this article only deals with the case when the input is integer.

==Simple version==
===Algorithm===
: &lt;math&gt; \gcd(x, y) =
 \begin{cases}
 x &amp; \mbox{if } x = y \\
 \gcd(x, y -x) &amp; \mbox{if } x &lt; y \\
 \gcd(y, x) &amp; \mbox{otherwise}.
 \end{cases}
&lt;/math&gt;

===Source code===
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd_simple.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y - X,
  gcd(X, Y1, G).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The simple version works well. However, it fails to compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; as it takes too many steps to reduce 19827345 to a small number by repeatedly subtracting 4.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd_simple.pl'].
 % gcd_simple.pl compiled 0.00 sec, 1,032 bytes
 
 Yes
 ?- gcd(4, 8, X).
 
 X = 4
 
 Yes
 ?- gcd(15, 120, X).
 
 X = 15
 
 Yes
 ?- gcd(4, 19827345, X).
 ERROR: Out of local stack
    Exception: (29,873) gcd(4, 19707881, _G19) ? abort
 % Execution Aborted
 ?-

==Tricky version==
===Algorithm===
We employ the modulo operator &lt;code&gt;mod&lt;/code&gt; rather than the repeated subtraction. Unlike the previous case, we have to test whether &lt;math&gt;y \mod x \equiv 0&lt;/math&gt; -- in this case, x is the gcd.
===Source code===
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y mod X,
  (Y1 = 0 -&gt; G = X; gcd(X, Y1, G)).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The tricky version can easily compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; because it employs the modulo operator &lt;code&gt;mod&lt;/code&gt; without resorting to the repeated subtraction.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd.pl'].
 % gcd.pl compiled 0.00 sec, 1,040 bytes
 
 Yes
 ?- gcd(4, 19827345, X).
 
 X = 1
 
 Yes

[[Category:Euclidean algorithm|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15425</id>
      <timestamp>2008-11-11T14:01:42Z</timestamp>
      <contributor>
        <ip>193.61.83.174</ip>
      </contributor>
      <comment>/* Source code */</comment>
      <text xml:space="preserve">This page explains how to implement the '''Euclidean algorithm''' in [http://en.wikipedia.org/wiki/Prolog Prolog]. The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] determines the greatest common divisor (gcd) of two integers without factoring. Although the Euclidean algorithm can be extended to compute the gcd of any [http://en.wikipedia.org/wiki/Euclidean_domain Euclidean domain] elements such as polynomials over a field, this article only deals with the case when the input is integer.

==Simple version==
===Algorithm===
: &lt;math&gt; \gcd(x, y) =
 \begin{cases}
 x &amp; \mbox{if } x = y \\
 \gcd(x, y -x) &amp; \mbox{if } x &lt; y \\
 \gcd(y, x) &amp; \mbox{otherwise}.
 \end{cases}
&lt;/math&gt;


gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The simple version works well. However, it fails to compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; as it takes too many steps to reduce 19827345 to a small number by repeatedly subtracting 4.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd_simple.pl'].
 % gcd_simple.pl compiled 0.00 sec, 1,032 bytes
 
 Yes
 ?- gcd(4, 8, X).
 
 X = 4
 
 Yes
 ?- gcd(15, 120, X).
 
 X = 15
 
 Yes
 ?- gcd(4, 19827345, X).
 ERROR: Out of local stack
    Exception: (29,873) gcd(4, 19707881, _G19) ? abort
 % Execution Aborted
 ?-

==Tricky version==
===Algorithm===
We employ the modulo operator &lt;code&gt;mod&lt;/code&gt; rather than the repeated subtraction. Unlike the previous case, we have to test whether &lt;math&gt;y \mod x \equiv 0&lt;/math&gt; -- in this case, x is the gcd.
===Source code===
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y mod X,
  (Y1 = 0 -&gt; G = X; gcd(X, Y1, G)).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The tricky version can easily compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; because it employs the modulo operator &lt;code&gt;mod&lt;/code&gt; without resorting to the repeated subtraction.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd.pl'].
 % gcd.pl compiled 0.00 sec, 1,040 bytes
 
 Yes
 ?- gcd(4, 19827345, X).
 
 X = 1
 
 Yes

[[Category:Euclidean algorithm|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15426</id>
      <timestamp>2008-11-11T19:19:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/193.61.83.174|193.61.83.174]] ([[User_talk:193.61.83.174|193.61.83.174]]); changed back to last version by [[User:Crypto|Crypto]]</comment>
      <text xml:space="preserve">This page explains how to implement the '''Euclidean algorithm''' in [http://en.wikipedia.org/wiki/Prolog Prolog]. The [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclidean algorithm] determines the greatest common divisor (gcd) of two integers without factoring. Although the Euclidean algorithm can be extended to compute the gcd of any [http://en.wikipedia.org/wiki/Euclidean_domain Euclidean domain] elements such as polynomials over a field, this article only deals with the case when the input is integer.

==Simple version==
===Algorithm===
: &lt;math&gt; \gcd(x, y) =
 \begin{cases}
 x &amp; \mbox{if } x = y \\
 \gcd(x, y -x) &amp; \mbox{if } x &lt; y \\
 \gcd(y, x) &amp; \mbox{otherwise}.
 \end{cases}
&lt;/math&gt;

===Source code===
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd_simple.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y - X,
  gcd(X, Y1, G).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The simple version works well. However, it fails to compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; as it takes too many steps to reduce 19827345 to a small number by repeatedly subtracting 4.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd_simple.pl'].
 % gcd_simple.pl compiled 0.00 sec, 1,032 bytes
 
 Yes
 ?- gcd(4, 8, X).
 
 X = 4
 
 Yes
 ?- gcd(15, 120, X).
 
 X = 15
 
 Yes
 ?- gcd(4, 19827345, X).
 ERROR: Out of local stack
    Exception: (29,873) gcd(4, 19707881, _G19) ? abort
 % Execution Aborted
 ?-

==Tricky version==
===Algorithm===
We employ the modulo operator &lt;code&gt;mod&lt;/code&gt; rather than the repeated subtraction. Unlike the previous case, we have to test whether &lt;math&gt;y \mod x \equiv 0&lt;/math&gt; -- in this case, x is the gcd.
===Source code===
&lt;codeblock language=prolog&gt;
&lt;&lt;gcd.pl&gt;&gt;=
gcd(X, Y, G) :- X = Y, G = X.
gcd(X, Y, G) :-
  X &lt; Y,
  Y1 is Y mod X,
  (Y1 = 0 -&gt; G = X; gcd(X, Y1, G)).
gcd(X, Y, G) :- X &gt; Y, gcd(Y, X, G).
&lt;/codeblock&gt;

===Execution result===
The tricky version can easily compute &lt;code&gt;gcd(4, 19827345)&lt;/code&gt; because it employs the modulo operator &lt;code&gt;mod&lt;/code&gt; without resorting to the repeated subtraction.
 crypto@crypto ~/gcd
 $ prolog
 Welcome to SWI-Prolog (Multi-threaded, Version 5.2.6)
 Copyright (c) 1990-2003 University of Amsterdam.
 SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
 and you are welcome to redistribute it under certain conditions.
 Please visit http://www.swi-prolog.org for details.
 
 For help, use ?- help(Topic). or ?- apropos(Word).
 
 ?- ['gcd.pl'].
 % gcd.pl compiled 0.00 sec, 1,040 bytes
 
 Yes
 ?- gcd(4, 19827345, X).
 
 X = 1
 
 Yes

[[Category:Euclidean algorithm|Prolog]]
[[Category:Programming language:Prolog]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Python)</title>
    <id>2795</id>
    <revision>
      <id>8144</id>
      <timestamp>2006-11-22T22:10:24Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial code dump</comment>
      <text xml:space="preserve">===a brief definition===
&lt;codeblock language=python&gt;
def gcd(a,b):
        &quot;&quot;&quot; the euclidean algorithm &quot;&quot;&quot;
        while a:
                a, b = b%a, a
        return b
&lt;/codeblock&gt;
===a brief digression===

The Euclidean Algorithm having been published for over 2300 years, and Knuth having devoted over 40 pages to it in ''The Art of Computer Programming'', there is very little to say about the implementation that can not be more profitably found elsewhere, such as the other language versions on this site.

We will, however, reflect a bit on the following text:

&lt;blockquote&gt;
''A program without a loop and a structured variable isn't worth writing.'' &amp;mdash; Alan J. Perlis
&lt;/blockquote&gt;

This program obviously clears the hurdle Perlis places for being worth writing.  It has a loop &amp;ndash; an unbounded loop? &amp;ndash; and it has a structured variable in the form of the pair of arguments &amp;ndash; &lt;code&gt;(a, b)&lt;/code&gt;.

What is not so obvious is that it is also a microcosm of expression evaluation.  When we evaluate an expression, in general we either use a projection operator in the code (head/tail, car/cdr, composite.component, [array element], etc.) to select a portion of the data and ignore the rest, or we use an injection tag in the data to select a portion of the code (if/else, case, subtype or polymorphic dispatch, etc.)  and ignore the rest, and the evaluation terminates when we can no longer make any reductions of either type.  In the GCD computation, we abstract all of that away, and instead use the modulo operator to select a portion of the arguments' factorizations, and ignore the rest.  The swapping of the roles of the &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt; arguments reflects the interleaving of selection (data chooses code) and projection (code chooses data) during evaluation, and &lt;code&gt;gcd()&lt;/code&gt; terminates just when it fails to find any more possible reductions.

This abstraction in terms of prime factors means that the variables are even more structured than we had first remarked.  Our state, in fact, consists of a pair of lists of prime factors.  This structure comes in handy when considering that potentially unbounded loop.  On each pass through the loop, we either toss out some unmatched factors, or swap the variables so we are in a position to do so on the next iteration.  Unless we are in a position to pass in &lt;math&gt;\infty&lt;/math&gt; as an argument, we must eventually reduce both arguments to duplicate lists of shared factors, and so the calculation converges.

When passing from this simple model to actual code, we lose the assurance of termination.  Part of the problem is that running code not only consists of evaluating expressions, but also applying abstractions.  In evaluation, as in following a river network downstream, the structures become simpler over time.  As soon as we add the possibility of application, as in following the ramifications of tree branches from the trunk out to the leaves, the structures become more complex over time.  In general, therefore, unbounded loops which contain applications may not converge as nicely.

''Question 1. when is it desirable to code a program that can be shown not to terminate?''

''Exercise 2. take a solution for non-termination and apply it to the Blue Screen Of Death.''

''Question 3. what is the relationship of logical cuts (and cut-free proofs) to function application?''

''Exercise 4. find a well-known historical algorithm that expresses the essence of '''apply''' (like the GCD computation expresses the essence of '''eval''') &amp;ndash; and add it to this site''

[[Category:Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>9001</id>
      <timestamp>2007-02-11T17:54:50Z</timestamp>
      <contributor>
        <username>Djura</username>
        <id>141</id>
      </contributor>
      <comment>Another version added</comment>
      <text xml:space="preserve">===a brief definition===
&lt;codeblock language=python&gt;
def gcd(a,b):
        &quot;&quot;&quot; the euclidean algorithm &quot;&quot;&quot;
        while a:
                a, b = b%a, a
        return b
&lt;/codeblock&gt;
====or using recursion:====
&lt;codeblock language=python&gt;
def gcd(a,b):
        &quot;&quot;&quot; the euclidean algorithm &quot;&quot;&quot;
        if b == 0:
                return a
        else:
                return gcd(b, (a%b))
&lt;/codeblock&gt;

===a brief digression===

The Euclidean Algorithm having been published for over 2300 years, and Knuth having devoted over 40 pages to it in ''The Art of Computer Programming'', there is very little to say about the implementation that can not be more profitably found elsewhere, such as the other language versions on this site.

We will, however, reflect a bit on the following text:

&lt;blockquote&gt;
''A program without a loop and a structured variable isn't worth writing.'' &amp;mdash; Alan J. Perlis
&lt;/blockquote&gt;

This program obviously clears the hurdle Perlis places for being worth writing.  It has a loop &amp;ndash; an unbounded loop? &amp;ndash; and it has a structured variable in the form of the pair of arguments &amp;ndash; &lt;code&gt;(a, b)&lt;/code&gt;.

What is not so obvious is that it is also a microcosm of expression evaluation.  When we evaluate an expression, in general we either use a projection operator in the code (head/tail, car/cdr, composite.component, [array element], etc.) to select a portion of the data and ignore the rest, or we use an injection tag in the data to select a portion of the code (if/else, case, subtype or polymorphic dispatch, etc.)  and ignore the rest, and the evaluation terminates when we can no longer make any reductions of either type.  In the GCD computation, we abstract all of that away, and instead use the modulo operator to select a portion of the arguments' factorizations, and ignore the rest.  The swapping of the roles of the &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt; arguments reflects the interleaving of selection (data chooses code) and projection (code chooses data) during evaluation, and &lt;code&gt;gcd()&lt;/code&gt; terminates just when it fails to find any more possible reductions.

This abstraction in terms of prime factors means that the variables are even more structured than we had first remarked.  Our state, in fact, consists of a pair of lists of prime factors.  This structure comes in handy when considering that potentially unbounded loop.  On each pass through the loop, we either toss out some unmatched factors, or swap the variables so we are in a position to do so on the next iteration.  Unless we are in a position to pass in &lt;math&gt;\infty&lt;/math&gt; as an argument, we must eventually reduce both arguments to duplicate lists of shared factors, and so the calculation converges.

When passing from this simple model to actual code, we lose the assurance of termination.  Part of the problem is that running code not only consists of evaluating expressions, but also applying abstractions.  In evaluation, as in following a river network downstream, the structures become simpler over time.  As soon as we add the possibility of application, as in following the ramifications of tree branches from the trunk out to the leaves, the structures become more complex over time.  In general, therefore, unbounded loops which contain applications may not converge as nicely.

''Question 1. when is it desirable to code a program that can be shown not to terminate?''

''Exercise 2. take a solution for non-termination and apply it to the Blue Screen Of Death.''

''Question 3. what is the relationship of logical cuts (and cut-free proofs) to function application?''

''Exercise 4. find a well-known historical algorithm that expresses the essence of '''apply''' (like the GCD computation expresses the essence of '''eval''') &amp;ndash; and add it to this site''

[[Category:Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16502</id>
      <timestamp>2009-09-08T09:34:20Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* a brief digression */</comment>
      <text xml:space="preserve">===a brief definition===
&lt;codeblock language=python&gt;
def gcd(a,b):
        &quot;&quot;&quot; the euclidean algorithm &quot;&quot;&quot;
        while a:
                a, b = b%a, a
        return b
&lt;/codeblock&gt;
====or using recursion:====
&lt;codeblock language=python&gt;
def gcd(a,b):
        &quot;&quot;&quot; the euclidean algorithm &quot;&quot;&quot;
        if b == 0:
                return a
        else:
                return gcd(b, (a%b))
&lt;/codeblock&gt;

===a brief digression===

The Euclidean Algorithm having been [http://www.cs.nmsu.edu/historical-projects/Projects/10-20-EuclidGCD.pdf published for over 2300 years], and Knuth having devoted over 40 pages to it in ''The Art of Computer Programming'', there is very little to say about the implementation that can not be more profitably found elsewhere, such as the other language versions on this site.

We will, however, reflect a bit on the following text:

&lt;blockquote&gt;
''A program without a loop and a structured variable isn't worth writing.'' &amp;mdash; Alan J. Perlis
&lt;/blockquote&gt;

This program obviously clears the hurdle Perlis places for being worth writing.  It has a loop &amp;ndash; an unbounded loop? &amp;ndash; and it has a structured variable in the form of the pair of arguments &amp;ndash; &lt;code&gt;(a, b)&lt;/code&gt;.

What is not so obvious is that it is also a microcosm of expression evaluation.  When we evaluate an expression, in general we either use a projection operator in the code (head/tail, car/cdr, composite.component, [array element], etc.) to select a portion of the data and ignore the rest, or we use an injection tag in the data to select a portion of the code (if/else, case, subtype or polymorphic dispatch, etc.)  and ignore the rest, and the evaluation terminates when we can no longer make any reductions of either type.  In the GCD computation, we abstract all of that away, and instead use the modulo operator to select a portion of the arguments' factorizations, and ignore the rest.  The swapping of the roles of the &lt;code&gt;a&lt;/code&gt; and &lt;code&gt;b&lt;/code&gt; arguments reflects the interleaving of selection (data chooses code) and projection (code chooses data) during evaluation, and &lt;code&gt;gcd()&lt;/code&gt; terminates just when it fails to find any more possible reductions.

This abstraction in terms of prime factors means that the variables are even more structured than we had first remarked.  Our state, in fact, consists of a pair of lists of prime factors.  This structure comes in handy when considering that potentially unbounded loop.  On each pass through the loop, we either toss out some unmatched factors, or swap the variables so we are in a position to do so on the next iteration.  Unless we are in a position to pass in &lt;math&gt;\infty&lt;/math&gt; as an argument, we must eventually reduce both arguments to duplicate lists of shared factors, and so the calculation converges.

When passing from this simple model to actual code, we lose the assurance of termination.  Part of the problem is that running code not only consists of evaluating expressions, but also applying abstractions.  In evaluation, as in following a river network downstream, the structures become simpler over time.  As soon as we add the possibility of application, as in following the ramifications of tree branches from the trunk out to the leaves, the structures become more complex over time.  In general, therefore, unbounded loops which contain applications may not converge as nicely.

''Question 1. when is it desirable to code a program that can be shown not to terminate?''

''Exercise 2. take a solution for non-termination and apply it to the Blue Screen Of Death.''

''Question 3. what is the relationship of logical cuts (and cut-free proofs) to function application?''

''Exercise 4. find a well-known historical algorithm that expresses the essence of '''apply''' (like the GCD computation expresses the essence of '''eval''') &amp;ndash; and add it to this site''

[[Category:Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Scala)</title>
    <id>3947</id>
    <revision>
      <id>16766</id>
      <timestamp>2010-07-27T01:01:32Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclid's Algorithm}}

This article describes a simple recursive [http://en.wikipedia.org/wiki/Scala Scala] implementation of [http://en.wikipedia.org/wiki/Euclidean_algorithm Euclid's Algorithm] for computing the greatest common divisor (GCD) of two integers.

== The Algorithm ==

The recursive implementation of the Algorithm depends on the equation

&lt;codeblock&gt;gcd(a, b) = gcd(b, a mod b)&lt;/codeblock&gt;

with the special case

&lt;codeblock&gt;gcd(a, 0) = a&lt;/codeblock&gt;

These equations give us the general and base case of a recursive function

&lt;codeblock language=scala&gt;
&lt;&lt;gcd method&gt;&gt;=
def gcd(a: Long, b: Long): Long = b match {
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
    }
}
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;base case&gt;&gt;=
       case 0 =&gt; a
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;general case&gt;&gt;=
       case _ =&gt; gcd(b, a % b)
&lt;/codeblock&gt;

== Sample code ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Euclid.scala&gt;&gt;=

object Euclid {
    &lt;&lt;gcd method&gt;&gt;

    def main(args: Array[String]) {
        val a = args(0).toLong
        val b = args(1).toLong

        println(gcd(a, b))
    }
}
&lt;/codeblock&gt;

[[Category:Euclid's Algorithm|Java]]
[[Category:Programming language:Java]]</text>
    </revision>
    <revision>
      <id>16778</id>
      <timestamp>2010-07-27T20:47:49Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a recursive [http://en.wikipedia.org/wiki/Scala Scala] implementation of the algorithm.

The ''gcd'' method requires that ''a'' and ''b'' are positive integers but doesn't require that &lt;math&gt;a&gt;b&lt;/math&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;gcd method&gt;&gt;=
    def gcd(a: Long, b: Long): Long = (a, b) match {
        &lt;&lt;trivial case&gt;&gt;
        &lt;&lt;reversed case&gt;&gt;
        &lt;&lt;base case&gt;&gt;
        &lt;&lt;general case&gt;&gt;
    }
&lt;/codeblock&gt;

The trivial case applies when ''a'' is equal to ''b'':

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;trivial case&gt;&gt;=
        case (a, `a`)        =&gt; a
&lt;/codeblock&gt;

The reversed case applies when &lt;math&gt;b&gt;a&lt;/math&gt;:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;reversed case&gt;&gt;=
        case (a, b) if b &gt; a =&gt; gcd(b, a)
&lt;/codeblock&gt;

The base case applies when ''b'' is equal to 0:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;base case&gt;&gt;=
        case (a, 0)          =&gt; a
&lt;/codeblock&gt;

Since &lt;math&gt;a&gt;b&lt;/math&gt; now holds, the first identity can be used for the general case:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;general case&gt;&gt;=
        case _               =&gt; gcd(b, a % b)
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Euclid.scala&gt;&gt;=

object Euclid {
    &lt;&lt;gcd method&gt;&gt;

    def main(args: Array[String]) {
        val a = args(0).toLong
        val b = args(1).toLong

        println(gcd(a, b))
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
scala Euclid 35 42
scala Euclid 35 40
scala Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16779</id>
      <timestamp>2010-07-27T20:53:12Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>[[Euclid's Algorithm (Scala)]] moved to [[Euclidean algorithm (Scala)]]: Bring the page into the list of implementations for the category.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

This article describes a recursive [http://en.wikipedia.org/wiki/Scala Scala] implementation of the algorithm.

The ''gcd'' method requires that ''a'' and ''b'' are positive integers but doesn't require that &lt;math&gt;a&gt;b&lt;/math&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;gcd method&gt;&gt;=
    def gcd(a: Long, b: Long): Long = (a, b) match {
        &lt;&lt;trivial case&gt;&gt;
        &lt;&lt;reversed case&gt;&gt;
        &lt;&lt;base case&gt;&gt;
        &lt;&lt;general case&gt;&gt;
    }
&lt;/codeblock&gt;

The trivial case applies when ''a'' is equal to ''b'':

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;trivial case&gt;&gt;=
        case (a, `a`)        =&gt; a
&lt;/codeblock&gt;

The reversed case applies when &lt;math&gt;b&gt;a&lt;/math&gt;:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;reversed case&gt;&gt;=
        case (a, b) if b &gt; a =&gt; gcd(b, a)
&lt;/codeblock&gt;

The base case applies when ''b'' is equal to 0:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;base case&gt;&gt;=
        case (a, 0)          =&gt; a
&lt;/codeblock&gt;

Since &lt;math&gt;a&gt;b&lt;/math&gt; now holds, the first identity can be used for the general case:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;general case&gt;&gt;=
        case _               =&gt; gcd(b, a % b)
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Euclid.scala&gt;&gt;=

object Euclid {
    &lt;&lt;gcd method&gt;&gt;

    def main(args: Array[String]) {
        val a = args(0).toLong
        val b = args(1).toLong

        println(gcd(a, b))
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
scala Euclid 35 42
scala Euclid 35 40
scala Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16781</id>
      <timestamp>2010-07-27T21:04:16Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <comment>Adjusted whitespace.</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The ''gcd'' method requires that ''a'' and ''b'' are positive integers but doesn't require that &lt;math&gt;a&gt;b&lt;/math&gt;.

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;gcd method&gt;&gt;=
def gcd(a: Long, b: Long): Long = (a, b) match {
    &lt;&lt;trivial case&gt;&gt;
    &lt;&lt;reversed case&gt;&gt;
    &lt;&lt;base case&gt;&gt;
    &lt;&lt;general case&gt;&gt;
}
&lt;/codeblock&gt;

The trivial case applies when ''a'' is equal to ''b'':

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;trivial case&gt;&gt;=
case (a, `a`)        =&gt; a
&lt;/codeblock&gt;

The reversed case applies when &lt;math&gt;b&gt;a&lt;/math&gt;:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;reversed case&gt;&gt;=
case (a, b) if b &gt; a =&gt; gcd(b, a)
&lt;/codeblock&gt;

The base case applies when ''b'' is equal to 0:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;base case&gt;&gt;=
case (a, 0)          =&gt; a
&lt;/codeblock&gt;

Since &lt;math&gt;a&gt;b&lt;/math&gt; now holds, the first identity can be used for the general case:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;general case&gt;&gt;=
case _               =&gt; gcd(b, a % b)
&lt;/codeblock&gt;

== Sample code and demonstration ==

Here's some code demonstrating how to use the above method:

&lt;codeblock language=&quot;scala&quot;&gt;
&lt;&lt;Euclid.scala&gt;&gt;=

object Euclid {
    &lt;&lt;gcd method&gt;&gt;

    def main(args: Array[String]) {
        val a = args(0).toLong
        val b = args(1).toLong

        println(gcd(a, b))
    }
}
&lt;/codeblock&gt;

If we compile and run the following command lines:

&lt;codeblock&gt;
scala Euclid 35 42
scala Euclid 35 40
scala Euclid 35 38
&lt;/codeblock&gt;

We get the following outputs: 

&lt;codeblock&gt;
7
5
1
&lt;/codeblock&gt;

[[Category:Euclidean algorithm|Scala]]
[[Category:Programming language:Scala]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Euclidean algorithm (Standard ML)</title>
    <id>3868</id>
    <revision>
      <id>16314</id>
      <timestamp>2009-03-29T05:36:00Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <comment>translated from ocaml</comment>
      <text xml:space="preserve">{{Category:Euclidean algorithm}}

The Euclidean algorithm is straightforward to describe in Standard ML, using a function that recurses on the remainder of the division of ''a'' by ''b'' until that remainder is 0.

&lt;codeblock language=&quot;sml&quot;&gt;
fun gcd (a, 0) = a
  | gcd (a, b) = gcd (b, a mod b)
&lt;/codeblock&gt;

Performing the Euclidean algorithm on an arbitrary list of integers is also relatively straight-forward using the above function. Note that 0 is an identity for gcd.

&lt;codeblock language=&quot;sml&quot;&gt;
val gcd_list = foldl gcd 0
&lt;/codeblock&gt;


[[Category:Euclidean algorithm|Standard ML]]
[[Category:Programming language:Standard ML]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Exponentiation by squaring (AWK/dc)</title>
    <id>2729</id>
    <revision>
      <id>7815</id>
      <timestamp>2006-10-14T14:53:19Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial code dump</comment>
      <text xml:space="preserve">{{codedump}}

==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

  a^0 = 1
  a^n = a * a^(n-1)

But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle  input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>7816</id>
      <timestamp>2006-10-14T14:54:26Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>typo</comment>
      <text xml:space="preserve">{{codedump}}

==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

  a^0 = 1
  a^n = a * a^(n-1)

But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>7818</id>
      <timestamp>2006-10-15T10:00:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>categories</comment>
      <text xml:space="preserve">{{codedump}}

==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

  a^0 = 1
  a^n = a * a^(n-1)

But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;


[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]</text>
    </revision>
    <revision>
      <id>7824</id>
      <timestamp>2006-10-15T17:27:25Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>mathified</comment>
      <text xml:space="preserve">{{codedump}}

==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;


[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]</text>
    </revision>
    <revision>
      <id>7825</id>
      <timestamp>2006-10-15T17:31:15Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>Category:Exponentiation by squaring:AWK/dc (per Special:WantedPages)</comment>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;


[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring:AWK/dc]]</text>
    </revision>
    <revision>
      <id>7827</id>
      <timestamp>2006-10-15T17:42:33Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>fix category</comment>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;


[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring]]</text>
    </revision>
    <revision>
      <id>7831</id>
      <timestamp>2006-10-15T23:16:34Z</timestamp>
      <contributor>
        <ip>81.62.33.16</ip>
      </contributor>
      <comment>cf Peasant multiplication</comment>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs arbitrary length integer arithmetic, while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;

''Exercise 5. compare exponentiation by squaring with [http://en.wikipedia.org/wiki/Multiplication_algorithm#Peasant_or_binary_multiplication multiplication by doubling].

[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring]]</text>
    </revision>
    <revision>
      <id>7842</id>
      <timestamp>2006-10-17T12:33:57Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>ref. arbitrary-precision arithmetic</comment>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs [[:Category:Arbitrary-precision_arithmetic|arbitrary length integer arithmetic]], while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
                                { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;

''Exercise 5. compare exponentiation by squaring with [http://en.wikipedia.org/wiki/Multiplication_algorithm#Peasant_or_binary_multiplication multiplication by doubling].

[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring|Exponentiation by squaring]]
[[Category:Arbitrary-precision_arithmetic]]</text>
    </revision>
    <revision>
      <id>9490</id>
      <timestamp>2007-03-15T15:05:54Z</timestamp>
      <contributor>
        <username>Pdelong</username>
        <id>153</id>
      </contributor>
      <comment>prompt wasn't getting printed otherwise</comment>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs [[:Category:Arbitrary-precision_arithmetic|arbitrary length integer arithmetic]], while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
BEGIN                           { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;

''Exercise 5. compare exponentiation by squaring with [http://en.wikipedia.org/wiki/Multiplication_algorithm#Peasant_or_binary_multiplication multiplication by doubling].

[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring|Exponentiation by squaring]]
[[Category:Arbitrary-precision_arithmetic]]</text>
    </revision>
    <revision>
      <id>17066</id>
      <timestamp>2011-02-19T19:00:55Z</timestamp>
      <contributor>
        <username>Yeatman</username>
        <id>2208</id>
      </contributor>
      <text xml:space="preserve">==the theory==

The straightforward way to exponentiate is via repeated multiplication, using the recurrence

&lt;math&gt;
\begin{matrix} a^0 &amp; = &amp; 1 \\ a^n &amp; = &amp; a a^{n-1} \end{matrix}
&lt;/math&gt;
 
But if we view the exponent as a binary number (which we can deconstruct bit by bit) instead of as a natural number (which we must deconstruct by decrementing), it's possible to build up the result with a much shorter sequence of multiplications.  The tradeoff is that instead of always multiplying by the base, we will be squaring repeatedly, and multiplying by the base only in the cases where we find &quot;1&quot; bits.

&lt;math&gt;
\begin{matrix}
a^0 &amp; = &amp; 1 \\ 
a^{s0} &amp; = &amp; { ( a^s ) }^2 \\
a^{s1} &amp; = &amp; a { ( a^s ) }^2 
\end{matrix}
&lt;/math&gt;

If one is
[[:Category:Compilers_and_programming_languages|folding constants during code generation]]
this is an easy tradeoff to make: a few more branches, taken once during compilation, can yield much shorter straight-line code paths, which will be executed many times.

To simulate this process, we will generate some code to evaluate an exponential (minimizing the multiplications) and then interpret it in &lt;code&gt;dc&lt;/code&gt;.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;evaluate expression&gt;&gt;=
function exponentiate(a,b)      { print genexpr(a,b) | &quot;dc&quot; }
&lt;/codeblock&gt;

Not only does the two-process split simulate the difference between compile-time calculation and run-time calculation, but it offers the additional advantage that &lt;code&gt;dc&lt;/code&gt; performs [[:Category:Arbitrary-precision_arithmetic|arbitrary length integer arithmetic]], while &lt;code&gt;awk&lt;/code&gt; on its own would silently shift over to floating point.  For instance, we can now evaluate:

  10^64
  10000000000000000000000000000000000000000000000000000000000000000
  2^128
  340282366920938463463374607431768211456

==the practice==

We want to produce output, so our expression will at least contain the &lt;code&gt;p&lt;/code&gt; command to print the result.  (this is done here rather than elsewhere to finesse AWK's lack of local variables)

The loop is rather straightforward.  We shift out bits from the bottom of the exponent and build up our expression.  It would be even simpler to shift &lt;code&gt;while(b &gt; 0)&lt;/code&gt;, but the rationale for special casing the final bit is given below.

''Exercise 1: recode with a loop which shifts the exponent all the way to 0, treating all bits identically''
''Exercise 2: add code to Ex. 1 to patch the final expression, removing excess multiplies''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;generate expression&gt;&gt;=
function genexpr(a,b) {
    e = &quot;p&quot;
    for(;;) {
        if(b &lt; 2) {
           &lt;&lt;most significant bit&gt;&gt;
            return e
        }
        &lt;&lt;lower order bits&gt;&gt;
        b = int(b/2)
    }
}
&lt;/codeblock&gt;

For most bits, we square (&lt;code&gt;d*&lt;/code&gt;) the running result from the higher order bits.  If the bit in question is a 1 bit, we also need a multiply by the base.

NB. we shift out from the bottom, so we process the exponent right-to-left.  But the final calculation is carried out left-to-right.  This is not a problem, as there is nothing constraining us to build the expression in the interpetation order, so we simply build it in the reverse.

''Question 3: can reverse-order generation be used to simplify tail-call elimination? &quot;

&lt;codeblock language=&quot;awk&gt;
&lt;&lt;lower order bits&gt;&gt;=
        if(b % 2)      e = &quot;d*&quot; a &quot;*&quot; e
        else           e = &quot;d*&quot;       e
&lt;/codeblock&gt;

Finally, we come to the most significant bit.  We could treat it like all the other bits, prepending a &quot;&lt;code&gt;1 &lt;/code&gt;&quot; to the expression to get things started (&lt;code&gt;dc&lt;/code&gt; is not sophisticated enough to figure out the unit for multiplication, and will complain bitterly about empty stacks), but taking advantage of a little constant propagation

  1 d*a* = a
  1 d*   = 1

we can trim a multiply or two from the final expression.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;most significant bit&gt;&gt;=
            if(b % 2)  e = a &quot; &quot; e
            else       e = 1 &quot; &quot; e
&lt;/codeblock&gt;

Note that we treat the value of &lt;code&gt;a&lt;/code&gt; as opaque throughout.

''Exercise 4: rewrite to generate the sequence of assembly instructions for an arbitrary base''

==wrapping up==

Now we just need a little glue to handle rudimentary input

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;handle input&gt;&gt;=
BEGIN                           { FS=&quot;^&quot; }
$1 ~ /[0-9]+/ &amp;&amp; $2 ~ /[0-9]+/  { exponentiate($1,$2); next }
BEGIN                           { print &quot;enter expressions of the form i^j&quot; }
&lt;/codeblock&gt;

and we can bundle up the script

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;expbysqr.awk&gt;&gt;=
#!/usr/bin/awk -f
&lt;&lt;handle input&gt;&gt;
&lt;&lt;generate expression&gt;&gt;
&lt;&lt;evaluate expression&gt;&gt;
&lt;/codeblock&gt;

''Exercise 5. compare exponentiation by squaring with [http://en.wikipedia.org/wiki/Multiplication_algorithm#Peasant_or_binary_multiplication multiplication by doubling].

[[Category:Programming language:AWK]]
[[Category:Programming language:dc]]
[[Category:Exponentiation by squaring|Exponentiation by squaring]]
[[Category:Arbitrary-precision_arithmetic]]
[[Category:Number theory]]</text>
    </revision>
  </page>
  <page>
    <title>Extended Euclidean algorithm (C Plus Plus)</title>
    <id>3982</id>
    <revision>
      <id>16979</id>
      <timestamp>2010-12-19T09:03:42Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <comment>revised from the Python version</comment>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
 crypto@crypto ~/python
 $ g++ eea.cpp; ./a.aout
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C++]]
[[Category:Environment:C++]]</text>
    </revision>
    <revision>
      <id>16980</id>
      <timestamp>2010-12-19T09:08:09Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
$ g++ eea.cpp; ./a.aout
-10 21 8
21 -10 8
-45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16981</id>
      <timestamp>2010-12-19T09:11:57Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

The algorithm is better described in the Python version.

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
 $ g++ eea.cpp; ./a.out 
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16982</id>
      <timestamp>2010-12-19T09:12:59Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

The algorithm is better described in the Python version.

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0 {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
 $ g++ eea.cpp; ./a.out 
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16983</id>
      <timestamp>2010-12-19T09:13:39Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

The algorithm is better described in the Python version.

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
 $ g++ eea.cpp; ./a.out 
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16984</id>
      <timestamp>2010-12-19T09:25:33Z</timestamp>
      <contributor>
        <username>Erel Segal</username>
        <id>2161</id>
      </contributor>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

The algorithm is better described in the Python version.

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
}
&lt;/codeblock&gt;
==Execution result==
 $ g++ eea.cpp; ./a.out 
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16991</id>
      <timestamp>2010-12-19T20:52:24Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This article describes a C++ implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

Given a,b, Find x,y,g that solve the equation:
:&lt;math&gt;ax + by = g = gcd(a,b)&lt;/math&gt;

The algorithm is better described in the Python version.

==Source==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea&gt;&gt;=
void eea (int a, int b,
        int&amp; gcd, int&amp; x, int&amp; y) {
        x=0, y=1; 
        int u=1, v=0, m, n, q, r;
        gcd = b;
        while (a!=0) {
                q=gcd/a; r=gcd%a;
                m=x-u*q; n=y-v*q;
                gcd=a; a=r; x=u; y=v; u=m; v=n;
        }
}
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;eea.cpp&gt;&gt;=
#include &lt;iostream&gt;
using namespace std;
&lt;&lt;eea&gt;&gt;
int main() {
  int gcd, x, y; 
  eea(352, 168, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(168, 352, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  eea(3458, 4864, gcd, x, y);
  cout &lt;&lt; x &lt;&lt; &quot; &quot; &lt;&lt; y &lt;&lt; &quot; &quot; &lt;&lt; gcd &lt;&lt; endl;
  return 0;
}
&lt;/codeblock&gt;
==Execution result==
 $ g++ eea.cpp; ./a.out 
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|C++]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Extended Euclidean algorithm (Python)</title>
    <id>2590</id>
    <revision>
      <id>7038</id>
      <timestamp>2006-07-18T13:28:50Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <text xml:space="preserve">This page explains the Python implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

==Algorithm==
For &lt;math&gt;u&lt;/math&gt; and &lt;math&gt;v&lt;/math&gt;, this algorithm finds &lt;math&gt;(u_1, u_2, u_3)&lt;/math&gt; such that &lt;math&gt;uu_1 + vu_2 = u_3 = \gcd(u, v)&lt;/math&gt;. We use auxiliary vectors &lt;math&gt;(v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(t_1, t_2, t_3)&lt;/math&gt; in the algorithm. The following equations always hold throughout the algorithm.

:&lt;math&gt;ut_1 + vt_2 = t_3&lt;/math&gt;
:&lt;math&gt;uu_1 + uu_2 = u_3&lt;/math&gt;
:&lt;math&gt;uv_1 + uv_2 = v_3&lt;/math&gt;

#(Initialization): &lt;math&gt;(u_1, u_2, u_3) \leftarrow (1, 0, u)&lt;/math&gt;, &lt;math&gt;(v_1, v_2, v_3) \leftarrow (0, 1, v)&lt;/math&gt;
# If &lt;math&gt;v_3 = 0&lt;/math&gt;, stop.
# Otherwise, do the following.
#* &lt;math&gt;q \leftarrow \lfloor u_3 / v_3 \rfloor&lt;/math&gt;
#* &lt;math&gt;(t_1, t_2, t_3) = (u_1, u_2, u_3) - (v_1, v_2, v_3)*q&lt;/math&gt;
#* &lt;math&gt;(u_1, u_2, u_3) \leftarrow (v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(v_1, v_2, v_3) \leftarrow (t_1, t_2, t_3)&lt;/math&gt;
#* return to 2.

==Source==
The algorithm is quite straightforward and it is not difficult to translate the algorithm into a Python source code.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea&gt;&gt;=
def eea(u, v):
	u1 = 1
	u2 = 0
	u3 = u
	v1 = 0
	v2 = 1
	v3 = v
	while v3 != 0:
		q = u3 / v3
		t1 = u1 - q * v1
		t2 = u2 - q * v2
		t3 = u3 - q * v3
		u1 = v1
		u2 = v2
		u3 = v3
		v1 = t1
		v2 = t2
		v3 = t3
	return u1, u2, u3
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.py&gt;&gt;=
&lt;&lt;eea&gt;&gt;

if __name__ == &quot;__main__&quot;:
	a, b, d = eea(352, 168)
	print a, b, d
	a, b, d = eea(168, 352)
	print a, b, d
	a, b, d = eea(3458, 4864)
	print a, b, d
&lt;/codeblock&gt;
==Execution result==
 crypto@crypto ~/python
 $ python eea.py
 -10 21 8
 21 -10 8
 -45 32 38

The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168). The second result means that the order of input numbers has no significant meaning. The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7041</id>
      <timestamp>2006-07-20T22:46:50Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Style</comment>
      <text xml:space="preserve">This article describes a Python implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

==Algorithm==
For &lt;math&gt;u&lt;/math&gt; and &lt;math&gt;v&lt;/math&gt;, this algorithm finds &lt;math&gt;(u_1, u_2, u_3)&lt;/math&gt; such that &lt;math&gt;uu_1 + vu_2 = u_3 = \gcd(u, v)&lt;/math&gt;. We use auxiliary vectors &lt;math&gt;(v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(t_1, t_2, t_3)&lt;/math&gt; in the algorithm. The following equations always hold throughout the algorithm.

:&lt;math&gt;ut_1 + vt_2 = t_3&lt;/math&gt;
:&lt;math&gt;uu_1 + uu_2 = u_3&lt;/math&gt;
:&lt;math&gt;uv_1 + uv_2 = v_3&lt;/math&gt;

#(Initialization): &lt;math&gt;(u_1, u_2, u_3) \leftarrow (1, 0, u)&lt;/math&gt;, &lt;math&gt;(v_1, v_2, v_3) \leftarrow (0, 1, v)&lt;/math&gt;
# If &lt;math&gt;v_3 = 0&lt;/math&gt;, stop.
# Otherwise, do the following.
#* &lt;math&gt;q \leftarrow \lfloor u_3 / v_3 \rfloor&lt;/math&gt;
#* &lt;math&gt;(t_1, t_2, t_3) = (u_1, u_2, u_3) - (v_1, v_2, v_3)*q&lt;/math&gt;
#* &lt;math&gt;(u_1, u_2, u_3) \leftarrow (v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(v_1, v_2, v_3) \leftarrow (t_1, t_2, t_3)&lt;/math&gt;
#* return to 2.

==Source==
The algorithm is quite straightforward and it is not difficult to translate the algorithm into a Python source code.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea&gt;&gt;=
def eea(u, v):
	u1 = 1
	u2 = 0
	u3 = u
	v1 = 0
	v2 = 1
	v3 = v
	while v3 != 0:
		q = u3 / v3
		t1 = u1 - q * v1
		t2 = u2 - q * v2
		t3 = u3 - q * v3
		u1 = v1
		u2 = v2
		u3 = v3
		v1 = t1
		v2 = t2
		v3 = t3
	return u1, u2, u3
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.py&gt;&gt;=
&lt;&lt;eea&gt;&gt;

if __name__ == &quot;__main__&quot;:
	a, b, d = eea(352, 168)
	print a, b, d
	a, b, d = eea(168, 352)
	print a, b, d
	a, b, d = eea(3458, 4864)
	print a, b, d
&lt;/codeblock&gt;
==Execution result==
 crypto@crypto ~/python
 $ python eea.py
 -10 21 8
 21 -10 8
 -45 32 38

The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168). The second result means that the order of input numbers has no significant meaning. The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7042</id>
      <timestamp>2006-07-22T06:34:47Z</timestamp>
      <contributor>
        <username>Crypto</username>
        <id>55</id>
      </contributor>
      <minor/>
      <comment>/* Execution result */</comment>
      <text xml:space="preserve">This article describes a Python implementation of [http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Extended Euclidean algorithm].

==Algorithm==
For &lt;math&gt;u&lt;/math&gt; and &lt;math&gt;v&lt;/math&gt;, this algorithm finds &lt;math&gt;(u_1, u_2, u_3)&lt;/math&gt; such that &lt;math&gt;uu_1 + vu_2 = u_3 = \gcd(u, v)&lt;/math&gt;. We use auxiliary vectors &lt;math&gt;(v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(t_1, t_2, t_3)&lt;/math&gt; in the algorithm. The following equations always hold throughout the algorithm.

:&lt;math&gt;ut_1 + vt_2 = t_3&lt;/math&gt;
:&lt;math&gt;uu_1 + uu_2 = u_3&lt;/math&gt;
:&lt;math&gt;uv_1 + uv_2 = v_3&lt;/math&gt;

#(Initialization): &lt;math&gt;(u_1, u_2, u_3) \leftarrow (1, 0, u)&lt;/math&gt;, &lt;math&gt;(v_1, v_2, v_3) \leftarrow (0, 1, v)&lt;/math&gt;
# If &lt;math&gt;v_3 = 0&lt;/math&gt;, stop.
# Otherwise, do the following.
#* &lt;math&gt;q \leftarrow \lfloor u_3 / v_3 \rfloor&lt;/math&gt;
#* &lt;math&gt;(t_1, t_2, t_3) = (u_1, u_2, u_3) - (v_1, v_2, v_3)*q&lt;/math&gt;
#* &lt;math&gt;(u_1, u_2, u_3) \leftarrow (v_1, v_2, v_3)&lt;/math&gt; and &lt;math&gt;(v_1, v_2, v_3) \leftarrow (t_1, t_2, t_3)&lt;/math&gt;
#* return to 2.

==Source==
The algorithm is quite straightforward and it is not difficult to translate the algorithm into a Python source code.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea&gt;&gt;=
def eea(u, v):
	u1 = 1
	u2 = 0
	u3 = u
	v1 = 0
	v2 = 1
	v3 = v
	while v3 != 0:
		q = u3 / v3
		t1 = u1 - q * v1
		t2 = u2 - q * v2
		t3 = u3 - q * v3
		u1 = v1
		u2 = v2
		u3 = v3
		v1 = t1
		v2 = t2
		v3 = t3
	return u1, u2, u3
&lt;/codeblock&gt;
The test driver is also given.
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;eea.py&gt;&gt;=
&lt;&lt;eea&gt;&gt;

if __name__ == &quot;__main__&quot;:
	a, b, d = eea(352, 168)
	print a, b, d
	a, b, d = eea(168, 352)
	print a, b, d
	a, b, d = eea(3458, 4864)
	print a, b, d
&lt;/codeblock&gt;
==Execution result==
 crypto@crypto ~/python
 $ python eea.py
 -10 21 8
 21 -10 8
 -45 32 38

* The first test case shows that -10 *352 + 21 * 168 = 8 and 8 is gcd(352, 168).
* The second result means that the order of input numbers has no significant meaning.
* The last result shows that -45 * 3458 + 32 * 4864 = 38 and 38 is gcd(3458, 4864).

[[Category:Extended Euclidean algorithm|Python]]
[[Category:Programming language:Python]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>FAT12 floppy image (Python)</title>
    <id>3675</id>
    <revision>
      <id>15451</id>
      <timestamp>2008-11-14T17:48:14Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{develop}}
==theory==

A filesystem is basically a container data structure; in order to read a filesystem (or mutate one efficiently) we would need to be able to handle all valid states, but in order to initialize one we are free to choose the simplest valid injection.

In this case, we attempt to build rudimentary DOS [http://en.wikipedia.org/wiki/File_Allocation_Table FAT12] floppy images; as this filesystem format is over three decades old, a direct route will be less than a screenful of lines.

==practice==

We use the following straightforward code to write the filesystem image:
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;writing image&gt;&gt;=
def mkimg(filename,blobs):
    f = open(filename, &quot;w&quot;)
    for off, data in blobs:
	f.seek(512*off)
	f.write(''.join(data))
    f.close()
&lt;/codeblock&gt;

Therefore, we describe our desired filesystem in terms of block offsets and the data which will be concatenated at that location.

The filesystem consists of the following areas:
* the Master Boot Record
* a File Allocation Table
* directory entries for each file
* and, of course, the data comprising each file's contents.

There are only a few details to watch out for:
* the FAT occurs twice, to provide a redundant spare
* we also arrange to write a zero block in the final sector, forcing the image to the desired size.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;image description&gt;&gt;=
[( 0,[open(param('-b',&quot;mbr.raw&quot;)).read()]),
 ( 1,fat),
 (10,fat),
 (19,[dirent(*e) for e in zip(files,offs,lens)])] +
[(31+o,[c]) for o,c in zip(offs,contents)] +
[(int(param('-s',&quot;2880&quot;))-1,[pack('512x')])]&lt;/codeblock&gt;

===directory entries===

Creating the directory entries is messy, but straightforward, especially because we ignore all metadata except for the file name, offset of its first block, and the file length.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillaries&gt;&gt;=
dosfn	=lambda f: &quot;%-8.8s%-3.3s&quot; % tuple((f.upper()+'.').split('.'))[:2]
dirent  =lambda f,o,l: pack('&lt;11s15xHI',dosfn(basename(f)),o,l)
&lt;/codeblock&gt;

===file data blocks===

Deciding where to place the file contents is also easy.  We don't have to deal with an arbitrary file system state, but can instead choose an easy state: the files are laid out one after the other contiguously on disk.

Because files are block-aligned, we round up the file sizes to the number of '''blocks''' taken by the file, then '''accum'''ulate the number of blocks taken up by the previous files to determine each file's starting offset.

Due to special interpretation of certain offset values in the FAT, we start the data area at block offset 2 instead of 0.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;calculate offsets&gt;&gt;=
offs    = accum([blocks(l,512) for l in lens],2)
&lt;&lt;ancillaries&gt;&gt;=
blocks	=lambda n,b: n/b + (n%b&gt;0)
accum   =lambda vs,v0: reduce(lambda l,r: l + [r+l[-1]],vs,[v0])
&lt;/codeblock&gt;

===the File Allocation Table===

Finally, encoding the FAT &amp;mdash; for the contiguous case &amp;mdash; is trivial.  The FAT is basically a disk-based linked list; the successor of each block within a file is the next block, so '''range(1,&amp;omega;)''' provides almost what we want.  The only problem would be that the final block of each file would then point to the start offset of the next one.  By changing each occurrence of a start offset to the EOF flag ('''0xfff''') we correctly mark the end of each file and preserve the property that the start of each file shouldn't have a predecessor.

The sole difficulty here is that FAT12 is a 12-bit encoding, meaning that each entry is 3 nybbles long and hence not byte-aligned.  We do the obvious thing, first expanding each FAT entry into its 3 component '''nybbles''' then using '''n2bytes''' to reduce each pair of nybbles to a byte value.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;encode FAT&gt;&gt;=
fat     = n2bytes(nybbles([(b in offs) and 0xfff or b
				for b in range(1,offs[-1]+1)]))
&lt;&lt;ancillaries&gt;&gt;=
nybbles =lambda vs: sum([(v&amp;0xf,(v&gt;&gt;4)&amp;0xf,(v&gt;&gt;8)&amp;0xf) for v in vs],())
n2bytes =lambda ns: [pack('B',o*0x10+e) for e,o in zip(ns[0::2],ns[1::2])]
&lt;/codeblock&gt;

==wrapping up==

Finally, we get the file contents and lengths in the obvious way...

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;get file data&gt;&gt;=
contents= [file(f).read() for f in files]
lens    = [len(c) for c in contents]
&lt;/codeblock&gt;

... and provide a simple command-line wrapper.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;mkfat12.py&gt;&gt;=
from struct import pack
from os.path import basename

&lt;&lt;ancillaries&gt;&gt;
&lt;&lt;writing image&gt;&gt;
def mkfat12(opts,files):
    if '-h' in opts:
        print &quot;Usage: [-b MBR] [-o output] [-s sector count] files...&quot;
        return

    param   = lambda f,d: (f in opts) and opts[f] or d
    &lt;&lt;get file data&gt;&gt;
    &lt;&lt;calculate offsets&gt;&gt;
    &lt;&lt;encode FAT&gt;&gt;
    mkimg(param('-o',&quot;a.raw&quot;),
         &lt;&lt;image description&gt;&gt;)

if __name__ == '__main__':
    import sys, getopt

    os,files = getopt.getopt(sys.argv[1:],&quot;b:o:s:h&quot;)
    mkfat12(dict(os),files)
&lt;/codeblock&gt;

===testing===

You should provide '''mbr.raw''' or use the '''-b''' option to specify a 512-byte Master Boot Record.  This can be copied from an existing floppy with something along the lines of:
&lt;pre&gt;
dd if=/dev/fd0 of=mbr.raw bs=512 count=1
&lt;/pre&gt;

The resulting output file (defaults to ''a.raw'' as a 1.44 MB floppy image) can be set as a virtual device for a PC emulator such as [http://www.kju-app.org/ Q] or Bochs, written to a physical floppy disk with '''dd(1)''', or even placed on a CD-ROM (depending upon burner software) as a bootstrap image.

[[Category:Programming language:Python]]
[[Category:File management tools]]
[[Category:Operating systems]]</text>
    </revision>
    <revision>
      <id>15456</id>
      <timestamp>2008-11-16T23:04:59Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>-develop, add 12-bit diagram</comment>
      <text xml:space="preserve">==theory==

A filesystem is basically a container data structure; in order to read a filesystem (or mutate one efficiently) we would need to be able to handle all valid states, but in order to initialize one we are free to choose the simplest valid injection.

In this case, we attempt to build rudimentary DOS [http://en.wikipedia.org/wiki/File_Allocation_Table FAT12] floppy images; as this filesystem format is over three decades old, a direct route will be less than a screenful of lines.

==practice==

We use the following straightforward code to write the filesystem image:
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;writing image&gt;&gt;=
def mkimg(filename,blobs):
    f = open(filename, &quot;w&quot;)
    for off, data in blobs:
	f.seek(512*off)
	f.write(''.join(data))
    f.close()
&lt;/codeblock&gt;

Therefore, we describe our desired filesystem in terms of block offsets and the data which will be concatenated at that location.

The filesystem consists of the following areas:
* the Master Boot Record
* a File Allocation Table
* directory entries for each file
* and, of course, the data comprising each file's contents.

There are only a few details to watch out for:
* the FAT occurs twice, to provide a redundant spare
* we also arrange to write a zero block in the final sector, forcing the image to the desired size.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;image description&gt;&gt;=
[( 0,[open(param('-b',&quot;mbr.raw&quot;)).read()]),
 ( 1,fat),
 (10,fat),
 (19,[dirent(*e) for e in zip(files,offs,lens)])] +
[(31+o,[c]) for o,c in zip(offs,contents)] +
[(int(param('-s',&quot;2880&quot;))-1,[pack('512x')])]&lt;/codeblock&gt;

===directory entries===

Creating the directory entries is messy, but straightforward, especially because we ignore all metadata except for the file name, offset of its first block, and the file length.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillaries&gt;&gt;=
dosfn	=lambda f: &quot;%-8.8s%-3.3s&quot; % tuple((f.upper()+'.').split('.'))[:2]
dirent  =lambda f,o,l: pack('&lt;11s15xHI',dosfn(basename(f)),o,l)
&lt;/codeblock&gt;

===file data blocks===

Deciding where to place the file contents is also easy.  We don't have to deal with an arbitrary file system state, but can instead choose an easy state: the files are laid out one after the other contiguously on disk.

Because files are block-aligned, we round up the file sizes to the number of '''blocks''' taken by the file, then '''accum'''ulate the number of blocks taken up by the previous files to determine each file's starting offset.

Due to special interpretation of certain offset values in the FAT, we start the data area at block offset 2 instead of 0.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;calculate offsets&gt;&gt;=
offs    = accum([blocks(l,512) for l in lens],2)
&lt;&lt;ancillaries&gt;&gt;=
blocks	=lambda n,b: n/b + (n%b&gt;0)
accum   =lambda vs,v0: reduce(lambda l,r: l + [r+l[-1]],vs,[v0])
&lt;/codeblock&gt;

===the File Allocation Table===

Finally, encoding the FAT &amp;mdash; for the contiguous case &amp;mdash; is trivial.  The FAT is basically a disk-based linked list; the successor of each block within a file is the next block, so '''range(1,&amp;omega;)''' provides almost what we want.  The only problem would be that the final block of each file would then point to the start offset of the next one.  By changing each occurrence of a start offset to the EOF flag ('''0xfff''') we correctly mark the end of each file and preserve the property that the start of each file shouldn't have a predecessor.

The sole difficulty here is that FAT12 is a 12-bit encoding, meaning that each entry is 3 nybbles long and hence not byte-aligned.  We do the obvious thing, first expanding each FAT entry into its 3 component '''nybbles''' then using '''n2bytes''' to reduce each pair of nybbles to a byte value.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;encode FAT&gt;&gt;=
fat     = n2bytes(nybbles([(b in offs) and 0xfff or b
				for b in range(1,offs[-1]+1)]))
&lt;&lt;ancillaries&gt;&gt;=
nybbles =lambda vs: sum([(v&amp;0xf,(v&gt;&gt;4)&amp;0xf,(v&gt;&gt;8)&amp;0xf) for v in vs],())
n2bytes =lambda ns: [pack('B',o*0x10+e) for e,o in zip(ns[0::2],ns[1::2])]
&lt;/codeblock&gt;

[[Image:Fat12.png]]

==wrapping up==

Finally, we get the file contents and lengths in the obvious way...

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;get file data&gt;&gt;=
contents= [file(f).read() for f in files]
lens    = [len(c) for c in contents]
&lt;/codeblock&gt;

... and provide a simple command-line wrapper.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;mkfat12.py&gt;&gt;=
from struct import pack
from os.path import basename

&lt;&lt;ancillaries&gt;&gt;
&lt;&lt;writing image&gt;&gt;
def mkfat12(opts,files):
    if '-h' in opts:
        print &quot;Usage: [-b MBR] [-o output] [-s sector count] files...&quot;
        return

    param   = lambda f,d: (f in opts) and opts[f] or d
    &lt;&lt;get file data&gt;&gt;
    &lt;&lt;calculate offsets&gt;&gt;
    &lt;&lt;encode FAT&gt;&gt;
    mkimg(param('-o',&quot;a.raw&quot;),
         &lt;&lt;image description&gt;&gt;)

if __name__ == '__main__':
    import sys, getopt

    os,files = getopt.getopt(sys.argv[1:],&quot;b:o:s:h&quot;)
    mkfat12(dict(os),files)
&lt;/codeblock&gt;

===testing===

You should provide '''mbr.raw''' or use the '''-b''' option to specify a 512-byte Master Boot Record.  This can be copied from an existing floppy with something along the lines of:
&lt;pre&gt;
dd if=/dev/fd0 of=mbr.raw bs=512 count=1
&lt;/pre&gt;

The resulting output file (defaults to ''a.raw'' as a 1.44 MB floppy image) can be set as a virtual device for a PC emulator such as [http://www.kju-app.org/ Q] or Bochs, written to a physical floppy disk with '''dd(1)''', or even placed on a CD-ROM (depending upon burner software) as a bootstrap image.

[[Category:Programming language:Python]]
[[Category:File management tools]]
[[Category:Operating systems]]</text>
    </revision>
    <revision>
      <id>16591</id>
      <timestamp>2009-12-04T08:37:31Z</timestamp>
      <contributor>
        <username>Spoon!</username>
        <id>1593</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">==theory==

A filesystem is basically a container data structure; in order to read a filesystem (or mutate one efficiently) we would need to be able to handle all valid states, but in order to initialize one we are free to choose the simplest valid injection.

In this case, we attempt to build rudimentary DOS [http://en.wikipedia.org/wiki/File_Allocation_Table FAT12] floppy images; as this filesystem format is over three decades old, a direct route will be less than a screenful of lines.

==practice==

We use the following straightforward code to write the filesystem image:
&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;writing image&gt;&gt;=
def mkimg(filename,blobs):
    f = open(filename, &quot;w&quot;)
    for off, data in blobs:
        f.seek(512*off)
        f.write(''.join(data))
    f.close()
&lt;/codeblock&gt;

Therefore, we describe our desired filesystem in terms of block offsets and the data which will be concatenated at that location.

The filesystem consists of the following areas:
* the Master Boot Record
* a File Allocation Table
* directory entries for each file
* and, of course, the data comprising each file's contents.

There are only a few details to watch out for:
* the FAT occurs twice, to provide a redundant spare
* we also arrange to write a zero block in the final sector, forcing the image to the desired size.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;image description&gt;&gt;=
[( 0,[open(param('-b',&quot;mbr.raw&quot;)).read()]),
 ( 1,fat),
 (10,fat),
 (19,[dirent(*e) for e in zip(files,offs,lens)])] +
[(31+o,[c]) for o,c in zip(offs,contents)] +
[(int(param('-s',&quot;2880&quot;))-1,[pack('512x')])]&lt;/codeblock&gt;

===directory entries===

Creating the directory entries is messy, but straightforward, especially because we ignore all metadata except for the file name, offset of its first block, and the file length.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;ancillaries&gt;&gt;=
dosfn	=lambda f: &quot;%-8.8s%-3.3s&quot; % tuple((f.upper()+'.').split('.'))[:2]
dirent  =lambda f,o,l: pack('&lt;11s15xHI',dosfn(basename(f)),o,l)
&lt;/codeblock&gt;

===file data blocks===

Deciding where to place the file contents is also easy.  We don't have to deal with an arbitrary file system state, but can instead choose an easy state: the files are laid out one after the other contiguously on disk.

Because files are block-aligned, we round up the file sizes to the number of '''blocks''' taken by the file, then '''accum'''ulate the number of blocks taken up by the previous files to determine each file's starting offset.

Due to special interpretation of certain offset values in the FAT, we start the data area at block offset 2 instead of 0.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;calculate offsets&gt;&gt;=
offs    = accum((blocks(l,512) for l in lens),2)
&lt;&lt;ancillaries&gt;&gt;=
blocks	=lambda n,b: n/b + (n%b&gt;0)
accum   =lambda vs,v0: reduce(lambda l,r: l + [r+l[-1]],vs,[v0])
&lt;/codeblock&gt;

===the File Allocation Table===

Finally, encoding the FAT &amp;mdash; for the contiguous case &amp;mdash; is trivial.  The FAT is basically a disk-based linked list; the successor of each block within a file is the next block, so '''range(1,&amp;omega;)''' provides almost what we want.  The only problem would be that the final block of each file would then point to the start offset of the next one.  By changing each occurrence of a start offset to the EOF flag ('''0xfff''') we correctly mark the end of each file and preserve the property that the start of each file shouldn't have a predecessor.

The sole difficulty here is that FAT12 is a 12-bit encoding, meaning that each entry is 3 nybbles long and hence not byte-aligned.  We do the obvious thing, first expanding each FAT entry into its 3 component '''nybbles''' then using '''n2bytes''' to reduce each pair of nybbles to a byte value.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;encode FAT&gt;&gt;=
fat     = n2bytes(nybbles((b in offs) and 0xfff or b
				for b in range(1,offs[-1]+1)))
&lt;&lt;ancillaries&gt;&gt;=
nybbles =lambda vs: sum(((v&amp;0xf,(v&gt;&gt;4)&amp;0xf,(v&gt;&gt;8)&amp;0xf) for v in vs),())
n2bytes =lambda ns: [pack('B',o*0x10+e) for e,o in zip(ns[0::2],ns[1::2])]
&lt;/codeblock&gt;

[[Image:Fat12.png]]

==wrapping up==

Finally, we get the file contents and lengths in the obvious way...

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;get file data&gt;&gt;=
contents= [file(f).read() for f in files]
lens    = [len(c) for c in contents]
&lt;/codeblock&gt;

... and provide a simple command-line wrapper.

&lt;codeblock language=&quot;python&quot;&gt;
&lt;&lt;mkfat12.py&gt;&gt;=
from struct import pack
from os.path import basename

&lt;&lt;ancillaries&gt;&gt;
&lt;&lt;writing image&gt;&gt;
def mkfat12(opts,files):
    if '-h' in opts:
        print &quot;Usage: [-b MBR] [-o output] [-s sector count] files...&quot;
        return

    param   = opts.get
    &lt;&lt;get file data&gt;&gt;
    &lt;&lt;calculate offsets&gt;&gt;
    &lt;&lt;encode FAT&gt;&gt;
    mkimg(param('-o',&quot;a.raw&quot;),
          &lt;&lt;image description&gt;&gt;)

if __name__ == '__main__':
    import sys, getopt

    os,files = getopt.getopt(sys.argv[1:],&quot;b:o:s:h&quot;)
    mkfat12(dict(os),files)
&lt;/codeblock&gt;

===testing===

You should provide '''mbr.raw''' or use the '''-b''' option to specify a 512-byte Master Boot Record.  This can be copied from an existing floppy with something along the lines of:
&lt;pre&gt;
dd if=/dev/fd0 of=mbr.raw bs=512 count=1
&lt;/pre&gt;

The resulting output file (defaults to ''a.raw'' as a 1.44 MB floppy image) can be set as a virtual device for a PC emulator such as [http://www.kju-app.org/ Q] or Bochs, written to a physical floppy disk with '''dd(1)''', or even placed on a CD-ROM (depending upon burner software) as a bootstrap image.

[[Category:Programming language:Python]]
[[Category:File management tools]]
[[Category:Operating systems]]</text>
    </revision>
  </page>
  <page>
    <title>Factorial (AWK)</title>
    <id>2841</id>
    <revision>
      <id>8222</id>
      <timestamp>2006-11-28T19:57:46Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>initial codedump</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&quot;&lt;&lt;catamorphism&gt;&gt;&quot;;&lt;&lt;anamorphism&gt;&gt;close(c)}
&lt;/codeblock&gt;

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this 'deforestation', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an 'online algorithm', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by replacing ''EOF'' with ''1'', and replacing each ''linefeed'' with ''*''.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
awk 'BEGIN{n=1}{n*=$1}END{print n}'
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8223</id>
      <timestamp>2006-11-28T19:59:21Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>fix string?</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;close(c)}
&lt;/codeblock&gt;

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this 'deforestation', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an 'online algorithm', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by replacing ''EOF'' with ''1'', and replacing each ''linefeed'' with ''*''.

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8224</id>
      <timestamp>2006-11-28T20:04:16Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* the catamorphism */</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;close(c)}
&lt;/codeblock&gt;

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this 'deforestation', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an 'online algorithm', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8225</id>
      <timestamp>2006-11-28T20:10:30Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* the anamorphism */</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;close(c)}
&lt;/codeblock&gt;

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this 'deforestation', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an 'online algorithm', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8226</id>
      <timestamp>2006-11-28T20:11:07Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* Factorial as a hylomorphism */</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;}
&lt;/codeblock&gt;

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this 'deforestation', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an 'online algorithm', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8227</id>
      <timestamp>2006-11-28T20:15:39Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* Factorial as a hylomorphism */</comment>
      <text xml:space="preserve">{{develop}}

==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (think analyze, or anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (think concatenate, or catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;}
&lt;/codeblock&gt;

''Question:  Are there programs that can't be expressed as hylomorphisms?''

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this ''deforestation'', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an ''online algorithm'', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8228</id>
      <timestamp>2006-11-28T20:19:12Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (cf. analyze, anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (cf. concatenate, catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;}
&lt;/codeblock&gt;

''Question:  Are there programs that can't be expressed as hylomorphisms?''

===the anamorphism===

Given a natural number ''N'' as input, we produce the set of naturals ''1..N''
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this ''deforestation'', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an ''online algorithm'', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8229</id>
      <timestamp>2006-11-28T20:26:18Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <comment>/* the anamorphism */</comment>
      <text xml:space="preserve">==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (cf. analyze, anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (cf. concatenate, catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;}
&lt;/codeblock&gt;

''Question:  Are there programs that can't be expressed as hylomorphisms?''

===the anamorphism===

Given a natural number ''N'' as input, we form the suffix list of its Peano representation.
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this ''deforestation'', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an ''online algorithm'', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, set of naturals.  The factorial is formed simply by:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
    <revision>
      <id>8230</id>
      <timestamp>2006-11-28T20:28:44Z</timestamp>
      <contributor>
        <username>Dave</username>
        <id>97</id>
      </contributor>
      <minor/>
      <comment>/* the catamorphism */</comment>
      <text xml:space="preserve">==Factorial as a hylomorphism==  

A ''hylomorphism'' is the functional programmer's way to say that he is doing some data processing with an intermediate data structure.  His theory may involve mumbling something about Functors and Algebraic Data Types, but his practice will follow the well-worn steps of early 1970's COBOL coders confronted with a ''structure clash'' (as advocated by [http://en.wikipedia.org/wiki/Jackson_Structured_Programming Jackson Structured Programming]).

The hylomorphism has two components: an ''anamorphism'' (cf. analyze, anabolic), which divides a complex structure into simpler parts (and has as its hardware parallel the ''demux''), and a ''catamorphism'' (cf. concatenate, catabolic), which builds up a complex structure out of simpler parts (and has as its hardware parallel the ''mux'').

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;fact.awk&gt;&gt;=
#!/bin/awk -f
{c=&lt;&lt;catamorphism&gt;&gt;;&lt;&lt;anamorphism&gt;&gt;}
&lt;/codeblock&gt;

''Question:  Are there programs that can't be expressed as hylomorphisms?''

===the anamorphism===

Given a natural number ''N'' as input, we form the suffix list of its Peano representation.
:&lt;math&gt;
\begin{matrix}
S(n) &amp; \mapsto &amp; n+1, anamorphism(n) \\
0        &amp; \mapsto &amp;  EOF
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;anamorphism&gt;&gt;=
while($1){print $1--|c}close(c)
&lt;/codeblock&gt;

Note that instead of generating an intermediate data structure, we use a pipe to connect the two processes.  In the late 1990's, functional programmers called this ''deforestation'', and used it to reduce pressure on their garbage collectors.  In the late 1960's, dp programmers called this an ''online algorithm'', and used it to avoid waiting several minutes while their tapes rewound.

===the catamorphism===

We take as input an EOF-terminated, linefeed-separated, stream of naturals.  The factorial is formed simply by evaluating this input under the following map:
:&lt;math&gt;
\begin{matrix}
linefeed &amp; \mapsto &amp; * \\
EOF        &amp; \mapsto &amp; 1  
\end{matrix}
&lt;/math&gt;

&lt;codeblock language=&quot;awk&quot;&gt;
&lt;&lt;catamorphism&gt;&gt;=
&quot;awk 'BEGIN{n=1}{n*=$1}END{print n}'&quot;
&lt;/codeblock&gt;

[[Category:Number theory|AWK]]
[[Category:Programming language:AWK]]</text>
    </revision>
  </page>
  <page>
    <title>Factorial (Pascal)</title>
    <id>2978</id>
    <revision>
      <id>8820</id>
      <timestamp>2007-02-03T19:44:22Z</timestamp>
      <contributor>
        <username>Aledubr</username>
        <id>135</id>
      </contributor>
      <text xml:space="preserve">In mathematics, the [http://en.wikipedia.org/wiki/Factorial factorial] of a positive integer n is the product of all positive integers less than or equal to n. This is written as n! and pronounced &quot;n factorial&quot;, or colloquially &quot;n shriek&quot;, &quot;n bang&quot; or &quot;n crit&quot;. The notation n! was introduced by Christian Kramp in 1808.

==Definition==

The factorial function is formally defined by

:&lt;math&gt; n!=\prod_{k=1}^n k \qquad \mbox{for all } n \in \mathbb{N} \ge 0. \!&lt;/math&gt;

For example,

:&lt;math&gt;5 ! = 1\cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120 \ &lt;/math&gt;

The above definition incorporates the convention that

:&lt;math&gt;0! = 1 \ &lt;/math&gt;

as an instance of the convention that the product of no numbers at all is 1.  This fact for factorials is useful, because

* the recursive relation &lt;math&gt;(n + 1)! = n! \times (n + 1)&lt;/math&gt; works for &lt;math&gt;n = 0&lt;/math&gt;;
* this definition makes many identities in combinatorics valid for zero sizes.

==Computation==

The numeric value of '''n!''' can be calculated by repeated multiplication if '''n''' is not too large. That is basically what pocket calculators do. The largest factorial that most calculators can handle is &lt;math&gt;69!&lt;/math&gt;, because &lt;math&gt;70! &gt; 10^{100}&lt;/math&gt;. In practice, most software applications use only small factorials which can be computed by direct multiplication or table lookup. Larger values are often approximated in terms of floating-point estimates of the [http://en.wikipedia.org/wiki/Gamma_function Gamma function], usually with [http://en.wikipedia.org/wiki/Stirling%27s_formula Stirling's formula].

Here we'll create a very simple Pascal program to compute smaller factorials &lt;math&gt;(0\le n\le 170)&lt;/math&gt;. It uses a for-to-do loop.

&lt;codeblock language=pascal&gt;
&lt;&lt;Factorial.pas&gt;&gt;=

program Factorial;
    {The program computes 0! through 170!}

var
  i, x : integer; {''i'' here stands for iteration}
  fact : real;    {Usually factorials are so large that we
                   can't use integer here}

begin
  writeln ('Enter the value of the factorial');
  readln (x);
  fact:=1; {As we can't multiply by 0, our first number should be 1}

for i:=1 to x do  {Here is our loop}
                 
   fact :=fact*i;
   writeln(x,'! is ',fact);

readln; {The semicolon is not obligatory here}

end.

&lt;/codeblock&gt;


[[Category:Programming language:AWK]]
[[Category:Environment:Portable]]
[[Category:Number theory|AWK]]</text>
    </revision>
    <revision>
      <id>8821</id>
      <timestamp>2007-02-03T19:46:55Z</timestamp>
      <contributor>
        <username>Aledubr</username>
        <id>135</id>
      </contributor>
      <text xml:space="preserve">In mathematics, the [http://en.wikipedia.org/wiki/Factorial factorial] of a positive integer n is the product of all positive integers less than or equal to n. This is written as n! and pronounced &quot;n factorial&quot;, or colloquially &quot;n shriek&quot;, &quot;n bang&quot; or &quot;n crit&quot;. The notation n! was introduced by Christian Kramp in 1808.

==Definition==

The factorial function is formally defined by

:&lt;math&gt; n!=\prod_{k=1}^n k \qquad \mbox{for all } n \in \mathbb{N} \ge 0. \!&lt;/math&gt;

For example,

:&lt;math&gt;5 ! = 1\cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120 \ &lt;/math&gt;

The above definition incorporates the convention that

:&lt;math&gt;0! = 1 \ &lt;/math&gt;

as an instance of the convention that the product of no numbers at all is 1.  This fact for factorials is useful, because

* the recursive relation &lt;math&gt;(n + 1)! = n! \times (n + 1)&lt;/math&gt; works for &lt;math&gt;n = 0&lt;/math&gt;;
* this definition makes many identities in combinatorics valid for zero sizes.

==Computation==

The numeric value of '''n!''' can be calculated by repeated multiplication if '''n''' is not too large. That is basically what pocket calculators do. The largest factorial that most calculators can handle is &lt;math&gt;69!&lt;/math&gt;, because &lt;math&gt;70! &gt; 10^{100}&lt;/math&gt;. In practice, most software applications use only small factorials which can be computed by direct multiplication or table lookup. Larger values are often approximated in terms of floating-point estimates of the [http://en.wikipedia.org/wiki/Gamma_function Gamma function], usually with [http://en.wikipedia.org/wiki/Stirling%27s_formula Stirling's formula].

Here we'll create a very simple Pascal program to compute smaller factorials &lt;math&gt;(0\le n\le 170)&lt;/math&gt;. It uses a for-to-do loop.

&lt;codeblock language=pascal&gt;
&lt;&lt;Factorial.pas&gt;&gt;=

program Factorial;
    {The program computes 0! through 170!}

var
  i, x : integer; {''i'' here stands for iteration}
  fact : real;    {Usually factorials are so large that we
                   can't use integer here}

begin
  writeln ('Enter the value of the factorial');
  readln (x);
  fact:=1; {As we can't multiply by 0, our first number should be 1}

for i:=1 to x do  {Here is our loop}
                 
   fact :=fact*i;
   writeln(x,'! is ',fact);

readln; {The semicolon is not obligatory here}

end.

&lt;/codeblock&gt;


[[Category:Programming language:Pascal]]
[[Category:Environment:Portable]]
[[Category:Number theory|Pascal]]</text>
    </revision>
  </page>
  <page>
    <title>Factorials with prime factorization (C)</title>
    <id>2336</id>
    <revision>
      <id>6206</id>
      <timestamp>2006-06-13T03:00:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Do sieve, multiplicity, import integer - still have to do exponentiation and multiplying out</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.c&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, integer p) {
    if (p &gt; n) return 0;
    if (p &gt; n/2): return 1
    int q = n, m = 0;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    static unsigned char* sieve =
        (unsigned int*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; i &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

TODO: finish

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6207</id>
      <timestamp>2006-06-13T03:00:23Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>{{develop}}</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.c&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, integer p) {
    if (p &gt; n) return 0;
    if (p &gt; n/2): return 1
    int q = n, m = 0;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    static unsigned char* sieve =
        (unsigned int*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; i &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

TODO: finish

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6213</id>
      <timestamp>2006-06-13T07:20:18Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Finish code - need to compile/test now</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, integer p) {
    if (p &gt; n) return 0;
    if (p &gt; n/2): return 1
    int q = n, m = 0;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    static unsigned char* sieve =
        (unsigned int*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; i &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int i;
    integer temp   = create_integer(base.num_components*power + 1);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
    return result;
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product:

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    integer result;
    int p;
    integer result   = create_integer(n*n + 1);
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6214</id>
      <timestamp>2006-06-13T07:26:40Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix compiler errors</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; i &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp   = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product:

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result   = create_integer(n*n + 1);
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6215</id>
      <timestamp>2006-06-13T07:29:44Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>i-&gt;j (bug fix)</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp   = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product:

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result   = create_integer(n*n + 1);
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6216</id>
      <timestamp>2006-06-13T07:56:09Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Better size for result</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp   = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;n\lceil{\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    double dn = (double)n;
    integer result =
      create_integer((n*((int)ceil(log((double)n)/log(2))) + 1)/COMPONENT_BITS);    
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6217</id>
      <timestamp>2006-06-13T07:56:55Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Headers</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp   = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;n\lceil{\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((n*((int)ceil(log((double)n)/log(2))) + 1)/COMPONENT_BITS);    
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6218</id>
      <timestamp>2006-06-13T08:03:49Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fix computation to be proper upper bound</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp   = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6219</id>
      <timestamp>2006-06-13T08:12:10Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Make temporary multiplication result holders double size to prevent overflow (I should really make these things dynamic...)</comment>
      <text xml:space="preserve">{{develop}}

{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6220</id>
      <timestamp>2006-06-13T08:17:15Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>It works! -develop, Sample output</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(bit=sizeof(power)*CHAR_BIT - 1; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 1.5 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux. We could achieve greater benefit by using a better multiplication algorithm.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6221</id>
      <timestamp>2006-06-13T09:07:53Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>An optimization, comments on time</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6114#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.2 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux. The obvious algorithm takes only 0.079 seconds - due to the overhead associated with squaring arbitrary-precision numbers, it takes very large arguments for this approach to gain the advantage. We could achieve greater benefit by using a better multiplication algorithm.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6223</id>
      <timestamp>2006-06-13T09:44:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Upgrade Arbitrary-precision_integer_arithmetic_(C) files for multiplication performance improvement</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.2 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux. The obvious algorithm takes only 0.079 seconds - due to the overhead associated with squaring arbitrary-precision numbers, it takes very large arguments for this approach to gain the advantage. We could achieve greater benefit by using a better multiplication algorithm.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6224</id>
      <timestamp>2006-06-13T10:23:36Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Parallel exponentiation</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.02 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux (not including generating the output string). The obvious algorithm takes about the same amount of time. For factorials in the range of thousands, the naive approach tends to do better, because this algorithm, although superior asymptotically, performs too many multiplications of two large numbers, which are expensive. We could achieve greater benefit by using a better multiplication algorithm, but first there is a way of rearranging our operations to drastically cut the number of multiplications of two large numbers we need to perform.

== Parallel exponentiation ==

The concept of this optimization is to reduce the number of calls to the expensive &lt;code&gt;multiply_integer&lt;/code&gt;. We perform these calls in two places in the simple algorithm above: whenever squaring a number during exponentiation, and whenever multiplying a prime power into our total product. Imagine we have a matrix where the columns each correspond to the bits of a single exponent, most significant at the top. For example, this is the matrix for 20!, with each column labelled with its corresponding prime:

&lt;math&gt;
\left[\begin{matrix}
\mathbf{2} &amp; \mathbf{3} &amp; \mathbf{5} &amp; \mathbf{7} &amp; \mathbf{11} &amp; \mathbf{13} &amp; \mathbf{17} &amp; \mathbf{23} \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp; 1 &amp; 1
\end{matrix}\right]
&lt;/math&gt;

In the above approach, we compute the contribution of each column separately and multiply them together. Alternatively, we can go by ''row'':

# Compute the entire prime factorization beforehand. This is fast.
# Starting with the top row, multiply in all of the factors occurring on the current row.
# Square the running product to get to the following row. Repeat until all rows have been visited.

This combines the two stages of exponentiation and multiplication of components, and we need only perform large multiplications when squaring. The code looks like this:

&lt;codeblock language=c&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int num_primes;
    int* p_list = malloc(sizeof(int)*n);
    int* exp_list = malloc(sizeof(int)*n);
    int p, i, bit;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    num_primes = 0;
    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        p_list[num_primes] = p;
        exp_list[num_primes] = multiplicity(n,p);
        num_primes++;
    }

    for(bit=sizeof(exp_list[0])*CHAR_BIT - 1; bit&gt;=0; bit--) {
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                break;
            }
        }
        if (i &lt; num_primes) {
            break;
        }
    }

    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                multiply_small_integer(result, p_list[i], result);
            }
        }
    }

    free_integer(temp);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Here's a test main for it:

&lt;codeblock language=c&gt;
&lt;&lt;pefactorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

The times for this method are considerably better. It outperforms the naive method for factorials as low as 110!, and outperforms it by about 45% for larger factorials, as this chart shows:

{|border=&quot;1&quot;
|'''n'''                || 10     || 100   || 500  || 1,000 || 5,000 || 10,000 || 50,000
|-
|'''Naive''' (ms)       || 0.0007 || 0.017 || 0.50 || 2.22  || 67.8  || 295 || 8960
|- 
|'''pefactorial''' (ms) || 0.0019 || 0.021 || 0.29 || 1.12  || 33.9  || 153 || 4960
|}

Times were taken on a 2.8 GhZ Pentium 4 CPU under Linux, compiled by gcc with &quot;-O3&quot;. Time to generate output string not included. For small arguments the main factorial call was placed in a long loop to facilitate accurate measurement.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6225</id>
      <timestamp>2006-06-13T10:24:07Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Parallel exponentiation */</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.02 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux (not including generating the output string). The obvious algorithm takes about the same amount of time. For factorials in the range of thousands, the naive approach tends to do better, because this algorithm, although superior asymptotically, performs too many multiplications of two large numbers, which are expensive. We could achieve greater benefit by using a better multiplication algorithm, but first there is a way of rearranging our operations to drastically cut the number of multiplications of two large numbers we need to perform.

== Parallel exponentiation ==

The concept of this optimization is to reduce the number of calls to the expensive &lt;code&gt;multiply_integer&lt;/code&gt;. We perform these calls in two places in the simple algorithm above: whenever squaring a number during exponentiation, and whenever multiplying a prime power into our total product. Imagine we have a matrix where the columns each correspond to the bits of a single exponent, most significant at the top. For example, this is the matrix for 20!, with each column labelled with its corresponding prime:

&lt;math&gt;
\left[\begin{matrix}
\mathbf{2} &amp; \mathbf{3} &amp; \mathbf{5} &amp; \mathbf{7} &amp; \mathbf{11} &amp; \mathbf{13} &amp; \mathbf{17} &amp; \mathbf{23} \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp; 1 &amp; 1
\end{matrix}\right]
&lt;/math&gt;

In the above approach, we compute the contribution of each column separately and multiply them together. Alternatively, we can go by ''row'':

# Compute the entire prime factorization beforehand. This is fast.
# Starting with the top row, multiply in all of the factors occurring on the current row. These are all multiplications by small numbers.
# Square the running product to get to the following row. Repeat until all rows have been visited.

This combines the two stages of exponentiation and multiplication of components, and we need only perform large multiplications when squaring. The code looks like this:

&lt;codeblock language=c&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int num_primes;
    int* p_list = malloc(sizeof(int)*n);
    int* exp_list = malloc(sizeof(int)*n);
    int p, i, bit;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    num_primes = 0;
    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        p_list[num_primes] = p;
        exp_list[num_primes] = multiplicity(n,p);
        num_primes++;
    }

    for(bit=sizeof(exp_list[0])*CHAR_BIT - 1; bit&gt;=0; bit--) {
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                break;
            }
        }
        if (i &lt; num_primes) {
            break;
        }
    }

    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                multiply_small_integer(result, p_list[i], result);
            }
        }
    }

    free_integer(temp);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Here's a test main for it:

&lt;codeblock language=c&gt;
&lt;&lt;pefactorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

The times for this method are considerably better. It outperforms the naive method for factorials as low as 110!, and outperforms it by about 45% for larger factorials, as this chart shows:

{|border=&quot;1&quot;
|'''n'''                || 10     || 100   || 500  || 1,000 || 5,000 || 10,000 || 50,000
|-
|'''Naive''' (ms)       || 0.0007 || 0.017 || 0.50 || 2.22  || 67.8  || 295 || 8960
|- 
|'''pefactorial''' (ms) || 0.0019 || 0.021 || 0.29 || 1.12  || 33.9  || 153 || 4960
|}

Times were taken on a 2.8 GhZ Pentium 4 CPU under Linux, compiled by gcc with &quot;-O3&quot;. Time to generate output string not included. For small arguments the main factorial call was placed in a long loop to facilitate accurate measurement.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6226</id>
      <timestamp>2006-06-13T10:26:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Parallel exponentiation */</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.02 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux (not including generating the output string). The obvious algorithm takes about the same amount of time. For factorials in the range of thousands, the naive approach tends to do better, because this algorithm, although superior asymptotically, performs too many multiplications of two large numbers, which are expensive. We could achieve greater benefit by using a better multiplication algorithm, but first there is a way of rearranging our operations to drastically cut the number of multiplications of two large numbers we need to perform.

== Parallel exponentiation ==

The concept of this optimization is to reduce the number of calls to the expensive &lt;code&gt;multiply_integer&lt;/code&gt;. We perform these calls in two places in the simple algorithm above: whenever squaring a number during exponentiation, and whenever multiplying a prime power into our total product. Imagine we have a matrix where the columns each correspond to the bits of a single exponent, most significant at the top. For example, this is the matrix for 20!, with each column labelled with its corresponding prime:

&lt;math&gt;
\left[\begin{matrix}
\mathbf{2} &amp; \mathbf{3} &amp; \mathbf{5} &amp; \mathbf{7} &amp; \mathbf{11} &amp; \mathbf{13} &amp; \mathbf{17} &amp; \mathbf{23} \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp; 1 &amp; 1
\end{matrix}\right]
&lt;/math&gt;

In the above approach, we compute the contribution of each column separately and multiply them together. Alternatively, we can go by ''row'':

# Compute the entire prime factorization beforehand. This is fast.
# Starting with the top row, multiply in all of the factors occurring on the current row. These are all multiplications by small numbers.
# Square the running product to get to the following row. Repeat until all rows have been visited.

This combines the two stages of exponentiation and multiplication of components, and we need only perform large multiplications when squaring. The code looks like this:

&lt;codeblock language=c&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int num_primes;
    int* p_list = malloc(sizeof(int)*n);
    int* exp_list = malloc(sizeof(int)*n);
    int p, i, bit;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    num_primes = 0;
    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        p_list[num_primes] = p;
        exp_list[num_primes] = multiplicity(n,p);
        num_primes++;
    }

    for(bit=sizeof(exp_list[0])*CHAR_BIT - 1; bit&gt;=0; bit--) {
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                break;
            }
        }
        if (i &lt; num_primes) {
            break;
        }
    }

    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                multiply_small_integer(result, p_list[i], result);
            }
        }
    }

    free_integer(temp);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Here's a test main for it:

&lt;codeblock language=c&gt;
&lt;&lt;pefactorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

The times for this method are considerably better. It outperforms the naive method for factorials as low as 110!, and outperforms it by about 45% for larger factorials, as this chart shows:

{|border=&quot;1&quot;
|'''n'''                || 10     || 100   || 500  || 1,000 || 5,000 || 10,000 || 50,000
|-
|'''Naive''' (ms)       || 0.0007 || 0.017 || 0.50 || 2.22  || 67.8  || 295 || 8960
|- 
|'''pefactorial''' (ms) || 0.0019 || 0.021 || 0.29 || 1.12  || 33.9  || 153 || 4960
|}

Times were taken on a 2.8 GhZ Pentium 4 CPU under Linux, compiled by gcc with &quot;-O3&quot;. Time to generate output string not included. For small arguments the main factorial call was placed in a long loop to facilitate accurate measurement. Times could be improved further by using a better multiplication algorithm, or one specialized to squaring.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
    <revision>
      <id>6227</id>
      <timestamp>2006-06-13T10:28:00Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>/* Parallel exponentiation */ Add factorization of 20! for clarity, fix prime</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

We begin by computing the sum above to find the exponent (power) of a prime number in the factorization of ''n''!. The numbers are all small here, so ordinary machine words will work fine.

&lt;codeblock language=python&gt;
&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;=
/* Return the power of the prime number p in the
   factorization of n! */
int multiplicity(int n, int p) {
    int q = n, m = 0;
    if (p &gt; n) return 0;
    if (p &gt; n/2) return 1;
    while (q &gt;= p) {
        q /= p;
        m += q;
    }
    return m;
}
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]. Emphasizing efficiency and simplicity over space, we use a byte array instead of a bit array (keep in mind that the end result will be much larger than this byte array).

&lt;codeblock language=python&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;=
unsigned char* prime_table(int n) {
    int i, j;
    unsigned char* sieve = (unsigned char*)calloc(n+1, sizeof(unsigned char));
    sieve[0] = sieve[1] = 1;
    for (i=2; i*i &lt;= n; i++)
        if (sieve[i] == 0)
            for (j=i*i; j &lt;= n; j+=i)
                sieve[j] = 1;
    return sieve;
}
&lt;/codeblock&gt;

Now it's time to take the prime factorization of ''n''! and actually compute the value of ''n''!. In C, standard 32-bit machine words can only hold factorials up to 12!, and 64-bit words only up to 20!, far below the range of numbers for which this algorithm is beneficial. For this reason, we will produce arbitrary-precision integers instead. Since C doesn't supply arbitrary-precision integers, we supply our own basic implementation from [[Arbitrary-precision integer arithmetic (C)]]:

&lt;codeblock language=c&gt;
&lt;&lt;integer.h&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.h&gt;&gt;

&lt;&lt;integer.c&gt;&gt;=
&lt;&lt;Arbitrary-precision_integer_arithmetic_(C)#6222#integer.c&gt;&gt;
&lt;/codeblock&gt;

The straightforward approach would be to calculate &lt;math&gt;p^a&lt;/math&gt; for each prime ''p'' by multiplying ''p'' by itself ''a'' times. But if we do this we derive no benefit over the obvious method of computing factorials. Instead, we will use [[:Category:Exponentiation by squaring|exponentiation by squaring]], which uses only at most &lt;math&gt;2\log a&lt;/math&gt; multiplies:

&lt;codeblock language=c&gt;
&lt;&lt;exponentiation function&gt;&gt;=
void exponent(unsigned int base, unsigned int power, integer result) {
    int bit;
    integer temp = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    bit=sizeof(power)*CHAR_BIT - 1;
    while ((power &amp; (1 &lt;&lt; bit)) == 0) bit--;
    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        if ((power &amp; (1 &lt;&lt; bit)) != 0) {
            multiply_small_integer(result, base, result);
        }
    }

    free_integer(temp);
}
&lt;/codeblock&gt;

To avoid performing extra multiplications for small powers, we skip any leading zero bits.

We're now prepared to write an efficient factorial function. It retrieves the list of primes, then for each one computes that prime raised to the appropriate exponent, multiplying the result into a running product. To determine the space needed to hold the factorial up front, we simply use &lt;math&gt;\lceil{n\log_2 n}+1\rceil&lt;/math&gt; bits, which [http://mathworld.wolfram.com/StirlingsApproximation.html Stirling's approximation] tells us is an upper bound for &lt;math&gt;\log_2 n!&lt;/math&gt;.

&lt;codeblock language=c&gt;
&lt;&lt;factorial function&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int p;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer p_raised = create_integer(result.num_components);
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        exponent(p, multiplicity(n,p), p_raised);
        multiply_integer(result, p_raised, temp);
        copy_integer(temp, result);
    }

    free_integer(temp);
    free_integer(p_raised);
    free(primes);
    return result;
}

&lt;&lt;header files&gt;&gt;=
#include &lt;math.h&gt;  /* for log() */
&lt;/codeblock&gt;

Finally, we write a simple command-line driver that takes a number and outputs its factorial:

&lt;codeblock language=c&gt;
&lt;&lt;factorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;exponentiation function&gt;&gt;
&lt;&lt;factorial function&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

Here's some sample output (all values are independently verified as correct):

&lt;pre&gt;
$ ./factorial 10
3628800
$ ./factorial 50
30414093201713378043612608166064768844377641568960512000000000000
$ ./factorial 500
12201368259911100687012387854230469262535743428031928421924135883\
85845373153881997605496447502203281863013616477148203584163378722\
07817720048078520515932928547790757193933060377296085908627042917\
45478824249127263443056701732707694610628023104526442188787894657\
54777149863494367781037644274033827365397471386477878495438489595\
53753799042324106127132698432774571554630997720278101456108118837\
37095310163563244329870295638966289116589747695720879269288712817\
80070265174507768410719624390394322536422605234945850129918571501\
24870696156814162535905669342381300885624924689156412677565448188\
65065938479517753608940057452389403357984763639449053130623237490\
66445048824665075946735862074637925184200459369692981022263971952\
59719094521782333175693458150855233282076282002340262690789834245\
17120062077146409794561161276291459512372299133401695523638509428\
85592018727433795173014586357570828355780158735432768888680120399\
88238470215146760544540766353598417443048012893831389688163948746\
96588175045069263653381750554781286400000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000000\
000000000000000000000000000000
&lt;/pre&gt;

The last value took about 0.02 seconds to generate on a Pentium 2.8 GhZ machine, compiled by gcc with the -O3 flag under Linux (not including generating the output string). The obvious algorithm takes about the same amount of time. For factorials in the range of thousands, the naive approach tends to do better, because this algorithm, although superior asymptotically, performs too many multiplications of two large numbers, which are expensive. We could achieve greater benefit by using a better multiplication algorithm, but first there is a way of rearranging our operations to drastically cut the number of multiplications of two large numbers we need to perform.

== Parallel exponentiation ==

The concept of this optimization is to reduce the number of calls to the expensive &lt;code&gt;multiply_integer&lt;/code&gt;. We perform these calls in two places in the simple algorithm above: whenever squaring a number during exponentiation, and whenever multiplying a prime power into our total product. Imagine we have a matrix where the columns each correspond to the bits of a single exponent, most significant at the top. For example, this is the matrix for 20!, with each column labelled with its corresponding prime:

20! = 2&lt;sup&gt;18&lt;/sup&gt; &amp;middot; 3&lt;sup&gt;8&lt;/sup&gt; &amp;middot; 5&lt;sup&gt;4&lt;/sup&gt; &amp;middot; 7&lt;sup&gt;2&lt;/sup&gt; &amp;middot; 11 &amp;middot; 13 &amp;middot; 17 &amp;middot; 19

&lt;math&gt;
\left[\begin{matrix}
\mathbf{2} &amp; \mathbf{3} &amp; \mathbf{5} &amp; \mathbf{7} &amp; \mathbf{11} &amp; \mathbf{13} &amp; \mathbf{17} &amp; \mathbf{19} \\
1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 1 &amp; 1 &amp; 1
\end{matrix}\right]
&lt;/math&gt;

In the above approach, we compute the contribution of each column separately and multiply them together. Alternatively, we can go by ''row'':

# Compute the entire prime factorization beforehand. This is fast.
# Starting with the top row, multiply in all of the factors occurring on the current row. These are all multiplications by small numbers.
# Square the running product to get to the following row. Repeat until all rows have been visited.

This combines the two stages of exponentiation and multiplication of components, and we need only perform large multiplications when squaring. The code looks like this:

&lt;codeblock language=c&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;=
integer factorial(int n) {
    unsigned char* primes = prime_table(n);
    int num_primes;
    int* p_list = malloc(sizeof(int)*n);
    int* exp_list = malloc(sizeof(int)*n);
    int p, i, bit;
    integer result =
      create_integer((int)ceil((n*log((double)n)/log(2) + 1)/COMPONENT_BITS));
    integer temp     = create_integer(result.num_components*2);
    set_zero_integer(result);
    result.c[0] = 1;

    num_primes = 0;
    for(p = 2; p &lt;= n; p++) {
        if (primes[p] == 1) continue;
        p_list[num_primes] = p;
        exp_list[num_primes] = multiplicity(n,p);
        num_primes++;
    }

    for(bit=sizeof(exp_list[0])*CHAR_BIT - 1; bit&gt;=0; bit--) {
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                break;
            }
        }
        if (i &lt; num_primes) {
            break;
        }
    }

    for( ; bit&gt;=0; bit--) {
        multiply_integer(result, result, temp);
        copy_integer(temp, result);
        for(i=0; i&lt;num_primes; i++) {
            if ((exp_list[i] &amp; (1 &lt;&lt; bit)) != 0) {
                multiply_small_integer(result, p_list[i], result);
            }
        }
    }

    free_integer(temp);
    free(primes);
    return result;
}
&lt;/codeblock&gt;

Here's a test main for it:

&lt;codeblock language=c&gt;
&lt;&lt;pefactorial.c&gt;&gt;=
&lt;&lt;header files&gt;&gt;
#include &lt;stdlib.h&gt;
#include &lt;stdio.h&gt;
#include &quot;integer.h&quot;

&lt;&lt;compute multiplicity of a prime in factorial n&gt;&gt;
&lt;&lt;sieve of Eratosthenes&gt;&gt;
&lt;&lt;parallel exponentiation factorial&gt;&gt;

int main(int argc, char* argv[]) {
    int n = atoi(argv[1]);
    puts(integer_to_string(factorial(n)));
    return 0;
}
&lt;/codeblock&gt;

The times for this method are considerably better. It outperforms the naive method for factorials as low as 110!, and outperforms it by about 45% for larger factorials, as this chart shows:

{|border=&quot;1&quot;
|'''n'''                || 10     || 100   || 500  || 1,000 || 5,000 || 10,000 || 50,000
|-
|'''Naive''' (ms)       || 0.0007 || 0.017 || 0.50 || 2.22  || 67.8  || 295 || 8960
|- 
|'''pefactorial''' (ms) || 0.0019 || 0.021 || 0.29 || 1.12  || 33.9  || 153 || 4960
|}

Times were taken on a 2.8 GhZ Pentium 4 CPU under Linux, compiled by gcc with &quot;-O3&quot;. Time to generate output string not included. For small arguments the main factorial call was placed in a long loop to facilitate accurate measurement. Times could be improved further by using a better multiplication algorithm, or one specialized to squaring.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:C]]</text>
    </revision>
  </page>
  <page>
    <title>Factorials with prime factorization (Python)</title>
    <id>1424</id>
    <revision>
      <id>1750</id>
      <timestamp>2006-03-03T13:03:05Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight sieve of Eratosthenes:

&lt;codeblock language=python&gt;
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        if exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            if exp != 0:
                multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Peter Luschny. [http://www.luschny.de/math/factorial/FastFactorialFunctions.htm &quot;Fast Factorial Functions&quot;]</text>
    </revision>
    <revision>
      <id>1752</id>
      <timestamp>2006-03-03T13:08:17Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>categories</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight sieve of Eratosthenes:

&lt;codeblock language=python&gt;
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        if exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            if exp != 0:
                multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Peter Luschny. [http://www.luschny.de/math/factorial/FastFactorialFunctions.htm &quot;Fast Factorial Functions&quot;]

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1754</id>
      <timestamp>2006-03-03T13:15:16Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>/* References */ add another reference that was used for a specific fact (it is unrelated to this particular algorithm, though)</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight sieve of Eratosthenes:

&lt;codeblock language=python&gt;
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        if exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            if exp != 0:
                multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Peter Luschny. [http://www.luschny.de/math/factorial/FastFactorialFunctions.htm &quot;Fast Factorial Functions&quot;]
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1755</id>
      <timestamp>2006-03-03T13:17:59Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>remove something redundant</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight sieve of Eratosthenes:

&lt;codeblock language=python&gt;
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Peter Luschny. [http://www.luschny.de/math/factorial/FastFactorialFunctions.htm &quot;Fast Factorial Functions&quot;]
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1756</id>
      <timestamp>2006-03-03T13:34:26Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>links, format</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1759</id>
      <timestamp>2006-03-03T13:43:07Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <comment>hmm...</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1760</id>
      <timestamp>2006-03-03T13:50:10Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... n]&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1763</id>
      <timestamp>2006-03-03T14:00:19Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;+=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>1880</id>
      <timestamp>2006-03-03T22:06:47Z</timestamp>
      <contributor>
        <username>Fredrik</username>
        <id>6</id>
      </contributor>
      <minor/>
      <comment>let's see if concatenation works now</comment>
      <text xml:space="preserve">The ''n'':th factorial, ''n''!, can be computed straightforwardly by multiplying together the range of integers 1, 2, ... ''n'' from the bottom up. However, if ''n'' is large, this becomes inefficient. The ''k'':th subproduct has roughly ''k'' log ''k'' digits, so multiplying by ''k''+1 (assumed to fit in a single machine word) takes ''k'' log ''k'' time. This leads to a total time of O(''n''&lt;sup&gt;2&lt;/sup&gt; log ''n'') for calculating ''n''!.

Many algorithms exist for splitting a product of many factors into smaller pieces to balance the size of each subproduct. However, there is a trick to factorials: we can find the ''prime factorization'' of ''n''! quickly, much more quickly than we can compute ''n''! itself. And we can do this without stepping through the list 1, 2, ..., ''n'' and factorizing each of these numbers. The crucial observation is that ''n''! must necessarily contain each prime number up to ''n'', and that the power of the prime ''p'' in ''n''! is given by

:&lt;math&gt;\sum_{i=1}^{\infty} \, \lfloor n/p^i \rfloor&lt;/math&gt;.

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

==References==
* Peter Luschny. ''[http://www.luschny.de/math/factorial/FastFactorialFunctions.htm Fast Factorial Functions]''
* Peter Borwein. &quot;On the Complexity of Calculating Factorials&quot;. ''Journal of Algorithms'' 6, 376-380 (1985)
* Xavier Gourdon &amp; Pascal Sebah. ''[http://numbers.computation.free.fr/Constants/Algorithms/splitting.html Binary splitting method]''

[[Category:Number theory]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>3168</id>
      <timestamp>2006-03-11T07:12:52Z</timestamp>
      <contributor>
        <ip>131.107.0.84</ip>
      </contributor>
      <comment>Replace header with category page block so I can make another language version</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

The sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>3169</id>
      <timestamp>2006-03-11T07:18:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>+context</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

In [http://en.wikipedia.org/Python_programming_language Python], the sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>4353</id>
      <timestamp>2006-05-03T18:33:04Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Fix Python WP link</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

In [http://en.wikipedia.org/wiki/Python_programming_language Python], the sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can done instead is performing recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>4814</id>
      <timestamp>2006-05-17T21:51:38Z</timestamp>
      <contributor>
        <ip>62.253.64.15</ip>
      </contributor>
      <comment>grammar</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

In [http://en.wikipedia.org/wiki/Python_programming_language Python], the sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can do instead is perform recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
    <revision>
      <id>16873</id>
      <timestamp>2010-09-23T13:22:39Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">'''Someone spent a lot of time and work on this... and I just deleted it! 

Mwhahahaha!''' &lt;nowiki&gt;:D&lt;/nowiki&gt;</text>
    </revision>
    <revision>
      <id>16897</id>
      <timestamp>2010-09-23T15:48:13Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:62.253.64.15|62.253.64.15]]</comment>
      <text xml:space="preserve">{{Category:Factorials with prime factorization}}

In [http://en.wikipedia.org/wiki/Python_programming_language Python], the sum can be implemented as follows:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def multiplicity(n, p):
    &quot;&quot;&quot;Return the power of the prime number p in the
    factorization of n!&quot;&quot;&quot;
    if p &gt; n: return 0
    if p &gt; n//2: return 1
    q, m = n, 0
    while q &gt;= p:
        q //= p
        m += q
    return m
&lt;/codeblock&gt;

We now need a way to obtain the prime numbers up to ''n'', for which purpose we implement a light-weight [[:Category:Sieve of Eratosthenes|sieve of Eratosthenes]]:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def primes(n):
    &quot;&quot;&quot;Generate a list of the prime numbers [2, 3, ... m] where
    m is the largest prime &lt;= n.&quot;&quot;&quot;
    n = n + 1
    sieve = range(n)
    sieve[:2] = [0, 0]
    for i in xrange(2, int(n**0.5)+1):
        if sieve[i]:
            for j in xrange(i**2, n, i):
                sieve[j] = 0
    # Filter out the composites, which have been replaced by 0's
    return [p for p in sieve if p]
&lt;/codeblock&gt;

&lt;!-- this explanation needs improvement --&gt;
Knowing the prime factors of ''n''!, and the exponent for each factor, all that needs to be done is taking powers. This is also the most important step of the calculation: if we just multiply all the primes together without further thought, no time will be saved. What we can do instead is perform recursive ''[[:Category:Exponentiation by squaring|exponentiation by squaring]]''. For exponentiation of a single integer, this is based on the fact that squaring the number cuts the remaining exponent in half. The technique can easily be applied to a list of numbers as well:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def powproduct(ns):
    &quot;&quot;&quot;Compute the explicit value of a factored integer
    given as a list of (base, exponent) pairs.&quot;&quot;&quot;
    if not ns:
        return 1
    units = 1
    multi = []
    for base, exp in ns:
        if exp == 0:
            continue
        elif exp == 1:
            units *= base
        else:
            if exp % 2:
                units *= base
            multi.append((base, exp//2))
    return units * powproduct(multi)**2
&lt;/codeblock&gt;

Wrapping things together, we have:

&lt;codeblock language=python&gt;
&lt;&lt;prime_factorial.py&gt;&gt;=
def factorial(n):
    return powproduct((p, multiplicity(n, p)) for p in primes(n))
&lt;/codeblock&gt;

In practice, this program will perform worse than one based on direct multiplication when ''n'' is small. A practical implementation should use an empirically determined cutoff to enable prime factorization only for very large ''n'', say, larger than a few hundred.

Many optimizations are also possible. The most obvious is to compute a large table of primes in advance instead of creating a list for each call to ''factorial'', another is to handle powers of two using binary shifting.

[[Category:Factorials with prime factorization]]
[[Category:Environment:Portable]]
[[Category:Programming language:Python]]</text>
    </revision>
  </page>
  <page>
    <title>Factorization with trial division (Scala)</title>
    <id>3911</id>
    <revision>
      <id>16506</id>
      <timestamp>2009-09-10T23:02:17Z</timestamp>
      <contributor>
        <username>Chaecker</username>
        <id>1883</id>
      </contributor>
      <comment>Added Factorization with trial division (Scala)</comment>
      <text xml:space="preserve">This is a tiny program that factorizes integers up to java.lang.Integer.MAX_VALUE, that is 2147483647.
(Takes a few seconds to complete.)

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt(x:Int,y:Int):List[Int]={
  if (x==y) return List(x)
  if(x%y==0)(y::fakt(x/y,y))
    else
  fakt(x,y+1)
}
def factor(n:Int)=fakt(n,2)

println(factor(120))
println(factor(java.lang.Integer.MAX_VALUE))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>16507</id>
      <timestamp>2009-09-10T23:06:49Z</timestamp>
      <contributor>
        <username>Chaecker</username>
        <id>1883</id>
      </contributor>
      <minor/>
      <comment>improved formatting</comment>
      <text xml:space="preserve">This is a tiny program that factorizes integers up to java.lang.Integer.MAX_VALUE, that is 2147483647.
(For that it takes a few seconds to complete.)

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt(x:Int, y:Int):List[Int]={
  if (x==y) return List(x)
  if (x%y==0)
    (y::fakt(x/y,y))
  else
    fakt(x,y+1)
}
def factor(n:Int) = fakt(n, 2)

println(factor(120))
println(factor(java.lang.Integer.MAX_VALUE))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>16508</id>
      <timestamp>2009-09-10T23:08:38Z</timestamp>
      <contributor>
        <username>Chaecker</username>
        <id>1883</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and java.lang.Integer.MAX_VALUE, that is 2147483647.
(For that it takes a few seconds to complete.)

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt(x:Int, y:Int):List[Int]={
  if (x==y) return List(x)
  if (x%y==0)
    (y::fakt(x/y,y))
  else
    fakt(x,y+1)
}
def factor(n:Int) = fakt(n, 2)

println(factor(120))
println(factor(java.lang.Integer.MAX_VALUE))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;</text>
    </revision>
    <revision>
      <id>16510</id>
      <timestamp>2009-09-13T19:46:27Z</timestamp>
      <contributor>
        <username>Chaecker</username>
        <id>1883</id>
      </contributor>
      <minor/>
      <comment>added categories</comment>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and java.lang.Integer.MAX_VALUE, that is 2147483647.
(For that it takes a few seconds to complete.)
x is the number to factorize, y is the lowest number not tested yet.

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt(x:Int, y:Int):List[Int]={
  if (x==y) return List(x)
  if (x%y==0)
    (y::fakt(x/y,y))
  else
    fakt(x,y+1)
}
def factor(n:Int) = fakt(n, 2)

println(factor(120))
println(factor(java.lang.Integer.MAX_VALUE))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16643</id>
      <timestamp>2010-01-25T13:41:02Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and &lt;tt&gt;scala.Int.MaxValue&lt;/tt&gt;, that is 2147483647.  ''x'' is the number to factorize, ''y'' is the lowest number not tested yet.

The recursive &lt;tt&gt;fakt&lt;/tt&gt; function matches ''x'' and ''y'' against a number of cases.  In the base case, ''y'' has reached the same value as ''x'':

&lt;codeblock language=scala&gt;
&lt;&lt;Base case: x equal to y&gt;&gt;=
case (`y`, _)        =&gt; List(x)
&lt;/codeblock&gt;

If ''x'' &amp;ne; ''y'', then the case may be that ''y'' divides ''x'' evenly.  If so, return a list consisting of ''y'' and the result of calling &lt;tt&gt;fakt&lt;/tt&gt; on the quotient ''x/y'' and ''y''.  Since ''x/y'' will be less than ''x'' but not less than ''y'', the recursion will eventually end.

&lt;codeblock language=scala&gt;
&lt;&lt;x evenly divided by y&gt;&gt;=
case _ if x % y == 0 =&gt; y :: fakt(x / y, y)
&lt;/codeblock&gt;

If ''y'' is equal to 2, try again using the value 3 for ''y''.

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by 2&gt;&gt;=
case (_, 2)          =&gt; fakt(x, 3)
&lt;/codeblock&gt;

If all else fails, try again using the next odd number (for further improvement, pick the next ''prime'' number instead).

&lt;codeblock language=scala&gt;
&lt;&lt;try again&gt;&gt;=
case _               =&gt; fakt(x, y+2)
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt (x: Int, y: Int): List[Int] = (x, y) match {

  &lt;&lt;Base case: x equal to y&gt;&gt;

  &lt;&lt;x evenly divided by y&gt;&gt;

  &lt;&lt;x not evenly divided by 2&gt;&gt;

  &lt;&lt;try again&gt;&gt;

}

def factor (n: Int) = {
  assert(n &gt; 0)
  fakt(n, 2)
}

println(factor(120))
println(factor(java.lang.Integer.MAX_VALUE))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16644</id>
      <timestamp>2010-01-25T13:41:55Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and &lt;tt&gt;scala.Int.MaxValue&lt;/tt&gt;, that is 2147483647.  ''x'' is the number to factorize, ''y'' is the lowest number not tested yet.

The recursive &lt;tt&gt;fakt&lt;/tt&gt; function matches ''x'' and ''y'' against a number of cases.  In the base case, ''y'' has reached the same value as ''x'':

&lt;codeblock language=scala&gt;
&lt;&lt;Base case: x equal to y&gt;&gt;=
case (`y`, _)        =&gt; List(x)
&lt;/codeblock&gt;

If ''x'' &amp;ne; ''y'', then the case may be that ''y'' divides ''x'' evenly.  If so, return a list consisting of ''y'' and the result of calling &lt;tt&gt;fakt&lt;/tt&gt; on the quotient ''x/y'' and ''y''.  Since ''x/y'' will be less than ''x'' but not less than ''y'', the recursion will eventually end.

&lt;codeblock language=scala&gt;
&lt;&lt;x evenly divided by y&gt;&gt;=
case _ if x % y == 0 =&gt; y :: fakt(x / y, y)
&lt;/codeblock&gt;

If ''y'' is equal to 2, try again using the value 3 for ''y''.

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by 2&gt;&gt;=
case (_, 2)          =&gt; fakt(x, 3)
&lt;/codeblock&gt;

If all else fails, try again using the next odd number (for further improvement, pick the next ''prime'' number instead).

&lt;codeblock language=scala&gt;
&lt;&lt;try again&gt;&gt;=
case _               =&gt; fakt(x, y+2)
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt (x: Int, y: Int): List[Int] = (x, y) match {

  &lt;&lt;Base case: x equal to y&gt;&gt;

  &lt;&lt;x evenly divided by y&gt;&gt;

  &lt;&lt;x not evenly divided by 2&gt;&gt;

  &lt;&lt;try again&gt;&gt;

}

def factor (n: Int) = {
  assert(n &gt; 0)
  fakt(n, 2)
}

println(factor(120))
println(factor(scala.Int.MaxValue))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16645</id>
      <timestamp>2010-01-25T13:59:55Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and &lt;tt&gt;scala.Int.MaxValue&lt;/tt&gt;, that is 2147483647.  ''x'' is the number to factorize, ''y'' is the lowest number not tested yet.

The recursive &lt;tt&gt;fakt&lt;/tt&gt; function matches ''x'' and ''y'' against a number of cases.  In the base case, ''y'' has reached the same value as ''x'':

&lt;codeblock language=scala&gt;
&lt;&lt;Base case: x equal to y&gt;&gt;=
case (`y`, _)        =&gt; List(x)
&lt;/codeblock&gt;

If ''x'' &amp;ne; ''y'', then the case may be that ''y'' divides ''x'' evenly.  If so, return a list consisting of ''y'' and the result of calling &lt;tt&gt;fakt&lt;/tt&gt; on the quotient ''x/y'' and ''y''.  Since ''x/y'' will be less than ''x'' but not less than ''y'', the recursion will eventually end.

&lt;codeblock language=scala&gt;
&lt;&lt;x evenly divided by y&gt;&gt;=
case _ if x % y == 0 =&gt; y :: fakt(x / y, y)
&lt;/codeblock&gt;

If ''y'' is equal to 2, try again using the value 3 for ''y''.

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by 2&gt;&gt;=
case (_, 2)          =&gt; fakt(x, 3)
&lt;/codeblock&gt;

If all else fails, try again using the next odd number (for further improvement, pick the next ''prime'' number instead).

&lt;codeblock language=scala&gt;
&lt;&lt;try a bigger y&gt;&gt;=
case _               =&gt; fakt(x, y+2)
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt (x: Int, y: Int): List[Int] = (x, y) match {

  &lt;&lt;Base case: x equal to y&gt;&gt;

  &lt;&lt;x evenly divided by y&gt;&gt;

  &lt;&lt;x not evenly divided by 2&gt;&gt;

  &lt;&lt;try a bigger y&gt;&gt;

}

def factor (n: Int) = {
  assert(n &gt; 0)
  fakt(n, 2)
}

println(factor(120))
println(factor(scala.Int.MaxValue))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16646</id>
      <timestamp>2010-01-25T14:09:21Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and &lt;tt&gt;scala.Int.MaxValue&lt;/tt&gt;, that is 2147483647.  ''x'' is the number to factorize, ''y'' is the lowest number not tested yet.

The recursive &lt;tt&gt;fakt&lt;/tt&gt; function matches ''x'' and ''y'' against a number of cases.  In the base case, ''y'' has reached the same value as ''x'':

&lt;codeblock language=scala&gt;
&lt;&lt;Base case: x equal to y&gt;&gt;=
case (`y`, _)        =&gt; List(x)
&lt;/codeblock&gt;

If ''x'' &amp;ne; ''y'', then the case may be that ''y'' divides ''x'' evenly.  If so, return a list consisting of ''y'' and the result of calling &lt;tt&gt;fakt&lt;/tt&gt; on the quotient ''x/y'' and ''y''.  Since ''x/y'' will be less than ''x'' but not less than ''y'', the recursion will eventually end.

&lt;codeblock language=scala&gt;
&lt;&lt;x evenly divided by y&gt;&gt;=
case _ if x % y == 0 =&gt; y :: fakt(x / y, y)
&lt;/codeblock&gt;

If ''y'' is equal to 2, try again using the value 3 for ''y''.

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by 2&gt;&gt;=
case (_, 2)          =&gt; fakt(x, 3)
&lt;/codeblock&gt;

If all else fails, try again using the next odd number (for further improvement, pick the next ''prime'' number instead).

&lt;codeblock language=scala&gt;
&lt;&lt;try a bigger y&gt;&gt;=
case _               =&gt; fakt(x, y+2)
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt (x: Int, y: Int): List[Int] = (x, y) match {

  &lt;&lt;Base case: x equal to y&gt;&gt;

  &lt;&lt;x evenly divided by y&gt;&gt;

  &lt;&lt;x not evenly divided by 2&gt;&gt;

  &lt;&lt;try a bigger y&gt;&gt;

}

def factor (n: Int) = {
  require(n &gt; 0)
  fakt(n, 2)
}

println(factor(120))
println(factor(scala.Int.MaxValue))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
    <revision>
      <id>16647</id>
      <timestamp>2010-01-25T14:18:14Z</timestamp>
      <contributor>
        <username>Peter Lewerin</username>
        <id>1960</id>
      </contributor>
      <comment>must ... stop ... looking ... at this article</comment>
      <text xml:space="preserve">This is a tiny program that factorizes integers between 2 and &lt;tt&gt;scala.Int.MaxValue&lt;/tt&gt;, that is 2147483647.  ''x'' is the number to factorize, ''y'' is the lowest number not tested yet.

The recursive &lt;tt&gt;fakt&lt;/tt&gt; function matches ''x'' and ''y'' against a number of cases.  In the base case, ''y'' has reached the same value as ''x'':

&lt;codeblock language=scala&gt;
&lt;&lt;Base case: x equal to y&gt;&gt;=
case (`y`, _)        =&gt; List(x)
&lt;/codeblock&gt;

If ''x'' &amp;ne; ''y'', then the case may be that ''y'' divides ''x'' evenly.  If so, return a list consisting of ''y'' and the result of calling &lt;tt&gt;fakt&lt;/tt&gt; on the quotient ''x/y'' and ''y''.  Since ''x/y'' will be less than ''x'' but not less than ''y'', the recursion will eventually end.

&lt;codeblock language=scala&gt;
&lt;&lt;x evenly divided by y&gt;&gt;=
case _ if x % y == 0 =&gt; y :: fakt(x / y, y)
&lt;/codeblock&gt;

If ''y'' is equal to 2, try again using the value 3 for ''y''.

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by 2, try 3&gt;&gt;=
case (_, 2)          =&gt; fakt(x, 3)
&lt;/codeblock&gt;

If all else fails, try again using the next odd number (for further improvement, pick the next ''prime'' number instead).

&lt;codeblock language=scala&gt;
&lt;&lt;x not evenly divided by y, try a bigger y&gt;&gt;=
case _               =&gt; fakt(x, y+2)
&lt;/codeblock&gt;

&lt;codeblock language=scala&gt;
&lt;&lt;factorize.scala&gt;&gt;=
def fakt (x: Int, y: Int): List[Int] = (x, y) match {

  &lt;&lt;Base case: x equal to y&gt;&gt;

  &lt;&lt;x evenly divided by y&gt;&gt;

  &lt;&lt;x not evenly divided by 2, try 3&gt;&gt;

  &lt;&lt;x not evenly divided by y, try a bigger y&gt;&gt;

}

def factor (n: Int) = {
  require(n &gt; 0)
  fakt(n, 2)
}

println(factor(120))
println(factor(scala.Int.MaxValue))
&lt;/codeblock&gt;
which we expect to produce:
&lt;pre&gt;
List(2, 2, 2, 3, 5)
List(2147483647)
&lt;/pre&gt;



[[Category:Factorization with trial division|Scala]]
[[Category:Programming language:Scala]]</text>
    </revision>
  </page>
  <page>
    <title>Fail Article</title>
    <id>3972</id>
    <revision>
      <id>16949</id>
      <timestamp>2010-09-24T20:24:09Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <comment>[[Fail Article]] moved to [[Fibonacci numbers (Oz)]]: rv</comment>
      <text xml:space="preserve">#REDIRECT [[Fibonacci numbers (Oz)]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers</title>
    <id>3338</id>
    <revision>
      <id>12813</id>
      <timestamp>2008-03-14T02:02:42Z</timestamp>
      <contributor>
        <username>Fonebone74</username>
        <id>1658</id>
      </contributor>
      <text xml:space="preserve">#REDIRECT [[Category:Fibonacci numbers]]</text>
    </revision>
    <revision>
      <id>12934</id>
      <timestamp>2008-03-30T02:21:43Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">#REDIRECT [[:Category:Fibonacci numbers]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (ALGOL 68)</title>
    <id>3612</id>
    <revision>
      <id>14948</id>
      <timestamp>2008-10-11T07:37:32Z</timestamp>
      <contributor>
        <username>NevilleDNZ</username>
        <id>1731</id>
      </contributor>
      <minor/>
      <comment>3rd try</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in ALGOL 68:

&lt;codeblock language=a68&gt;
&lt;&lt;fib.a68&gt;&gt;=
&lt;&lt;fib&gt;&gt;;
&lt;&lt;fastfib&gt;&gt;;
&lt;&lt;fastfib v2&gt;&gt;;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;a68&quot;&gt;
&lt;&lt;fib&gt;&gt;=
PROC fib = (INT n)INT:
(
  n &lt; 2 | n | fib(n-1) + fib(n-2)
)
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;a68&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
PROC fastfib = (INT n)INT:
(
  CASE n+1 IN
    0, 1
  OUT
    []INT init = (0, 1);
    [0:1]INT cache := init[@0];
    FOR i FROM UPB cache + 1 TO n DO
      cache[i MOD 2] := cache[0] + cache[1]
    OD;
    cache[n MOD 2]
  ESAC
)
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand.
&lt;codeblock language=&quot;a68&quot;&gt;
&lt;&lt;fastfib v2&gt;&gt;=
PROC fastfibv2 = (INT n)INT:
(
  IF n = 0 THEN
    0
  ELSE
    INT n0 := 0, n1 := 1, naux;
    FOR i FROM 2 TO n DO
      naux := n1;
      n1 := n0 + n1;
      n0 := naux
    OD;
    n1
  FI
)
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed ALGOL 68 ''int''s can only hold the first 92 Fibonacci numbers.  Note: [[ALGOL 68G]] ''LONG LONG INT'' can be set to any level of precision are run time.

== Test driver ==
&lt;codeblock language=&quot;a68&quot;&gt;
&lt;&lt;main&gt;&gt;=
main:
(
  FOR n FROM 0 TO 3*4 DO printf(($&quot;fib(&quot;g&quot;)=&quot;gl$, n, fib(n))) OD;
  FOR n FROM 0 TO 34 DO printf(($&quot;fastfib(&quot;g&quot;)=&quot;gl$, n, fastfib(n))) OD;
  FOR n FROM 0 TO 34 DO printf(($&quot;fastfib2(&quot;g&quot;)=&quot;gl$, n, fastfib v2(n))) OD
)
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|ALGOL 68]]
[[Category:Programming language:ALGOL 68]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Alice ML)</title>
    <id>2933</id>
    <revision>
      <id>8676</id>
      <timestamp>2007-01-25T19:45:30Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <comment>Initial version</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11859</id>
      <timestamp>2007-12-29T21:26:01Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>racliracaln</comment>
      <text xml:space="preserve">cchieltzelou
{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11908</id>
      <timestamp>2007-12-31T03:08:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12071</id>
      <timestamp>2008-01-12T19:00:20Z</timestamp>
      <contributor>
        <ip>190.3.28.120</ip>
      </contributor>
      <comment>getboc</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12072</id>
      <timestamp>2008-01-12T21:07:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12397</id>
      <timestamp>2008-01-30T18:53:43Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>orlaordar</comment>
      <text xml:space="preserve">baspaserrol
{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12418</id>
      <timestamp>2008-01-30T19:39:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12507</id>
      <timestamp>2008-02-17T19:27:58Z</timestamp>
      <contributor>
        <ip>64.118.89.74</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12522</id>
      <timestamp>2008-02-18T22:56:02Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/64.118.89.74|64.118.89.74]] ([[User_talk:64.118.89.74|64.118.89.74]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12607</id>
      <timestamp>2008-02-25T14:54:09Z</timestamp>
      <contributor>
        <ip>65.47.164.46</ip>
      </contributor>
      <comment>lielpa</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12608</id>
      <timestamp>2008-02-25T15:49:10Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12797</id>
      <timestamp>2008-03-13T03:15:56Z</timestamp>
      <contributor>
        <ip>211.119.242.46</ip>
      </contributor>
      <comment>c4troze</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12812</id>
      <timestamp>2008-03-14T02:00:52Z</timestamp>
      <contributor>
        <username>Fonebone74</username>
        <id>1658</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12850</id>
      <timestamp>2008-03-18T05:24:01Z</timestamp>
      <contributor>
        <ip>200.130.24.47</ip>
      </contributor>
      <comment>nomonorvar</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12861</id>
      <timestamp>2008-03-18T06:12:48Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.130.24.47|200.130.24.47]] ([[User_talk:200.130.24.47|200.130.24.47]]); changed back to last version by [[User:Fonebone74|Fonebone74]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13017</id>
      <timestamp>2008-04-10T04:18:02Z</timestamp>
      <contributor>
        <ip>219.148.206.37</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13018</id>
      <timestamp>2008-04-10T06:07:22Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13113</id>
      <timestamp>2008-04-17T09:34:57Z</timestamp>
      <contributor>
        <ip>89.132.12.128</ip>
      </contributor>
      <comment>ronocaeracel</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13118</id>
      <timestamp>2008-04-17T10:17:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14244</id>
      <timestamp>2008-08-10T10:54:23Z</timestamp>
      <contributor>
        <ip>143.210.36.238</ip>
      </contributor>
      <comment>sitboolo</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14245</id>
      <timestamp>2008-08-10T12:06:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14496</id>
      <timestamp>2008-08-28T05:25:37Z</timestamp>
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      </contributor>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14498</id>
      <timestamp>2008-08-28T06:28:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14592</id>
      <timestamp>2008-09-11T13:48:37Z</timestamp>
      <contributor>
        <ip>58.47.159.237</ip>
      </contributor>
      <comment>ololilet</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14597</id>
      <timestamp>2008-09-11T14:47:29Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/58.47.159.237|58.47.159.237]] ([[User_talk:58.47.159.237|58.47.159.237]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14697</id>
      <timestamp>2008-09-23T07:05:37Z</timestamp>
      <contributor>
        <ip>211.233.63.164</ip>
      </contributor>
      <comment>vicliricdom</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14701</id>
      <timestamp>2008-09-23T13:36:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14915</id>
      <timestamp>2008-10-09T16:00:31Z</timestamp>
      <contributor>
        <ip>61.186.95.141</ip>
      </contributor>
      <comment>laalrocacoc</comment>
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{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14918</id>
      <timestamp>2008-10-09T16:32:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.186.95.141|61.186.95.141]] ([[User_talk:61.186.95.141|61.186.95.141]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Import==
Alice ML requires any package imports to be located at the top of a script.  We will be using the RedBlack dictionary for the memoization.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
import functor MkRedBlackImpMap from &quot;x-alice:/lib/data/MkRedBlackImpMap&quot;
&lt;/codeblock&gt;

==Recursion==
A simple recursive solution can be constructed in Alice ML in a way that directly mirrors the mathematical definition of the function.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun fib 0 = 0
  | fib 1 = 1
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
  | fib _ = raise Domain
&lt;/codeblock&gt;

We use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.
&lt;codeblock language=aliceml&gt;
fun fib 0 = 0
  | fib 1 = 1
&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.
&lt;codeblock language=aliceml&gt;
  | fib n if (n &gt; 1) = fib(n - 1) + fib(n - 2)
&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the guards in pattern matching, Alice ML may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).
&lt;codeblock language=aliceml&gt;
  | fib _ = raise Domain
&lt;/codeblock&gt;

We can test the fib function in the following manner:
&lt;codeblock language=aliceml&gt;
- [fib 0, fib 1, fib 2, fib 3];
val it : int list = [0, 1, 1, 2]
- fib 7;
val it : int = 13
&lt;/codeblock&gt;

==Memoize==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
local
   structure Memo = MkRedBlackImpMap Int
   val table = Memo.map()
in
   fun memo_fib n =
      let
         val previously_computed_result = Memo.lookup(table, n)
      in
         case previously_computed_result of
            | SOME item =&gt; item
            | NONE =&gt;
               let
                  fun fib 0 = 0
                    | fib 1 = 1
                    | fib n if (n &gt; 1) = memo_fib(n - 1) + memo_fib(n - 2)
                    | fib _ = raise Domain
                  val result = fib n
               in
                  Memo.insert(table, n, result);
                  result
               end
      end
end
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;memo&lt;/code&gt; dictionary. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

With the [http://en.wikipedia.org/wiki/Memoization memoized] version, larger Fibonacci numbers can be found in no time:
&lt;codeblock language=aliceml&gt;
- memo_fib 44;
val it : int = 701408733
&lt;/codeblock&gt;

==Iteration==
To calculate the ''n''th Fibonacci number in only ''n'' steps, we can also start with 0 and 1 and iteratively add up items ''n'' times:

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun iterative_fib n =
   let
      fun fib (a, b, 0) = b
        | fib (a, b, count) if (n &gt; 0) = fib(a + b, a, count - 1)
        | fib _ = raise Domain
   in
      fib(1, 0, n)
   end
&lt;/codeblock&gt;

==Streams==
One can also use streams in Alice ML to build the Fibonacci numbers in a lazy fashion.  The Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun lazy fibgen (a, b) =
   a :: fibgen(b, a + b)

val fibs = fibgen(0, 1)
&lt;/codeblock&gt;

To get the 40th number in the sequence, we can pull it from the list in the following manner:
&lt;codeblock language=aliceml&gt;
- List.nth(fibs, 40);
val it : int = 102334155
&lt;/codeblock&gt;

==Unlimited Integer Sizes==
The standard size of an integer in Alice ML is restricted to 31 bits (Int.minInt = ~1073741824 to Int.maxInt = 1073741823).  In order to handle numbers outside of this range, the type for the numbers should be changed to IntInf.  Since Alice ML doesn't currently support IntInf constants, we'll declare some values to hold 0 and 1.

&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
val inf_0 = IntInf.fromInt 0
val inf_1 = IntInf.fromInt 1
&lt;/codeblock&gt;

Since we are interested in large values, we'll use the iterative version of fib to showcase how to write a fib function using infinite integers:
&lt;codeblock language=aliceml&gt;
&lt;&lt;fib.aml&gt;&gt;=
fun inf_iterative_fib n =
   let
      fun fib (a, b, count) if (count = inf_0) = b : IntInf.t
        | fib (a, b, count) if (count &gt; inf_0) = fib(a + b, a, count - inf_1)
        | fib _ = raise Domain
   in
      fib(inf_1, inf_0, n)
   end
&lt;/codeblock&gt;

The inf_ackermann allows us to compute results with a large number of digits:
&lt;codeblock language=aliceml&gt;
- inf_iterative_fib (IntInf.fromInt 100);
val it : IntInf.t = 354224848179261915075
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Alice_ML]]
[[Category:Programming language:Alice_ML]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (C Plus Plus templates)</title>
    <id>1697</id>
    <revision>
      <id>2739</id>
      <timestamp>2006-03-07T01:01:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers implemeted with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2740</id>
      <timestamp>2006-03-07T01:05:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Link to C-version</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers implemeted with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of fibonacci numbers.

[[Category:Fibonacci numbers]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2741</id>
      <timestamp>2006-03-07T01:11:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Fibonacci numbers (C Plus Plus) moved to Fibonacci numbers (C Plus Plus templates)</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers implemeted with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of fibonacci numbers.

[[Category:Fibonacci numbers]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2747</id>
      <timestamp>2006-03-07T02:22:31Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>sp</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of fibonacci numbers.

[[Category:Fibonacci numbers]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2749</id>
      <timestamp>2006-03-07T02:26:44Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>capitalize Fibonacci</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4728</id>
      <timestamp>2006-05-14T20:04:14Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10975</id>
      <timestamp>2007-09-27T11:37:19Z</timestamp>
      <contributor>
        <ip>65.44.66.100</ip>
      </contributor>
      <text xml:space="preserve">cdroneltlil
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10980</id>
      <timestamp>2007-09-28T14:34:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert strange text</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10985</id>
      <timestamp>2007-09-29T21:53:53Z</timestamp>
      <contributor>
        <ip>64.118.89.74</ip>
      </contributor>
      <text xml:space="preserve">rolcrellidom
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10986</id>
      <timestamp>2007-09-29T22:17:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert strange text</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11141</id>
      <timestamp>2007-10-12T17:40:47Z</timestamp>
      <contributor>
        <ip>87.101.244.9</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11144</id>
      <timestamp>2007-10-12T17:44:50Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11454</id>
      <timestamp>2007-11-02T14:09:32Z</timestamp>
      <contributor>
        <ip>148.167.202.141</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11457</id>
      <timestamp>2007-11-02T15:08:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11494</id>
      <timestamp>2007-11-08T22:03:12Z</timestamp>
      <contributor>
        <ip>64.251.25.61</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11499</id>
      <timestamp>2007-11-09T00:26:52Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/64.251.25.61|64.251.25.61]] ([[User_talk:64.251.25.61|64.251.25.61]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11708</id>
      <timestamp>2007-11-24T19:50:11Z</timestamp>
      <contributor>
        <ip>210.22.158.132</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11710</id>
      <timestamp>2007-11-24T21:53:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11774</id>
      <timestamp>2007-12-05T13:14:08Z</timestamp>
      <contributor>
        <ip>216.58.96.135</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11775</id>
      <timestamp>2007-12-05T13:32:49Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/216.58.96.135|216.58.96.135]] ([[User_talk:216.58.96.135|216.58.96.135]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11812</id>
      <timestamp>2007-12-10T12:41:46Z</timestamp>
      <contributor>
        <ip>200.201.194.100</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11813</id>
      <timestamp>2007-12-10T13:56:37Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11856</id>
      <timestamp>2007-12-29T21:23:00Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>c4tzelsite</comment>
      <text xml:space="preserve">aceltatracel
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11905</id>
      <timestamp>2007-12-31T03:08:11Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11985</id>
      <timestamp>2008-01-09T09:30:43Z</timestamp>
      <contributor>
        <ip>147.46.7.54</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11999</id>
      <timestamp>2008-01-09T16:33:28Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/147.46.7.54|147.46.7.54]] ([[User_talk:147.46.7.54|147.46.7.54]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12394</id>
      <timestamp>2008-01-30T18:51:50Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>acrelc4</comment>
      <text xml:space="preserve">basrov
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12415</id>
      <timestamp>2008-01-30T19:39:32Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12500</id>
      <timestamp>2008-02-17T09:11:43Z</timestamp>
      <contributor>
        <ip>64.118.89.74</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12503</id>
      <timestamp>2008-02-17T11:32:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12535</id>
      <timestamp>2008-02-20T16:17:05Z</timestamp>
      <contributor>
        <ip>200.68.73.193</ip>
      </contributor>
      <comment>erropasvize</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12541</id>
      <timestamp>2008-02-21T06:14:14Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.68.73.193|200.68.73.193]] ([[User_talk:200.68.73.193|200.68.73.193]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12655</id>
      <timestamp>2008-03-01T02:50:08Z</timestamp>
      <contributor>
        <ip>195.250.160.37</ip>
      </contributor>
      <comment>elcvibocl</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12656</id>
      <timestamp>2008-03-01T09:15:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12876</id>
      <timestamp>2008-03-21T09:09:14Z</timestamp>
      <contributor>
        <ip>218.83.153.62</ip>
      </contributor>
      <comment>varbonodelt</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12879</id>
      <timestamp>2008-03-21T16:11:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13027</id>
      <timestamp>2008-04-10T19:05:25Z</timestamp>
      <contributor>
        <ip>60.244.124.101</ip>
      </contributor>
      <comment>alertroc</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13028</id>
      <timestamp>2008-04-10T21:19:52Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/60.244.124.101|60.244.124.101]] ([[User_talk:60.244.124.101|60.244.124.101]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13831</id>
      <timestamp>2008-07-01T20:36:29Z</timestamp>
      <contributor>
        <ip>203.177.74.136</ip>
      </contributor>
      <comment>nooroud</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13832</id>
      <timestamp>2008-07-01T21:31:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14149</id>
      <timestamp>2008-07-30T21:22:58Z</timestamp>
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      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14150</id>
      <timestamp>2008-07-30T22:27:00Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/218.92.8.165|218.92.8.165]] ([[User_talk:218.92.8.165|218.92.8.165]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14475</id>
      <timestamp>2008-08-26T08:03:31Z</timestamp>
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        <ip>118.175.255.10</ip>
      </contributor>
      <comment>cocald</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14476</id>
      <timestamp>2008-08-26T09:19:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/118.175.255.10|118.175.255.10]] ([[User_talk:118.175.255.10|118.175.255.10]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15112</id>
      <timestamp>2008-10-18T23:43:03Z</timestamp>
      <contributor>
        <ip>189.73.195.210</ip>
      </contributor>
      <comment>oudronace</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15120</id>
      <timestamp>2008-10-19T05:38:34Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers implemented with a template in C++: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.cpp&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;iostream&gt;
&lt;/codeblock&gt;

== Template ==

&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;fib&gt;&gt;=
template&lt;unsigned int n&gt; struct fib
{
	static const unsigned int result=fib&lt;n-1&gt;::result+fib&lt;n-2&gt;::result;
};

template&lt;&gt; struct fib&lt;1&gt;
{
	static const unsigned int result=1;
};

template&lt;&gt; struct fib&lt;0&gt;
{
	static const unsigned int result=0;
};
&lt;/codeblock&gt;

== Test driver ==

The Fibonacci numbers will be calculated at compile-time, when the ''fib'' template class is instantiated.
&lt;codeblock language=&quot;c++&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	std::cout&lt;&lt;&quot;fib&lt;1&gt;=&quot;&lt;&lt;fib&lt;1&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;2&gt;=&quot;&lt;&lt;fib&lt;2&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;3&gt;=&quot;&lt;&lt;fib&lt;3&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;4&gt;=&quot;&lt;&lt;fib&lt;4&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;5&gt;=&quot;&lt;&lt;fib&lt;5&gt;::result&lt;&lt;'\n';

	std::cout&lt;&lt;&quot;fib&lt;40&gt;=&quot;&lt;&lt;fib&lt;40&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;41&gt;=&quot;&lt;&lt;fib&lt;41&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;42&gt;=&quot;&lt;&lt;fib&lt;42&gt;::result&lt;&lt;'\n';
	std::cout&lt;&lt;&quot;fib&lt;43&gt;=&quot;&lt;&lt;fib&lt;43&gt;::result&lt;&lt;'\n';
	return 0;
}
&lt;/codeblock&gt;

See [[Fibonacci numbers (C)]] for runtime calculation of Fibonacci numbers.

[[Category:Fibonacci numbers|C Plus Plus templates]]
[[Category:Programming language:C Plus Plus]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (C Plus Plus)</title>
    <id>1698</id>
    <revision>
      <id>2742</id>
      <timestamp>2006-03-07T01:11:17Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Fibonacci numbers (C Plus Plus) moved to Fibonacci numbers (C Plus Plus templates): Moving to C Plus Plus templates because we could reasonably have a &quot;normal&quot; C++ version that computes fib at runtime</comment>
      <text xml:space="preserve">#redirect [[Fibonacci numbers (C Plus Plus templates)]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (C)</title>
    <id>1659</id>
    <revision>
      <id>2622</id>
      <timestamp>2006-03-06T19:26:57Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C:

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;10; ++n) printf(&quot;fib(%d)=%d\n&quot;, n, fib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2641</id>
      <timestamp>2006-03-06T20:25:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak to fix cats</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;10; ++n) printf(&quot;fib(%d)=%d\n&quot;, n, fib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2665</id>
      <timestamp>2006-03-06T20:54:32Z</timestamp>
      <contributor>
        <ip>62.97.249.114</ip>
      </contributor>
      <comment>Fast implementation</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2667</id>
      <timestamp>2006-03-06T20:58:52Z</timestamp>
      <contributor>
        <ip>62.97.249.114</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2723</id>
      <timestamp>2006-03-06T23:25:11Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Note about limitations of machine word size</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4729</id>
      <timestamp>2006-05-14T20:04:30Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>9324</id>
      <timestamp>2007-03-02T21:23:18Z</timestamp>
      <contributor>
        <ip>83.133.10.191</ip>
      </contributor>
      <comment>added spaces for readability</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10710</id>
      <timestamp>2007-07-19T16:03:40Z</timestamp>
      <contributor>
        <ip>89.180.114.141</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  for (i = 0; i &lt; n; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10711</id>
      <timestamp>2007-07-19T16:18:22Z</timestamp>
      <contributor>
        <ip>89.180.114.141</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11871</id>
      <timestamp>2007-12-29T21:46:53Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>erdeldarro</comment>
      <text xml:space="preserve">roc4tcnalil
{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11920</id>
      <timestamp>2007-12-31T03:10:37Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12095</id>
      <timestamp>2008-01-13T11:48:05Z</timestamp>
      <contributor>
        <ip>125.33.52.61</ip>
      </contributor>
      <comment>catanoricpas</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12102</id>
      <timestamp>2008-01-13T13:58:22Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15642</id>
      <timestamp>2008-12-17T23:28:27Z</timestamp>
      <contributor>
        <ip>211.115.218.116</ip>
      </contributor>
      <comment>FIELD_OTHER</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

FIELD_MESSAGE_basrosi

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15646</id>
      <timestamp>2008-12-18T03:53:01Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/211.115.218.116|211.115.218.116]] ([[User_talk:211.115.218.116|211.115.218.116]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in C: 

&lt;codeblock language=c&gt;
&lt;&lt;fib.c&gt;&gt;=
&lt;&lt;includes&gt;&gt;
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;includes&gt;&gt;=
#include&lt;stdio.h&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fib&gt;&gt;=
unsigned int fib(unsigned int n)
{
	return n &lt; 2 ? n : fib(n-1) + fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in an array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib&gt;&gt;=
unsigned int fastfib(unsigned int n)
{
	unsigned int a[3];
	unsigned int *p=a;
	unsigned int i;

	for(i=0; i&lt;=n; ++i) {
		if(i&lt;2) *p=i;
		else {
			if(p==a) *p=*(a+1)+*(a+2);
			else if(p==a+1) *p=*a+*(a+2);
			else *p=*a+*(a+1);
		}
		if(++p&gt;a+2) p=a;
	}

	return p==a?*(p+2):*(p-1);
}
&lt;/codeblock&gt;
This iteration implementation is fast and easy to understand. 
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;fastfib_v2&gt;&gt;=
unsigned int fastfib_v2 (unsigned int n)
{
  unsigned int n0 = 0;
  unsigned int n1 = 1;
  unsigned int naux;
  unsigned int i;
  if (n == 0)
    return 0;
  for (i=0; i &lt; n-1; i++) {
    naux = n1;
    n1 = n0 + n1;
    n0 = naux;
  }
  return n1;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine signed C ''int''s can only hold the first 92 Fibonacci numbers.

== Test driver ==
&lt;codeblock language=&quot;c&quot;&gt;
&lt;&lt;main&gt;&gt;=
int main()
{
	unsigned int n;
	for(n=0; n&lt;35; ++n) printf(&quot;fib(%u)=%u\n&quot;, n, fib(n));
	for(n=0; n&lt;35; ++n) printf(&quot;fastfib(%u)=%u\n&quot;, n, fastfib(n));
        for(n=0; n&lt;35; ++n) printf(&quot;fastfib_v2(%u)=%u\n&quot;, n, fastfib(n));
	return 0;
}
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|C]]
[[Category:Programming language:C]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (E)</title>
    <id>2986</id>
    <revision>
      <id>8861</id>
      <timestamp>2007-02-06T03:49:24Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>initial rev</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
var fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;. We encapsulate both the memoization cache and the &lt;code&gt;fib&lt;/code&gt; function in an object with a single method, &lt;code&gt;run&lt;/code&gt; (which E calls by default if no other methods are available.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
def makeFib() {
  &lt;&lt;fibmap&gt;&gt;

  def fib { 
    to run(n :(int &gt;= 0)) :int {
      if (!fibs.maps(n)) {
        fibs[n] := fib(n-1) + fib(n-2)
      }
      return fibs[n]
    }
  }
  return fib
}

&lt;/codeblock&gt;

Because the memoized &lt;code&gt;fib&lt;/code&gt; function is wrapped in an object, we have to make an object before we can test the function. However, since we used of the &lt;code&gt;run&lt;/code&gt; method to define the &lt;code&gt;fib&lt;/code&gt; function, the resulting object can be treated as if it is a function (i.e. there's no need to explicitly call a method by name):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

def fib := makeFib()
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purelt recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>9553</id>
      <timestamp>2007-03-22T05:17:35Z</timestamp>
      <contributor>
        <ip>68.122.193.176</ip>
      </contributor>
      <comment>Removed unnecessary complexity (nesting, methods, explanation,....)</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
var fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoizing &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>9554</id>
      <timestamp>2007-03-22T05:19:51Z</timestamp>
      <contributor>
        <ip>68.122.193.176</ip>
      </contributor>
      <comment>The fibs variable need not be assignable</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoizing &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>9555</id>
      <timestamp>2007-03-22T05:20:41Z</timestamp>
      <contributor>
        <ip>68.122.193.176</ip>
      </contributor>
      <comment>/* Recursion with memoization&lt;!-- NOT memorization --&gt; */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11868</id>
      <timestamp>2007-12-29T21:45:19Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>caceldro</comment>
      <text xml:space="preserve">alcaelriccn
{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11917</id>
      <timestamp>2007-12-31T03:09:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12035</id>
      <timestamp>2008-01-11T09:44:05Z</timestamp>
      <contributor>
        <ip>66.226.75.71</ip>
      </contributor>
      <comment>domreltroc</comment>
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{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12036</id>
      <timestamp>2008-01-11T09:48:08Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12434</id>
      <timestamp>2008-01-31T02:25:34Z</timestamp>
      <contributor>
        <ip>67.19.102.98</ip>
      </contributor>
      <comment>cachirolo</comment>
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{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12441</id>
      <timestamp>2008-01-31T05:26:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/67.19.102.98|67.19.102.98]] ([[User_talk:67.19.102.98|67.19.102.98]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15604</id>
      <timestamp>2008-12-17T08:31:20Z</timestamp>
      <contributor>
        <ip>61.14.43.10</ip>
      </contributor>
      <comment>/* Recursion with memoization&lt;!-- NOT memorization --&gt; */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memorization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15605</id>
      <timestamp>2008-12-17T08:32:01Z</timestamp>
      <contributor>
        <ip>61.14.43.10</ip>
      </contributor>
      <comment>/* Recursion with memorization&lt;!-- NOT memorization --&gt; */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here we present several ways to compute the Fibonacci numbers using the language [http://www.erights.org E].

==Recursion==
The recursive definition can be translated directly into E as follows:  

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_recursive.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

def fib(n :(int &gt;= 0)) :int {
  switch (n) {
    match == 0 { return 0 }
    match == 1 { return 1 }
    match _    { return fib(n-1) + fib(n-2) }
  }
}

&lt;&lt;testing&gt;&gt;
&lt;/codeblock&gt;

Here we've used a guard to ensure that the &lt;code&gt;fib&lt;/code&gt; function cannot be passed a negative number (which would result in an infinite recursion).

We can test the &lt;code&gt;fib&lt;/code&gt; function using a simple for-loop 

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;testing&gt;&gt;=
for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

which produces the following output:

  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

==Recursion with memoization&lt;!-- NOT memorization --&gt;==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating fib(''n'') requires calculating two smaller Fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate fib(''n'') is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations. 

The memoization cache is an E ''FlexMap'' consisting of entries composed of a key &lt;code&gt;n&lt;/code&gt;, and a corresponding value &lt;code&gt;fib(n)&lt;/code&gt;. We initialize the map with the first two Fibonacci numbers (the &lt;code&gt;.diverge()&lt;/code&gt; turns the initial constant map into a mutable FlexMap):

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fibmap&gt;&gt;=
def fibs := [0 =&gt; 0, 1 =&gt; 1].diverge()
&lt;/codeblock&gt;

The memoized &lt;code&gt;fib&lt;/code&gt; function recursively computes and stores the value of &lt;code&gt;fib(n)&lt;/code&gt; if it hasn't been previously stored in the &lt;code&gt;fibs&lt;/code&gt; map. Otherwise it simply returns the memoized value of &lt;code&gt;fib(n)&lt;/code&gt;.

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib object&gt;&gt;=
&lt;&lt;fibmap&gt;&gt;

def fib(n :(int &gt;= 0)) :int {
  if (!fibs.maps(n)) {
    fibs[n] := fib(n-1) + fib(n-2)
  }
  return fibs[n]
}

&lt;/codeblock&gt;

We can now use the memoized &lt;code&gt;fib&lt;/code&gt; function just as we used the purely recursive one:

&lt;codeblock language=&quot;elanguage&quot;&gt;
&lt;&lt;fib_memo.e&gt;&gt;=
#!/usr/bin/env rune

pragma.syntax(&quot;0.9&quot;)

&lt;&lt;fib object&gt;&gt;

for i in 0..20 {
  print(&quot; &quot;, fib(i))
}
&lt;/codeblock&gt;

One interesting test of our memoized &lt;code&gt;fib&lt;/code&gt; function is to compare the execution time required for the purely recursive and memoized version of &lt;code&gt;fib&lt;/code&gt;:

 $ time ./fib_recursive.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    5m3.129s
 user    4m26.099s
 sys     0m4.572s

 $ time ./fib_memo.e
  0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 real    0m12.297s
 user    0m10.252s
 sys     0m0.601s

The memoized version of the &lt;code&gt;fib&lt;/code&gt; function is clearly substantially faster than the purely recursive version. In addition, based on timing results for a simple E Hello World program

 $ time ./helloworld.e 
 Hello World!
 
 real    0m10.667s
 user    0m9.293s
 sys     0m0.563s

it's clear that a significant chunk of the reported execution time for the memoized &lt;code&gt;fib&lt;/code&gt; function is startup overhead for the E interpreter.


[[Category:Fibonacci numbers|E]]
[[Category:Programming language:E]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Eiffel)</title>
    <id>1885</id>
    <revision>
      <id>4091</id>
      <timestamp>2006-04-11T04:44:24Z</timestamp>
      <contributor>
        <username>Leland McInnes</username>
        <id>4</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

The Fibonacci numbers in Eiffel:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

== Recursive ==

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
        fib(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            do
                inspect n
                    when 0 then Result := 0
                    when 1 then Result := 1
                    else
                        Result := fib(n-1) + fib(n-2)
                end --inspect
                
            end --fib
&lt;/codeblock&gt;

== Iteration ==

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
        fib_iterative(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            local
                prev1, prev2 : INTEGER
                i : INTEGER
            do
                prev1 := 0
                
                -- Ensure correct behaviour for n = 0
                if n = 0 then 
                    Result := 0
                else
                    Result := 1
                end
                
                from
                    i := 1
                until
                    i &gt;= n
                loop
                    prev2 := prev1
                    prev1 := Result
                    Result := prev2 + Result
                    i := i + 1
                end --loop
                
            end --fib_iterative
&lt;/codeblock&gt;

== Testing ==
Finally, we can test both versions by including the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
        make is
            local
                i : INTEGER
            do
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib(i))
                    io.put_new_line
                    i := i + 1
                end --loop
                
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib_iterative(i))
                    io.put_new_line
                    i := i + 1
                end --loop                
            end --make
&lt;/codeblock&gt;

[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4092</id>
      <timestamp>2006-04-11T04:45:03Z</timestamp>
      <contributor>
        <username>Leland McInnes</username>
        <id>4</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

The Fibonacci numbers in Eiffel:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

== Recursive ==

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
        fib(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            do
                inspect n
                    when 0 then Result := 0
                    when 1 then Result := 1
                    else
                        Result := fib(n-1) + fib(n-2)
                end --inspect
                
            end --fib
&lt;/codeblock&gt;

== Iteration ==

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
        fib_iterative(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            local
                prev1, prev2 : INTEGER
                i : INTEGER
            do
                prev1 := 0
                
                -- Ensure correct behaviour for n = 0
                if n = 0 then 
                    Result := 0
                else
                    Result := 1
                end
                
                from
                    i := 1
                until
                    i &gt;= n
                loop
                    prev2 := prev1
                    prev1 := Result
                    Result := prev2 + Result
                    i := i + 1
                end --loop
                
            end --fib_iterative
&lt;/codeblock&gt;

== Testing ==
Finally, we can test both versions by including the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
        make is
            local
                i : INTEGER
            do
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib(i))
                    io.put_new_line
                    i := i + 1
                end --loop
                
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib_iterative(i))
                    io.put_new_line
                    i := i + 1
                end --loop                
            end --make
&lt;/codeblock&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4094</id>
      <timestamp>2006-04-11T04:51:35Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rearrange</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
        fib(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            do
                inspect n
                    when 0 then Result := 0
                    when 1 then Result := 1
                    else
                        Result := fib(n-1) + fib(n-2)
                end --inspect
                
            end --fib
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
        fib_iterative(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            local
                prev1, prev2 : INTEGER
                i : INTEGER
            do
                prev1 := 0
                
                -- Ensure correct behaviour for n = 0
                if n = 0 then 
                    Result := 0
                else
                    Result := 1
                end
                
                from
                    i := 1
                until
                    i &gt;= n
                loop
                    prev2 := prev1
                    prev1 := Result
                    Result := prev2 + Result
                    i := i + 1
                end --loop
                
            end --fib_iterative
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
        make is
            local
                i : INTEGER
            do
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib(i))
                    io.put_new_line
                    i := i + 1
                end --loop
                
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib_iterative(i))
                    io.put_new_line
                    i := i + 1
                end --loop                
            end --make
&lt;/codeblock&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4095</id>
      <timestamp>2006-04-11T04:53:51Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Recursive */ indentation</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib(n: INTEGER) : INTEGER is
    require
        n &gt;= 0
    do
        inspect n
            when 0 then Result := 0
            when 1 then Result := 1
            else
                Result := fib(n-1) + fib(n-2)
        end --inspect
                
    end --fib
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
        fib_iterative(n: INTEGER) : INTEGER is
            require
                n &gt;= 0
            local
                prev1, prev2 : INTEGER
                i : INTEGER
            do
                prev1 := 0
                
                -- Ensure correct behaviour for n = 0
                if n = 0 then 
                    Result := 0
                else
                    Result := 1
                end
                
                from
                    i := 1
                until
                    i &gt;= n
                loop
                    prev2 := prev1
                    prev1 := Result
                    Result := prev2 + Result
                    i := i + 1
                end --loop
                
            end --fib_iterative
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
        make is
            local
                i : INTEGER
            do
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib(i))
                    io.put_new_line
                    i := i + 1
                end --loop
                
                from 
                    i := 0
                until
                    i &gt; 10
                loop
                    io.put_integer(fib_iterative(i))
                    io.put_new_line
                    i := i + 1
                end --loop                
            end --make
&lt;/codeblock&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4096</id>
      <timestamp>2006-04-11T05:00:33Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>indentation</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib(n: INTEGER) : INTEGER is
    require
        n &gt;= 0
    do
        inspect n
            when 0 then Result := 0
            when 1 then Result := 1
            else
                Result := fib(n-1) + fib(n-2)
        end --inspect
                
    end --fib
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative(n: INTEGER) : INTEGER is
    require
        n &gt;= 0
    local
        prev1, prev2 : INTEGER
        i : INTEGER
    do
        prev1 := 0
                
        -- Ensure correct behaviour for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end --loop
                
    end --fib_iterative
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make is
    local
        i : INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer(fib(i))
            io.put_new_line
            i := i + 1
        end --loop
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer(fib_iterative(i))
            io.put_new_line
            i := i + 1
        end --loop                
    end --make
&lt;/codeblock&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>4731</id>
      <timestamp>2006-05-14T20:05:03Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib(n: INTEGER) : INTEGER is
    require
        n &gt;= 0
    do
        inspect n
            when 0 then Result := 0
            when 1 then Result := 1
            else
                Result := fib(n-1) + fib(n-2)
        end --inspect
                
    end --fib
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative(n: INTEGER) : INTEGER is
    require
        n &gt;= 0
    local
        prev1, prev2 : INTEGER
        i : INTEGER
    do
        prev1 := 0
                
        -- Ensure correct behaviour for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end --loop
                
    end --fib_iterative
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

    creation
        make
    
    feature
        &lt;&lt;recursive fibonacci&gt;&gt;

        &lt;&lt;iterative fibonacci&gt;&gt;

        &lt;&lt;test&gt;&gt;

end --FIBONACCI
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make is
    local
        i : INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer(fib(i))
            io.put_new_line
            i := i + 1
        end --loop
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer(fib_iterative(i))
            io.put_new_line
            i := i + 1
        end --loop                
    end --make
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>10901</id>
      <timestamp>2007-08-18T05:41:03Z</timestamp>
      <contributor>
        <ip>68.108.252.200</ip>
      </contributor>
      <comment>Updated to Eiffel ECMA style</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER is
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make is
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>10902</id>
      <timestamp>2007-08-18T05:41:52Z</timestamp>
      <contributor>
        <ip>68.108.252.200</ip>
      </contributor>
      <comment>Forgot to remove some is which are not needed anymore in the Eiffel ECMA  specification</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11022</id>
      <timestamp>2007-10-03T01:07:46Z</timestamp>
      <contributor>
        <ip>212.72.30.140</ip>
      </contributor>
      <text xml:space="preserve">erricorc4
{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11040</id>
      <timestamp>2007-10-04T04:12:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/212.72.30.140|212.72.30.140]] ([[User_talk:212.72.30.140|212.72.30.140]]); changed back to last version by [[User:68.108.252.200|68.108.252.200]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11150</id>
      <timestamp>2007-10-12T18:42:37Z</timestamp>
      <contributor>
        <ip>213.61.157.93</ip>
      </contributor>
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{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11158</id>
      <timestamp>2007-10-12T20:08:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11298</id>
      <timestamp>2007-10-26T10:25:24Z</timestamp>
      <contributor>
        <ip>47.230.0.45</ip>
      </contributor>
      <text xml:space="preserve">c4trolo
{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11310</id>
      <timestamp>2007-10-26T14:43:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11425</id>
      <timestamp>2007-10-30T18:06:08Z</timestamp>
      <contributor>
        <ip>213.85.226.110</ip>
      </contributor>
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{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11426</id>
      <timestamp>2007-10-30T18:59:08Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11473</id>
      <timestamp>2007-11-06T15:09:35Z</timestamp>
      <contributor>
        <ip>212.124.234.37</ip>
      </contributor>
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{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11476</id>
      <timestamp>2007-11-06T17:10:46Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/212.124.234.37|212.124.234.37]] ([[User_talk:212.124.234.37|212.124.234.37]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11853</id>
      <timestamp>2007-12-29T21:20:06Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>passitb</comment>
      <text xml:space="preserve">rolmoncmon
{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>11902</id>
      <timestamp>2007-12-31T03:08:00Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>13240</id>
      <timestamp>2008-04-28T10:46:37Z</timestamp>
      <contributor>
        <ip>222.73.228.7</ip>
      </contributor>
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{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>13241</id>
      <timestamp>2008-04-28T11:15:21Z</timestamp>
      <contributor>
        <ip>83.77.82.185</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>15973</id>
      <timestamp>2009-01-17T08:00:20Z</timestamp>
      <contributor>
        <ip>221.120.250.106</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

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=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>15980</id>
      <timestamp>2009-01-17T15:59:31Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/221.120.250.106|221.120.250.106]] ([[User_talk:221.120.250.106|221.120.250.106]]); changed back to last version by [[User:83.77.82.185|83.77.82.185]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16125</id>
      <timestamp>2009-02-06T09:43:52Z</timestamp>
      <contributor>
        <ip>201.229.208.2</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

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=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16133</id>
      <timestamp>2009-02-06T10:57:32Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/201.229.208.2|201.229.208.2]] ([[User_talk:201.229.208.2|201.229.208.2]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16141</id>
      <timestamp>2009-02-06T14:13:49Z</timestamp>
      <contributor>
        <ip>67.19.148.234</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

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=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16144</id>
      <timestamp>2009-02-06T15:57:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/67.19.148.234|67.19.148.234]] ([[User_talk:67.19.148.234|67.19.148.234]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16151</id>
      <timestamp>2009-02-06T21:18:07Z</timestamp>
      <contributor>
        <ip>59.56.174.199</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

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=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16153</id>
      <timestamp>2009-02-06T21:21:56Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/59.56.174.199|59.56.174.199]] ([[User_talk:59.56.174.199|59.56.174.199]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
    <revision>
      <id>16860</id>
      <timestamp>2010-09-23T13:09:44Z</timestamp>
      <contributor>
        <username>Woooop</username>
        <id>2124</id>
      </contributor>
      <text xml:space="preserve">Daniel Mayne ate this page! :L</text>
    </revision>
    <revision>
      <id>16909</id>
      <timestamp>2010-09-23T15:53:34Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/Woooop|Woooop]] ([[User_talk:Woooop|Woooop]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

== Implementation ==

There are several different ways to implement the Fibonacci numbers in Eiffel.

=== Recursive ===

The most direct translation of the mathematical definition is as a recursive function, which can be implemented as an Eiffel feature as follows:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=
fib (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    do
        inspect n
        when 0 then Result := 0
        when 1 then Result := 1
        else
            Result := fib (n-1) + fib (n-2)
        end     
    end
&lt;/codeblock&gt;

=== Iteration ===

Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;iterative fibonacci&gt;&gt;=
fib_iterative (n: INTEGER): INTEGER
    require
        n_non_negative: n &gt;= 0
    local
        prev1, prev2: INTEGER
        i: INTEGER
    do
        prev1 := 0
                
            -- Ensure correct behavior for n = 0
        if n = 0 then 
            Result := 0
        else
            Result := 1
        end
                
        from
            i := 1
        until
            i &gt;= n
        loop
            prev2 := prev1
            prev1 := Result
            Result := prev2 + Result
            i := i + 1
        end     
    end
&lt;/codeblock&gt;

== Testing the &lt;code&gt;FIBONACCI&lt;/code&gt; class ==
We can pull both implementations together into a single class, in order to facilitate testing. 
&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;Fibonacci.e&gt;&gt;=
class FIBONACCI

create
    make
    
feature
    &lt;&lt;recursive fibonacci&gt;&gt;

    &lt;&lt;iterative fibonacci&gt;&gt;

    &lt;&lt;test&gt;&gt;

end
&lt;/codeblock&gt;

The test harness consists of the following feature:

&lt;codeblock language=&quot;eiffel&quot;&gt;
&lt;&lt;test&gt;&gt;=
make
    local
        i: INTEGER
    do
        from 
            i := 0
        until
           i &gt; 10
        loop
            io.put_integer (fib (i))
            io.put_new_line
            i := i + 1
        end
                
        from 
            i := 0
        until
            i &gt; 10
        loop
            io.put_integer (fib_iterative (i))
            io.put_new_line
            i := i + 1
        end
    end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Eiffel]]
[[Category:Programming language:Eiffel]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Erlang)</title>
    <id>3647</id>
    <revision>
      <id>10424</id>
      <timestamp>2007-06-02T14:37:10Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}


== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1]).

&lt;&lt;regular recursive fibonacci&gt;&gt;

&lt;&lt;tail recursive fibonacci&gt;&gt;

&lt;/codeblock&gt;



[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10427</id>
      <timestamp>2007-06-02T19:26:32Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added test section</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Test module ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, print_nfibos/2]).

%% print fibo arg. and result with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;

&lt;&lt;tail recursive fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to tail recursive &quot;fun fib:fibo2/1&quot; and you will get the same result.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10428</id>
      <timestamp>2007-06-02T19:29:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Test module */  comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;

&lt;&lt;tail recursive fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to tail recursive &quot;fun fib:fibo2/1&quot; and you will get the same result.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10432</id>
      <timestamp>2007-06-02T23:41:29Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Testing with the bytecode interpreter */ precision</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;

&lt;&lt;tail recursive fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to tail recursive &quot;fun fib:fibo2/1&quot; and you will get the same result, but faster.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10477</id>
      <timestamp>2007-06-11T02:58:51Z</timestamp>
      <contributor>
        <username>Horndude77</username>
        <id>164</id>
      </contributor>
      <comment>added fast algorithm</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Fast tail recursive fibonacci ==
Using the following formula we can derive a few useful identities to speed up the computation.
:&lt;math&gt;\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^n =
       \begin{pmatrix} F_{n+1} &amp; F_n \\
                       F_n     &amp; F_{n-1} \end{pmatrix}.
&lt;/math&gt;

Here are the useful identities:

:&lt;math&gt;F_{n+m} = F_{n-1} F_m + F_n F_{m+1} = (F_{n+1} - F_n) F_m + F_n F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{n+m+1} = F_n F_m + F_{n+1} F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{2n} = 2F_n F_{n+1} - F_n^2&lt;/math&gt;
:&lt;math&gt;F_{2n+1} = F_n^2 + F_{n+1}^2&lt;/math&gt;

If we can keep track of pairs of fibonacci numbers we end up with an algorithm identical to [[:Category:Exponentiation_by_squaring|exponentiation by squaring]]:

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fast fibonacci&gt;&gt;=
fibo3(N) -&gt;
    {Fib, _} = fibo3(N, {1, 1}, {0, 1}),
    Fib.

fibo3(0, _, Pair) -&gt; Pair;
fibo3(N, {Fib1, Fib2}, Pair) when N rem 2 == 0 -&gt;
    SquareFib1 = Fib1*Fib1,
    fibo3(N div 2, {2*Fib1*Fib2 - SquareFib1, SquareFib1 + Fib2*Fib2}, Pair);
fibo3(N, {FibA1, FibA2}=Pair, {FibB1, FibB2}) -&gt;
    fibo3(N-1, Pair, {FibA1*FibB2 + FibB1*(FibA2 - FibA1), FibA1*FibB1 + FibA2*FibB2}).
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, fibo3/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;
&lt;&lt;fast fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to &quot;fun fib:fibo2/1&quot; or &quot;fun fib:fibo3/1&quot; and you will get the same result, but faster.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16623</id>
      <timestamp>2010-01-13T09:17:40Z</timestamp>
      <contributor>
        <username>Murashi</username>
        <id>1964</id>
      </contributor>
      <minor/>
      <comment>/* Testing with the bytecode interpreter */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Fast tail recursive fibonacci ==
Using the following formula we can derive a few useful identities to speed up the computation.
:&lt;math&gt;\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^n =
       \begin{pmatrix} F_{n+1} &amp; F_n \\
                       F_n     &amp; F_{n-1} \end{pmatrix}.
&lt;/math&gt;

Here are the useful identities:

:&lt;math&gt;F_{n+m} = F_{n-1} F_m + F_n F_{m+1} = (F_{n+1} - F_n) F_m + F_n F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{n+m+1} = F_n F_m + F_{n+1} F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{2n} = 2F_n F_{n+1} - F_n^2&lt;/math&gt;
:&lt;math&gt;F_{2n+1} = F_n^2 + F_{n+1}^2&lt;/math&gt;

If we can keep track of pairs of fibonacci numbers we end up with an algorithm identical to [[:Category:Exponentiation_by_squaring|exponentiation by squaring]]:

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fast fibonacci&gt;&gt;=
fibo3(N) -&gt;
    {Fib, _} = fibo3(N, {1, 1}, {0, 1}),
    Fib.

fibo3(0, _, Pair) -&gt; Pair;
fibo3(N, {Fib1, Fib2}, Pair) when N rem 2 == 0 -&gt;
    SquareFib1 = Fib1*Fib1,
    fibo3(N div 2, {2*Fib1*Fib2 - SquareFib1, SquareFib1 + Fib2*Fib2}, Pair);
fibo3(N, {FibA1, FibA2}=Pair, {FibB1, FibB2}) -&gt;
    fibo3(N-1, Pair, {FibA1*FibB2 + FibB1*(FibA2 - FibA1), FibA1*FibB1 + FibA2*FibB2}).
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, fibo3/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;
&lt;&lt;fast fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the [http://www.college-paper.org/ college essay] output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to &quot;fun fib:fibo2/1&quot; or &quot;fun fib:fibo3/1&quot; and you will get the same result, but faster.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16624</id>
      <timestamp>2010-01-13T09:18:51Z</timestamp>
      <contributor>
        <username>Murashi</username>
        <id>1964</id>
      </contributor>
      <minor/>
      <comment>/* Fast tail recursive fibonacci */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Fast tail recursive fibonacci ==
Using the following formula we can derive a few useful identities to speed up the computation.
:&lt;math&gt;\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^n =
       \begin{pmatrix} F_{n+1} &amp; F_n \\
                       F_n     &amp; F_{n-1} \end{pmatrix}.
&lt;/math&gt;

Here are the useful identities:

:&lt;math&gt;F_{n+m} = F_{n-1} F_m + F_n F_{m+1} = (F_{n+1} - F_n) F_m + F_n F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{n+m+1} = F_n F_m + F_{n+1} F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{2n} = 2F_n F_{n+1} - F_n^2&lt;/math&gt;
:&lt;math&gt;F_{2n+1} = F_n^2 + F_{n+1}^2&lt;/math&gt;

If we can keep track of pairs of fibonacci numbers we end up with an algorithm [http://www.college-paper.org/ college papers] identical to [[:Category:Exponentiation_by_squaring|exponentiation by squaring]]:

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fast fibonacci&gt;&gt;=
fibo3(N) -&gt;
    {Fib, _} = fibo3(N, {1, 1}, {0, 1}),
    Fib.

fibo3(0, _, Pair) -&gt; Pair;
fibo3(N, {Fib1, Fib2}, Pair) when N rem 2 == 0 -&gt;
    SquareFib1 = Fib1*Fib1,
    fibo3(N div 2, {2*Fib1*Fib2 - SquareFib1, SquareFib1 + Fib2*Fib2}, Pair);
fibo3(N, {FibA1, FibA2}=Pair, {FibB1, FibB2}) -&gt;
    fibo3(N-1, Pair, {FibA1*FibB2 + FibB1*(FibA2 - FibA1), FibA1*FibB1 + FibA2*FibB2}).
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, fibo3/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;
&lt;&lt;fast fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the [http://www.college-paper.org/ college essay] output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to &quot;fun fib:fibo2/1&quot; or &quot;fun fib:fibo3/1&quot; and you will get the same result, but faster.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16625</id>
      <timestamp>2010-01-13T11:47:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Here are the fibo functions possible in this all functional language and runtime.

To test them we pass the function as parameter to the print_nfibos/2.

== The fibonacci function ==

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;regular recursive fibonacci&gt;&gt;=

fibo(0) -&gt; 0 ;
fibo(1) -&gt; 1 ;
fibo(N) when N &gt; 0 -&gt; fibo(N-1) + fibo(N-2) .

&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr( 0, Result, _Next) -&gt; Result ;  %% last recursion output

fibo2_tr( Iter, Result, Next) when Iter &gt; 0 -&gt; fibo2_tr( Iter -1, Next, Result + Next) .

fibo2( N) -&gt; fibo2_tr( N, 0, 1) .
&lt;/codeblock&gt;

== Fast tail recursive fibonacci ==
Using the following formula we can derive a few useful identities to speed up the computation.
:&lt;math&gt;\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^n =
       \begin{pmatrix} F_{n+1} &amp; F_n \\
                       F_n     &amp; F_{n-1} \end{pmatrix}.
&lt;/math&gt;

Here are the useful identities:

:&lt;math&gt;F_{n+m} = F_{n-1} F_m + F_n F_{m+1} = (F_{n+1} - F_n) F_m + F_n F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{n+m+1} = F_n F_m + F_{n+1} F_{m+1}&lt;/math&gt;
:&lt;math&gt;F_{2n} = 2F_n F_{n+1} - F_n^2&lt;/math&gt;
:&lt;math&gt;F_{2n+1} = F_n^2 + F_{n+1}^2&lt;/math&gt;

If we can keep track of pairs of fibonacci numbers we end up with an algorithm identical to [[:Category:Exponentiation_by_squaring|exponentiation by squaring]]:

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fast fibonacci&gt;&gt;=
fibo3(N) -&gt;
    {Fib, _} = fibo3(N, {1, 1}, {0, 1}),
    Fib.

fibo3(0, _, Pair) -&gt; Pair;
fibo3(N, {Fib1, Fib2}, Pair) when N rem 2 == 0 -&gt;
    SquareFib1 = Fib1*Fib1,
    fibo3(N div 2, {2*Fib1*Fib2 - SquareFib1, SquareFib1 + Fib2*Fib2}, Pair);
fibo3(N, {FibA1, FibA2}=Pair, {FibB1, FibB2}) -&gt;
    fibo3(N-1, Pair, {FibA1*FibB2 + FibB1*(FibA2 - FibA1), FibA1*FibB1 + FibA2*FibB2}).
&lt;/codeblock&gt;

== Test module ==

Let's print N fibonacci numbers in ascending order.

&lt;codeblock language=&quot;erlang&quot;&gt;
&lt;&lt;fib.erl&gt;&gt;=

-module(fib).
-export([fibo/1, fibo2/1, fibo3/1, print_nfibos/2]).

%% print fibo arg. and result, with function as parameter

print_nfibos( N, FiboFunc) -&gt; printfibos( N, FiboFunc, 0).

printfibos( 0, FiboFunc, N) -&gt;  %% last recursion
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]) ;

printfibos( Iter, FiboFunc, N) when Iter &gt; 0 -&gt; 
   Res = FiboFunc(N),
   io:fwrite(&quot;~w ~w~n&quot;, [N, Res]),
   printfibos( Iter -1, FiboFunc, N +1).

&lt;&lt;regular recursive fibonacci&gt;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;
&lt;&lt;fast fibonacci&gt;&gt;

&lt;/codeblock&gt;

== Testing with the bytecode interpreter ==

&lt;pre&gt;
erl&gt; c(fib). %% compile fib.erl to bytecode
{ok,fib}
&gt; fib:print_nfibos(10, fun fib:fibo/1). %% print n fibo values with function fib:fibo/1
&lt;/pre&gt;

produces the output

&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
ok
&lt;/pre&gt;

Change the second parameter to &quot;fun fib:fibo2/1&quot; or &quot;fun fib:fibo3/1&quot; and you will get the same result, but faster.

[[Category:Fibonacci numbers|Erlang]]
[[Category:Programming language:Erlang]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (FORTRAN)</title>
    <id>3910</id>
    <revision>
      <id>16492</id>
      <timestamp>2009-08-16T13:36:13Z</timestamp>
      <contributor>
        <username>Vital303</username>
        <id>1868</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in FORTRAN: 


&lt;codeblock language=&quot;fortran&quot;&gt;
&lt;&lt;fib.f90&gt;&gt;=
program main
  implicit none
  interface 
     function fib(n)
       integer, intent(in) :: n 
       integer :: fib
     end function fib
  end interface

  print *, fib(10)
end program main

recursive function fib (n)  result (fnum) 
  integer, intent(in)  :: n
  integer :: fnum
  if (n&lt;2) then 
     fnum = n
  else
     fnum = fib(n-1) + fib(n-2)
  endif
end function fib
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>16493</id>
      <timestamp>2009-08-16T13:37:47Z</timestamp>
      <contributor>
        <username>Vital303</username>
        <id>1868</id>
      </contributor>
      <comment>/* Implementation */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in FORTRAN: 


&lt;codeblock language=&quot;fortran&quot;&gt;
&lt;&lt;fib.f90&gt;&gt;=
program main
  implicit none
  interface 
     function fib(n)
       integer, intent(in) :: n 
       integer :: fib
     end function fib
  end interface

  print *, fib(10)
end program main

recursive function fib (n)  result (fnum) 
  integer, intent(in)  :: n
  integer :: fnum
  if (n&lt;2) then 
     fnum = n
  else
     fnum = fib(n-1) + fib(n-2)
  endif
end function fib
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|FORTRAN]]
[[Category:Programming language:FORTRAN]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16494</id>
      <timestamp>2009-08-16T13:38:26Z</timestamp>
      <contributor>
        <username>Vital303</username>
        <id>1868</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in FORTRAN: 
&lt;codeblock language=&quot;fortran&quot;&gt;
&lt;&lt;fib.f90&gt;&gt;=
program main
  implicit none
  interface 
     function fib(n)
       integer, intent(in) :: n 
       integer :: fib
     end function fib
  end interface

  print *, fib(10)
end program main

recursive function fib (n)  result (fnum) 
  integer, intent(in)  :: n
  integer :: fnum
  if (n&lt;2) then 
     fnum = n
  else
     fnum = fib(n-1) + fib(n-2)
  endif
end function fib
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|FORTRAN]]
[[Category:Programming language:FORTRAN]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16495</id>
      <timestamp>2009-08-16T13:40:56Z</timestamp>
      <contributor>
        <username>Vital303</username>
        <id>1868</id>
      </contributor>
      <minor/>
      <comment>Change category</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in FORTRAN: 
&lt;codeblock language=&quot;fortran&quot;&gt;
&lt;&lt;fib.f90&gt;&gt;=
program main
  implicit none
  interface 
     function fib(n)
       integer, intent(in) :: n 
       integer :: fib
     end function fib
  end interface

  print *, fib(10)
end program main

recursive function fib (n)  result (fnum) 
  integer, intent(in)  :: n
  integer :: fnum
  if (n&lt;2) then 
     fnum = n
  else
     fnum = fib(n-1) + fib(n-2)
  endif
end function fib
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|FORTRAN]]
[[Category:Programming language:Fortran]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Forth)</title>
    <id>2860</id>
    <revision>
      <id>8318</id>
      <timestamp>2006-12-09T19:02:24Z</timestamp>
      <contributor>
        <username>IanOsgood</username>
        <id>121</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11862</id>
      <timestamp>2007-12-29T21:31:53Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>eltpasbo</comment>
      <text xml:space="preserve">sitletoour
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11911</id>
      <timestamp>2007-12-31T03:09:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12400</id>
      <timestamp>2008-01-30T18:57:36Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>letocov</comment>
      <text xml:space="preserve">rolc4trelch
{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12421</id>
      <timestamp>2008-01-30T19:39:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12652</id>
      <timestamp>2008-02-29T18:35:07Z</timestamp>
      <contributor>
        <ip>61.133.87.226</ip>
      </contributor>
      <comment>c4telttrsitl</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12654</id>
      <timestamp>2008-02-29T19:18:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12734</id>
      <timestamp>2008-03-08T03:08:59Z</timestamp>
      <contributor>
        <ip>217.172.56.209</ip>
      </contributor>
      <comment>cliracc4tno</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12736</id>
      <timestamp>2008-03-08T07:29:01Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13001</id>
      <timestamp>2008-04-07T18:44:19Z</timestamp>
      <contributor>
        <ip>202.44.32.9</ip>
      </contributor>
      <comment>sitctaouacvi</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13005</id>
      <timestamp>2008-04-08T01:53:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.44.32.9|202.44.32.9]] ([[User_talk:202.44.32.9|202.44.32.9]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14793</id>
      <timestamp>2008-09-30T06:34:31Z</timestamp>
      <contributor>
        <ip>218.249.12.133</ip>
      </contributor>
      <comment>olochicaboc</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14795</id>
      <timestamp>2008-09-30T10:06:34Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15084</id>
      <timestamp>2008-10-17T19:46:26Z</timestamp>
      <contributor>
        <ip>202.239.172.2</ip>
      </contributor>
      <comment>oucerc4tc4tc</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15087</id>
      <timestamp>2008-10-17T21:25:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.239.172.2|202.239.172.2]] ([[User_talk:202.239.172.2|202.239.172.2]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The Fibonacci numbers in Forth: 

&lt;codeblock language=forth&gt;
&lt;&lt;fib.fs&gt;&gt;=
&lt;&lt;fib-iter&gt;&gt;
&lt;&lt;fib-rec&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

Note that even these implementations are only suitable for small values of ''n'', since the Fibonacci function grows exponentially and even on a 64-bit machine unsigned Forth cells can only hold the first 92 Fibonacci numbers.

== Iteration ==
This is the easiest way to calculate fibonacci numbers. The values of fib&lt;sub&gt;i-2&lt;/sub&gt; and fib&lt;sub&gt;i-1&lt;/sub&gt; are stored on the stack, to avoid all the recalculations in the recursive implementation.

'''( n -- f )''' is a ''stack comment'' documenting the inputs (n) and outputs (fib&lt;sub&gt;n&lt;/sub&gt;) of the function. It is only a comment, but this style is a de facto standard.

'''0 1 rot''' ( 0 1 n ) sets up the initial terms of the sequence and rotates the loop count to the top of the stack.

'''0 ?do ... loop''' ( n -- ) takes the count from the stack leaving the two previous Fibonacci terms on the stack for the body of the loop.  '''?do''' does an initial check against the limit compared to '''do'''.

'''over''' ( a b -- a b a ) copies the item under the top of the stack to the top. '''dup''' ( a -- a a ) duplicates the top item on the stack.

'''+''' ( a b -- a+b ) adds the top two items on the stack, in this case fib&lt;sub&gt;n-1&lt;/sub&gt; and fib&lt;sub&gt;n-2&lt;/sub&gt;, yielding fib&lt;sub&gt;n&lt;/sub&gt;.

'''swap''' ( a b -- b a ) swaps the top two items on the stack.

'''drop''' ( a -- ) gets rid of the extra term before returning from the function.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-iter&gt;&gt;=
: fib-iter ( n -- f )
  0 1 rot 0 ?do over + swap loop drop ;
&lt;/codeblock&gt;

== Recursive ==
This is a recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

'''dup 2 u&lt; if exit then''' returns n if it is 0 or 1.  u&lt; is an unsigned comparison compared to &lt;.

'''1-''' ( n -- n-1 ) is the decrement operator.

'''recurse''' causes the current function to recurse.

&lt;codeblock language=forth&gt;
&lt;&lt;fib-rec&gt;&gt;=
: fib-rec ( n -- f )
  dup 2 u&lt; if exit then
  1- dup recurse  swap 1- recurse  + ;
&lt;/codeblock&gt;

== Test driver ==
This test driver treats the two Fibonacci functions anonymously.  ''' ' fib-iter''' returns the ''execution token'' or ''xt'' of the word, and '''execute''' performs its action. An xt is similar to a C language function pointer.

&lt;codeblock language=forth&gt;
&lt;&lt;main&gt;&gt;=
: test ( xt count -- )
  0 do
    i over execute .
  loop drop ;

cr .( fib-iter 0..9: )  ' fib-iter 10 test
cr .( fib-rec  0..9: )  ' fib-rec  10 test
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Forth]]
[[Category:Programming language:Forth]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Haskell)</title>
    <id>1695</id>
    <revision>
      <id>2719</id>
      <timestamp>2006-03-06T22:59:31Z</timestamp>
      <contributor>
        <username>Ruediger Hanke</username>
        <id>16</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n &gt; 1   = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4732</id>
      <timestamp>2006-05-14T20:05:19Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n &gt; 1   = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6635</id>
      <timestamp>2006-07-06T16:04:30Z</timestamp>
      <contributor>
        <ip>69.233.174.102</ip>
      </contributor>
      <comment>Use pattern matching instead of guards</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6637</id>
      <timestamp>2006-07-06T17:37:02Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Recursion */ include both guards and pattern-matching</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. 
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10485</id>
      <timestamp>2007-06-15T21:40:45Z</timestamp>
      <contributor>
        <ip>62.216.205.56</ip>
      </contributor>
      <comment>/* Recursion */ Remark: Second def. of fib wrong for n &lt; 0.</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10491</id>
      <timestamp>2007-06-16T04:49:56Z</timestamp>
      <contributor>
        <username>Michael T. Richter</username>
        <id>780</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci.hs&gt;&gt;=
fibs :: [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

fastfib n = fibs !! n
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10492</id>
      <timestamp>2007-06-16T04:53:59Z</timestamp>
      <contributor>
        <username>Michael T. Richter</username>
        <id>780</id>
      </contributor>
      <comment>/* Infinite Lists */ Changed output file and structured code in a non-polluting way.</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11015</id>
      <timestamp>2007-10-03T01:05:18Z</timestamp>
      <contributor>
        <ip>88.198.25.14</ip>
      </contributor>
      <text xml:space="preserve">viouvi
{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11033</id>
      <timestamp>2007-10-04T04:09:57Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/88.198.25.14|88.198.25.14]] ([[User_talk:88.198.25.14|88.198.25.14]]); changed back to last version by [[User:Michael T. Richter|Michael T. Richter]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11217</id>
      <timestamp>2007-10-13T08:06:55Z</timestamp>
      <contributor>
        <ip>222.221.6.144</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11218</id>
      <timestamp>2007-10-13T08:18:12Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11332</id>
      <timestamp>2007-10-27T16:00:21Z</timestamp>
      <contributor>
        <ip>196.20.65.210</ip>
      </contributor>
      <text xml:space="preserve">racdar
{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11333</id>
      <timestamp>2007-10-27T16:02:18Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/196.20.65.210|196.20.65.210]] ([[User_talk:196.20.65.210|196.20.65.210]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11525</id>
      <timestamp>2007-11-10T01:00:57Z</timestamp>
      <contributor>
        <ip>147.8.104.142</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11527</id>
      <timestamp>2007-11-10T07:43:51Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11578</id>
      <timestamp>2007-11-15T22:49:16Z</timestamp>
      <contributor>
        <ip>146.145.112.131</ip>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11580</id>
      <timestamp>2007-11-16T00:14:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/146.145.112.131|146.145.112.131]] ([[User_talk:146.145.112.131|146.145.112.131]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11845</id>
      <timestamp>2007-12-29T21:08:55Z</timestamp>
      <contributor>
        <ip>80.156.84.40</ip>
      </contributor>
      <comment>conoor</comment>
      <text xml:space="preserve">lialtab
{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11894</id>
      <timestamp>2007-12-31T03:04:55Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11990</id>
      <timestamp>2008-01-09T13:53:14Z</timestamp>
      <contributor>
        <username>BasdaRclet</username>
        <id>1580</id>
      </contributor>
      <minor/>
      <comment>zelmon</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11995</id>
      <timestamp>2008-01-09T16:20:36Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/BasdaRclet|BasdaRclet]] ([[User_talk:BasdaRclet|BasdaRclet]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12389</id>
      <timestamp>2008-01-30T18:40:07Z</timestamp>
      <contributor>
        <ip>203.94.149.92</ip>
      </contributor>
      <comment>rolracbolaco</comment>
      <text xml:space="preserve">basvielctas
{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12410</id>
      <timestamp>2008-01-30T19:39:23Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/203.94.149.92|203.94.149.92]] ([[User_talk:203.94.149.92|203.94.149.92]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12768</id>
      <timestamp>2008-03-10T20:57:54Z</timestamp>
      <contributor>
        <ip>202.108.60.61</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12769</id>
      <timestamp>2008-03-10T21:36:39Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.108.60.61|202.108.60.61]] ([[User_talk:202.108.60.61|202.108.60.61]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12822</id>
      <timestamp>2008-03-14T23:59:23Z</timestamp>
      <contributor>
        <ip>211.119.242.40</ip>
      </contributor>
      <comment>acelc4tg</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12823</id>
      <timestamp>2008-03-15T01:27:14Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/211.119.242.40|211.119.242.40]] ([[User_talk:211.119.242.40|211.119.242.40]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12969</id>
      <timestamp>2008-04-04T08:04:44Z</timestamp>
      <contributor>
        <ip>122.1.110.151</ip>
      </contributor>
      <comment>liouclaor</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12970</id>
      <timestamp>2008-04-04T08:59:31Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13423</id>
      <timestamp>2008-05-21T00:46:15Z</timestamp>
      <contributor>
        <ip>72.55.188.165</ip>
      </contributor>
      <comment>trocropasa</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13425</id>
      <timestamp>2008-05-21T02:34:53Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/72.55.188.165|72.55.188.165]] ([[User_talk:72.55.188.165|72.55.188.165]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14147</id>
      <timestamp>2008-07-30T14:52:31Z</timestamp>
      <contributor>
        <ip>218.10.111.106</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14148</id>
      <timestamp>2008-07-30T16:01:41Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/218.10.111.106|218.10.111.106]] ([[User_talk:218.10.111.106|218.10.111.106]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14857</id>
      <timestamp>2008-10-07T08:05:52Z</timestamp>
      <contributor>
        <ip>216.155.133.68</ip>
      </contributor>
      <comment>rollino</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14860</id>
      <timestamp>2008-10-07T08:50:58Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/216.155.133.68|216.155.133.68]] ([[User_talk:216.155.133.68|216.155.133.68]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15047</id>
      <timestamp>2008-10-16T03:33:21Z</timestamp>
      <contributor>
        <ip>196.21.64.112</ip>
      </contributor>
      <comment>sitleto</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15057</id>
      <timestamp>2008-10-16T04:00:43Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/196.21.64.112|196.21.64.112]] ([[User_talk:196.21.64.112|196.21.64.112]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15128</id>
      <timestamp>2008-10-19T09:59:57Z</timestamp>
      <contributor>
        <ip>74.92.67.82</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15132</id>
      <timestamp>2008-10-19T14:22:00Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/74.92.67.82|74.92.67.82]] ([[User_talk:74.92.67.82|74.92.67.82]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15314</id>
      <timestamp>2008-10-26T15:27:06Z</timestamp>
      <contributor>
        <ip>66.206.33.3</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15315</id>
      <timestamp>2008-10-26T18:46:56Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15345</id>
      <timestamp>2008-10-29T16:07:15Z</timestamp>
      <contributor>
        <ip>61.219.11.146</ip>
      </contributor>
      <comment>ligett</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15346</id>
      <timestamp>2008-10-29T16:08:46Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.219.11.146|61.219.11.146]] ([[User_talk:61.219.11.146|61.219.11.146]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16601</id>
      <timestamp>2009-12-29T13:24:56Z</timestamp>
      <contributor>
        <username>Tomvdp</username>
        <id>1957</id>
      </contributor>
      <comment>/* Infinite Lists */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
A recursive implementation that calculates the nth Fibonacci number can be written remarkably close to the mathematical definition:

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_recursive.hs&gt;&gt;=
fib :: Integer -&gt; Integer
fib n
    | n == 0  = 0
    | n == 1  = 1
    | n  &gt; 1  = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

Alternatively, the recursive &lt;code&gt;fib&lt;/code&gt; function can be written using pattern-matching instead of guards. This looks less like the mathematical definition, but is more concise. (And also, strictly speaking, wrong for inputs less than zero, for fib doesn't terminate in this case.)
&lt;codeblock language=haskell&gt;
fib :: Integer -&gt; Integer
fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
&lt;/codeblock&gt;

==Infinite Lists==

The recursive definition is elegant but inefficient since for each call of &lt;code&gt;fib&lt;/code&gt; with &lt;math&gt;n &gt; 1&lt;/math&gt; we are recalculating Fibonacci numbers that had already been calculated before. Another issue is the stack, &lt;code&gt;fib&lt;/code&gt; is not tail recursive and so we risk a stack overflow.

We can utilize Haskell's laziness and define our Fibonacci numbers as an infinite lazy list. This is less readable, but takes only linear time.

&lt;codeblock language=haskell&gt;
&lt;&lt;fibonacci_fast.hs&gt;&gt;=
fib :: Int -&gt; Integer
fib n = fibs !! n
  where
    fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
&lt;/codeblock&gt;

where &lt;code&gt;zipWith&lt;/code&gt; is a function defined in the Haskell prelude which builds a new list by taking the head element of each list and applying a function (here &lt;code&gt;+&lt;/code&gt;) to them. For example:

&lt;codeblock&gt;
*Main&gt; zipWith (+) [0,1,2] [3, 4, 5] 
[3,5,7]
&lt;/codeblock&gt;

As the list is being calculated, &lt;code&gt;zipWith&lt;/code&gt; unfolds as follows:

&lt;codeblock&gt;
0 : 1 : zipWith (+) (0 : 1 : ...) (1 : ...)
0 : 1 : (0 + 1) : zipWith (+) (1 : 1 : ...) (1 : ...)
0 : 1 : 1 : (1 + 1) : zipWith (+) (1 : 2 : ...) (2 : ...)
0 : 1 : 1 : 2 : (1 + 2) : zipWith (+) (2 : 3 : ...) (3 : ...)
&lt;/codeblock&gt;

You can compare the speed yourself if you calculate the 25th Fibonacci number at the Haskell interactive prompt using &lt;code&gt;fib&lt;/code&gt; and &lt;code&gt;fastfib&lt;/code&gt;. &lt;code&gt;fib&lt;/code&gt; will take some time while &lt;code&gt;fastfib&lt;/code&gt; will give you the result instantly.

[[Category:Fibonacci numbers|Haskell]]
[[Category:Programming language:Haskell]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Hume)</title>
    <id>3801</id>
    <revision>
      <id>10026</id>
      <timestamp>2007-05-13T21:49:06Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>new</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

Lets bound nfib execution. 

The handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds

             -- alternate constraint
             --    within 10KB ;  -- Heap constraint (compiler only, does not work with interpreter)

&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=
box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))
handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting to 0\n&quot;)) -- set nextn to 0
;
&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=
box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))
handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;



[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]</text>
    </revision>
    <revision>
      <id>10027</id>
      <timestamp>2007-05-13T22:11:10Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added exec. and output</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

Lets bound nfib execution. 

The handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds

             -- alternate constraint
             --    within 10KB ;  -- Heap constraint (compiler only, does not work with interpreter)

&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

With the interpreter
&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]</text>
    </revision>
    <revision>
      <id>10028</id>
      <timestamp>2007-05-13T22:22:57Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added section divisors</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==
Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in time and space ==

Lets bound nfib execution. 

The &quot;Hume Report&quot; handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds

             -- alternate constraint
             --    within 10KB ;  -- Heap constraint (compiler only, it does not work with the interpreter)

&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wwiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]</text>
    </revision>
    <revision>
      <id>10029</id>
      <timestamp>2007-05-13T22:26:51Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Wwiring the automaton */ typo error</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==
Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in time and space ==

Lets bound nfib execution. 

The &quot;Hume Report&quot; handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds

             -- alternate constraint
             --    within 10KB ;  -- Heap constraint (compiler only, it does not work with the interpreter)

&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]</text>
    </revision>
    <revision>
      <id>10030</id>
      <timestamp>2007-05-13T22:33:31Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Bounding fibonacci in time and space */ added comments</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==
Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in time and space ==

Lets bound nfib execution. 

The &quot;Hume Report&quot; handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 10KB ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]</text>
    </revision>
    <revision>
      <id>10037</id>
      <timestamp>2007-05-14T10:25:23Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>added notes</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==
Let's use the regular recursive model, which execution grows exponentially, to experiment with execution bounding capabilities.
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in time and space ==

Lets bound nfib execution. 

The &quot;Hume Report&quot; handbook speaks about Time, Heap and Stack bounding. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 10KB ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10039</id>
      <timestamp>2007-05-15T09:07:20Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>expression retouch</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 10KB ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10042</id>
      <timestamp>2007-05-15T10:24:27Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* The Hume automaton */ added a state value cap</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 10KB ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 999 -&gt; (0, (*, *, &quot;Top value reached, resetting n to 0&quot;)) -- set nextn to 0, * means ignored output
 | n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10043</id>
      <timestamp>2007-05-15T10:26:08Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* The Hume automaton */ missing LF</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 10KB ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 999 -&gt; (0, (*, *, &quot;Top value reached, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10044</id>
      <timestamp>2007-05-15T11:06:17Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Bounding fibonacci in Time and Space */ more credible heap constraint</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 
&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The Hume automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow

match
 999 -&gt; (0, (*, *, &quot;Top value reached, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs
   (fib.n, output) ; --outputs
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10115</id>
      <timestamp>2007-05-16T07:58:23Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added comments and exception</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, EUnbeleivable

match
 999 -&gt; raise EUnbelievable &quot;999 reached&quot;
 | n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10117</id>
      <timestamp>2007-05-16T08:01:21Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>typo error</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, EUnbelievable

match
 999 -&gt; raise EUnbelievable &quot;999 reached&quot;
 | n -&gt; (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10118</id>
      <timestamp>2007-05-16T08:07:05Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* The automaton */  added if clause</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap '(' stack ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, EUnbelievable

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10119</id>
      <timestamp>2007-05-16T08:14:56Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Bounding fibonacci in Time and Space */  better names in description</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap_space '(' stack_space ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, EUnbelievable

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint. The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10120</id>
      <timestamp>2007-05-16T08:21:14Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Testing with the compiler */  added comments</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

The &quot;Hume Report&quot; handbook speaks about bounding syntax like ''within time ',' heap_space '(' stack_space ')' raise MyException''. (No examples at lang. site)
Note. It seems a work in progress, since the parser rejects the multiconstraint syntax specified in the handbook and the associated raise clause for user defined exceptions does not work.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.

                             -- alternate Heap constraint, raises HeapOverflow exception if surpassed.
             --    within 100B ;  --  (compiler only, it does not work with the interpreter)
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, EUnbelievable

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The heap overflow is raised even if you remove the heap constraint (it seems it does not work). The expected output string does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10126</id>
      <timestamp>2007-05-16T10:42:28Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>changing heap /stack constraint to the proper place</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an expression. Heap and Stack space bounding should be at ''box'' (thread) level.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
-- within 100B (50B)  -- heap_space ( stack_space) cost bounding -- I miss something to make it work

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Change to the Heap constraint.

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10127</id>
      <timestamp>2007-05-16T10:47:04Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Testing with the compiler */ removing unnecessary instruction</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an expression. Heap and Stack space bounding should be at ''box'' (thread) level.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
-- within 100B (50B)  -- heap_space ( stack_space) cost bounding -- I miss something to make it work

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10128</id>
      <timestamp>2007-05-16T11:29:18Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Bounding fibonacci in Time and Space */ comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

nfib :: integer -&gt; integer ;

nfib 0 = 1;
nfib 1 = 1;
nfib n = 1 + nfib(n-1) + nfib (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded nfib

bnfib :: integer -&gt; integer ;

bnfib n = (nfib n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout exception if surpassed.
&lt;/codeblock&gt;

== The automaton ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
-- within 100B (50B)  -- heap_space ( stack_space) cost bounding -- I miss something to make it work

match
 n -&gt; if n &gt;= 999 then raise EUnbelievable &quot;999 reached&quot;
                  else (n+1, (n, bnfib n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
Caught timeout, resetting n to 0
0 1
1 1
2 3
3 5
...
&lt;/pre&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 3
3 5
4 9
5 15
6 25
7 41
8 67
9 109
10 177
11 287
12 465
13 753
14 1219
15 1973
Heap overflow
0 1
1 1
2 3
3 5
4 9
5 15
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10219</id>
      <timestamp>2007-05-17T11:10:12Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>separate interpreter / compiler versions due to implementation differences</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

  -- bounded fibo

  bfibo :: integer -&gt; integer ;

  bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10220</id>
      <timestamp>2007-05-17T11:11:05Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Bounding fibonacci in Time and Space */  indentation</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10221</id>
      <timestamp>2007-05-17T11:12:56Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Wiring the automaton */ comments</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10222</id>
      <timestamp>2007-05-17T11:21:27Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>extra preliminary comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound nfib costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10223</id>
      <timestamp>2007-05-17T11:25:38Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Bounding fibonacci in Time and Space */ correction due to function rename</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10224</id>
      <timestamp>2007-05-17T11:27:02Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Testing with the compiler */ retouch</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 1;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
Caught timeout, resetting n to 0
0 1
1 1
2 2
3 3
4 5

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 1
1 1
2 2
3 3
4 5
5 8
6 13
7 21
8 34
9 55
10 89
11 144
12 233
13 377
14 610
15 987
16 1597
Heap overflow
0 1
1 1
2 2
3 3
4 5
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10233</id>
      <timestamp>2007-05-17T17:24:07Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>function def. correction</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10234</id>
      <timestamp>2007-05-17T17:45:28Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* The automaton (compiler version) */  added comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions are recoverable.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10262</id>
      <timestamp>2007-05-18T20:20:00Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* The automaton (compiler version) */ comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable&quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                  else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10263</id>
      <timestamp>2007-05-18T20:22:26Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>indentation and minor details</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ s ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable s -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- ++ string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10264</id>
      <timestamp>2007-05-18T20:30:04Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>better var name</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable msg -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n as string) ++ &quot; reached&quot;
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable msg -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10298</id>
      <timestamp>2007-05-22T08:37:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added compound exception</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Add first the compiler directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10299</id>
      <timestamp>2007-05-22T12:44:39Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>changed compiler instructions</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibonacci function&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Bounding fibonacci in Time and Space ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded fibonacci&gt;&gt;=

-- bounded fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 50ms ;  -- Time constraint to 50 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (future work)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;fibonacci function&gt;&gt; 

  &lt;&lt;bounded fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. The expected output string at HeapOverflow exception dispatch does not show, which may be understood if the Heap is invalidated.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10318</id>
      <timestamp>2007-05-25T09:48:14Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added tail recursive version</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 next result = result ;
fibo2_tr n next result = fibo2_tr (n-1) (result+next) next ; 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 1 0 ;
&lt;/codeblock&gt;


== Bounding fibonacci ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Time constraint to 10 miliseconds, still not working for compiler
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Time constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3

...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (not working, on to-do list)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. Compiler Exceptions do not output as expected, only the Exception name is printed. Time, Heap and Stack constraints seem not enabled.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10319</id>
      <timestamp>2007-05-25T10:01:15Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Testing with the interpreter */ result as obtained</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 next result = result ;
fibo2_tr n next result = fibo2_tr (n-1) (result+next) next ; 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 1 0 ;
&lt;/codeblock&gt;


== Bounding fibonacci ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Time constraint to 10 miliseconds, still not working for compiler
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Time constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (not working, on to-do list)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. Compiler Exceptions do not output as expected, only the Exception name is printed. Time, Heap and Stack constraints seem not enabled.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

wich produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10320</id>
      <timestamp>2007-05-25T10:19:41Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Testing with the compiler */  typo error</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 next result = result ;
fibo2_tr n next result = fibo2_tr (n-1) (result+next) next ; 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 1 0 ;
&lt;/codeblock&gt;


== Bounding fibonacci ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Time constraint to 10 miliseconds, still not working for compiler
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Time constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (not working, on to-do list)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. Compiler Exceptions do not output as expected, only the Exception name is printed. Time, Heap and Stack constraints seem not enabled.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10331</id>
      <timestamp>2007-05-26T20:26:36Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Tail recursive fibonacci */ comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

(fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) as (result, next)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci ==

Lets bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only, on to-do list) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Time constraint to 10 miliseconds, still not working for compiler
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Time constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (not working, on to-do list)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. Compiler Exceptions do not output as expected, only the Exception name is printed. Time, Heap and Stack constraints seem not enabled.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10332</id>
      <timestamp>2007-05-26T20:34:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Bounding fibonacci */ comments</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

(fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) as (result, next)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton (compiler version) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 100B (50B)  -- heap_space ( stack_space) cost bounding   (not working, on to-do list)

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. Compiler Exceptions do not output as expected, only the Exception name is printed. Time, Heap and Stack constraints seem not enabled.

&lt;pre&gt;
humec -lotsaspace fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
11 89
12 144
13 233
14 377
15 610
16 987
Heap overflow
0 0
1 1
2 1
3 2
4 3
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10333</id>
      <timestamp>2007-05-26T20:56:59Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>arranged compiler problem due to switch misuse</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

(fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) as (result, next)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints work correctly, the timeout system has some bug. 

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10334</id>
      <timestamp>2007-05-26T21:24:32Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Tail recursive fibonacci */ better expressed</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) as (result, next)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints work correctly, the timeout system has some bug. 

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10335</id>
      <timestamp>2007-05-26T21:29:32Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Tail recursive fibonacci */  oops</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next)

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints work correctly, the timeout system has some bug. 

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10336</id>
      <timestamp>2007-05-26T21:55:58Z</timestamp>
      <contributor>
        <ip>89.130.22.183</ip>
      </contributor>
      <comment>/* Tail recursive fibonacci */ comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of two consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints work correctly, the timeout system has some bug. 

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10395</id>
      <timestamp>2007-05-29T17:17:40Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>comment</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of two consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10396</id>
      <timestamp>2007-05-29T17:21:53Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Tail recursive fibonacci */ oops</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr n result next = fibo2_tr (n-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10429</id>
      <timestamp>2007-06-02T19:40:36Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>/* Tail recursive fibonacci */  better var name</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

fib&lt;sub&gt;n&lt;/sub&gt; = first item in (a, b)&lt;sub&gt;n&lt;/sub&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;
fibo2_tr iter result next = fibo2_tr (iter-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10436</id>
      <timestamp>2007-06-03T11:20:30Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>added guard equivalent domain check</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

exception EIllegalArg :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = if n &lt; 0 then raise EIllegalArg &quot;fibo negative argument: &quot; ++ (n as string)
                  else fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

fib&lt;sub&gt;n&lt;/sub&gt; = first item in (a, b)&lt;sub&gt;n&lt;/sub&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;                            -- last recursion, take first item
fibo2_tr iter result next = fibo2_tr (iter-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = if n &lt; 0 then raise EIllegalArg &quot;fibo2 negative argument: &quot; ++ (n as string)
                   else fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable, EIllegalArg

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
 | EIllegalArg msg -&gt; (0, (*, *, msg))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable, EIllegalArg
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
 | EIllegalArg msg -&gt; (0, (*, *, msg))

;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10437</id>
      <timestamp>2007-06-03T11:29:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>exception message</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

exception EIllegalArg :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = if n &lt; 0 then raise EIllegalArg &quot;fibo negative argument: &quot; ++ (n as string)
                  else fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

fib&lt;sub&gt;n&lt;/sub&gt; = first item in (a, b)&lt;sub&gt;n&lt;/sub&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;                            -- last recursion, take first item
fibo2_tr iter result next = fibo2_tr (iter-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = if n &lt; 0 then raise EIllegalArg &quot;fibo2 negative argument: &quot; ++ (n as string)
                   else fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable, EIllegalArg

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
 | EIllegalArg msg -&gt; (0, (*, *, &quot;IllegalArg: &quot; ++ msg ++ &quot;\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable, EIllegalArg
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
 | EIllegalArg msg -&gt; (0, (*, *, msg))

;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage, only the exception name is printed. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
    <revision>
      <id>10476</id>
      <timestamp>2007-06-10T23:14:07Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <comment>comments</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

Let's use the regular recursive model, which execution costs grows exponentially, to experiment with the language capabilities of bounding algorithms in Time, Heap and Stack costs.

As the compiler and the interpreter implement slightly different subsets of the language, separate code block versions are provided when needed.

== Declarations ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;I/O bindings and typedefs&gt;&gt;=

stream output to &quot;std_out&quot;;

type integer = int 32 ; 

exception EUnbelievable :: (integer, string) ;

exception EIllegalArg :: string ;

&lt;/codeblock&gt;

== The fibonacci function ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;recursive fibonacci&gt;&gt;=

fibo :: integer -&gt; integer ;

fibo 0 = 0;
fibo 1 = 1;
fibo n = if n &lt; 0 then raise EIllegalArg &quot;fibo negative argument: &quot; ++ (n as string)
                  else fibo(n-1) + fibo (n-2);
&lt;/codeblock&gt;

== Tail recursive fibonacci ==
Given that the series of pairs of consecutive fibo values can be expressed in the following way

S&lt;sub&gt;0&lt;/sub&gt; = (fib&lt;sub&gt;0&lt;/sub&gt;, fib&lt;sub&gt;1&lt;/sub&gt;) = (0, 1) ;

for n &gt;= 1, succ (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) = (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n+1&lt;/sub&gt;) =  (fib&lt;sub&gt;n&lt;/sub&gt;, fib&lt;sub&gt;n-1&lt;/sub&gt; + fib&lt;sub&gt;n&lt;/sub&gt;) ;

Naming (fib&lt;sub&gt;n-1&lt;/sub&gt;, fib&lt;sub&gt;n&lt;/sub&gt;) as (result, next) then succ (result, next) = (next, (result+next))

fib&lt;sub&gt;n&lt;/sub&gt; = first item in (a, b)&lt;sub&gt;n&lt;/sub&gt;

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;tail recursive fibonacci&gt;&gt;=

fibo2_tr :: integer -&gt; integer -&gt; integer -&gt; integer ;
fibo2_tr 0 result next = result ;                            -- last recursion, take first item
fibo2_tr iter result next = fibo2_tr (iter-1) next (result+next); 

fibo2 :: integer -&gt; integer ;
fibo2 n = if n &lt; 0 then raise EIllegalArg &quot;fibo2 negative argument: &quot; ++ (n as string)
                   else fibo2_tr n 0 1;
&lt;/codeblock&gt;

== Bounding fibonacci in Time ==

Let's bound fibo costs. 

Only time bounding is admitted in an &lt;expr&gt;. Heap and Stack space bounding is admitted in the context of a within-constraint on boxes (compiler only) (Hume Report 2.1.4).

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded regular recursive fibonacci&gt;&gt;=

-- bounded regular recursive fibo

bfibo :: integer -&gt; integer ;

bfibo n = (fibo n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;


&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;bounded tail recursive fibonacci&gt;&gt;=

-- bounded tail recursive fibo

bfibo2 :: integer -&gt; integer ;

bfibo2 n = (fibo2 n) within 10ms ;  -- Constraint to 10 miliseconds, raises Timeout
&lt;/codeblock&gt;

== The automaton (interpreter version) ==

Main program loop.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the interpreter&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, EUnbelievable, EIllegalArg

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo2 n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | EUnbelievable (n, msg) -&gt; (0, (*, *, &quot;Unbelievable: &quot; ++ (n as string) ++ msg ++ &quot;, resetting n to 0\n&quot;))
 | EIllegalArg msg -&gt; (0, (*, *, &quot;IllegalArg: &quot; ++ msg ++ &quot;\n&quot;))
;

&lt;/codeblock&gt;

== Wiring the automaton ==
Wiring thread level box I/O
&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;wirings&gt;&gt;=

wire fib 
   (fib.nextn initially 0) --inputs (get fib.n from fib.nextn)
   (fib.n, output) ; --outputs (put fib.nextn to fib.n, result to output)
&lt;/codeblock&gt;

== The whole program (interpreter version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-i.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;tail recursive fibonacci&gt;&gt;

  &lt;&lt;bounded tail recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the interpreter&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the interpreter ==

&lt;pre&gt;
./hume fibo-i.hume
&lt;/pre&gt;

Produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
6 8
7 13
8 21
9 34
10 55
Caught timeout, resetting n to 0
0 0
1 1
2 1
3 2
4 3
...
&lt;/pre&gt;

== The automaton, heap and stack bounded  (compiler only) ==

Main program loop. Heap and Stack are discarded after each cycle making garbage collection unneeded. Because of this HeapOverflow or StackOverflow exceptions do not end execution.

It must be compiled without the switch &quot;-lotsaspace&quot; which overrides the Heap and Stack constraint. If no Heap and Stack constraint is set, then &quot;-lotsaspace&quot; is needed since they seem to default to 0, expecting an explicit setting.

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;automaton box for the compiler&gt;&gt;=

box fib
in (n::integer)
out (nextn::integer, result::(integer, integer, string))
handles Timeout, HeapOverflow, StackOverflow, EUnbelievable, EIllegalArg
within 400B (200B)  -- heap_space ( stack_space) cost bounding

match
 n -&gt; if n &gt;= 99 then raise EUnbelievable (n, &quot;reached&quot;)
                 else (n+1, (n, bfibo n, &quot;\n&quot;))

handle
 Timeout e -&gt; ( 0, (*, *, &quot;Caught timeout, resetting n to 0\n&quot;)) -- set nextn to 0, * means ignored output
 | HeapOverflow e -&gt; ( 0, (*, *, &quot;Caught HeapOverflow, resetting n to 0\n&quot;))
 | StackOverflow e -&gt; ( 0, (*, *, &quot;Caught StackOverflow, resetting n to 0\n&quot;))
 | EUnbelievable (n, msg) -&gt; (0, (n, *, &quot;Unbelievable value reached, resetting n to 0\n&quot;)) -- string concat. not admitted here by compiler
 | EIllegalArg msg -&gt; (0, (*, *, msg))

;

&lt;/codeblock&gt;

== The whole program (compiler version) ==

&lt;codeblock language=&quot;hume&quot;&gt;
&lt;&lt;fibo-c.hume&gt;&gt;=

  &lt;&lt;I/O bindings and typedefs&gt;&gt;

  &lt;&lt;recursive fibonacci&gt;&gt; 

  &lt;&lt;bounded regular recursive fibonacci&gt;&gt; 

  &lt;&lt;automaton box for the compiler&gt;&gt;

  &lt;&lt;wirings&gt;&gt; 
&lt;/codeblock&gt;

== Testing with the compiler ==

Lets compile and try.
Compile from the compiler folder
Add first the . directory to the PATH.

Note. There is an error about output that I can't manage. Exceptions don't show the expected output, they only print the exception name. Heap and Stack constraints generate or not the corresponding exceptions adjusting values, but I could not adjust the time constraint of ''bfibo'' to show its exception.

&lt;pre&gt;
humec fibo-c.hume
./fibo-c
&lt;/pre&gt;

which produces the output
&lt;pre&gt;
0 0
1 1
2 1
3 2
4 3
5 5
Stack overflow
0 0
1 1
2 1
3 2
...
&lt;/pre&gt;

[[Category:Fibonacci numbers|Hume]]
[[Category:Programming language:Hume]]
[[Category:Environment:Linux]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Icon)</title>
    <id>2205</id>
    <revision>
      <id>5364</id>
      <timestamp>2006-05-29T22:10:16Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>recursive, iterative</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;25 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;25 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5365</id>
      <timestamp>2006-05-29T22:11:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>test: 30 numbers</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11858</id>
      <timestamp>2007-12-29T21:24:42Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>norolmonricn</comment>
      <text xml:space="preserve">corocade
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11907</id>
      <timestamp>2007-12-31T03:08:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12396</id>
      <timestamp>2008-01-30T18:53:02Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>bocertrvardo</comment>
      <text xml:space="preserve">acelcn
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12417</id>
      <timestamp>2008-01-30T19:39:46Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12433</id>
      <timestamp>2008-01-31T00:40:10Z</timestamp>
      <contributor>
        <ip>218.106.244.90</ip>
      </contributor>
      <comment>dronzelsite</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12440</id>
      <timestamp>2008-01-31T05:25:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/218.106.244.90|218.106.244.90]] ([[User_talk:218.106.244.90|218.106.244.90]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12511</id>
      <timestamp>2008-02-18T18:06:09Z</timestamp>
      <contributor>
        <ip>60.191.220.45</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12525</id>
      <timestamp>2008-02-18T22:57:15Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/60.191.220.45|60.191.220.45]] ([[User_talk:60.191.220.45|60.191.220.45]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12846</id>
      <timestamp>2008-03-18T03:57:15Z</timestamp>
      <contributor>
        <ip>200.130.24.47</ip>
      </contributor>
      <comment>sitc4t</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12857</id>
      <timestamp>2008-03-18T06:11:07Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.130.24.47|200.130.24.47]] ([[User_talk:200.130.24.47|200.130.24.47]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13250</id>
      <timestamp>2008-04-30T12:49:46Z</timestamp>
      <contributor>
        <ip>193.147.184.49</ip>
      </contributor>
      <comment>liracrocol</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13251</id>
      <timestamp>2008-04-30T13:41:16Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13771</id>
      <timestamp>2008-06-24T18:35:53Z</timestamp>
      <contributor>
        <ip>208.69.181.72</ip>
      </contributor>
      <comment>pasacdombo</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13772</id>
      <timestamp>2008-06-24T20:02:37Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/208.69.181.72|208.69.181.72]] ([[User_talk:208.69.181.72|208.69.181.72]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14098</id>
      <timestamp>2008-07-24T14:31:07Z</timestamp>
      <contributor>
        <ip>194.97.50.4</ip>
      </contributor>
      <comment>riccoal</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14100</id>
      <timestamp>2008-07-24T15:36:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/194.97.50.4|194.97.50.4]] ([[User_talk:194.97.50.4|194.97.50.4]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14501</id>
      <timestamp>2008-08-28T15:39:18Z</timestamp>
      <contributor>
        <ip>61.145.121.124</ip>
      </contributor>
      <comment>vargetoug</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14502</id>
      <timestamp>2008-08-28T15:51:20Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.145.121.124|61.145.121.124]] ([[User_talk:61.145.121.124|61.145.121.124]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15230</id>
      <timestamp>2008-10-23T11:46:21Z</timestamp>
      <contributor>
        <ip>212.118.158.68</ip>
      </contributor>
      <comment>rooudelel</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15233</id>
      <timestamp>2008-10-23T12:06:19Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/212.118.158.68|212.118.158.68]] ([[User_talk:212.118.158.68|212.118.158.68]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15370</id>
      <timestamp>2008-10-30T21:02:41Z</timestamp>
      <contributor>
        <ip>201.65.138.4</ip>
      </contributor>
      <comment>elgetct</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15372</id>
      <timestamp>2008-10-30T21:16:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/201.65.138.4|201.65.138.4]] ([[User_talk:201.65.138.4|201.65.138.4]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Icon_programming_language Icon].

&lt;codeblock language=icon&gt;
&lt;&lt;fib.i&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=icon&gt;
&lt;&lt;fib&gt;&gt;=
procedure fib(n)
	if n&lt;2 then return n
	else return fib(n-1)+fib(n-2)
end



&lt;/codeblock&gt;

== Iterative ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, we store the two previous numbers in local variables.

&lt;codeblock language=icon&gt;
&lt;&lt;fastfib&gt;&gt;=
procedure fastfib(n)
	local prevfib, currfib, nfib
	nfib:=2
	prevfib:=1
	currfib:=1
	while nfib&lt;n do {
		prevfib:=:currfib
		currfib+:=prevfib
		nfib+:=1
	}
	return currfib
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=icon&gt;
&lt;&lt;test&gt;&gt;=
procedure main()
	local n

	n:=1
	while n&lt;30 do {
		write(fib(n))
		n+:=1 
	}

	n:=1
	while n&lt;30 do {
		write(fastfib(n))
		n+:=1 
	}
end
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Icon]]
[[Category:Programming language:Icon]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Java)</title>
    <id>3589</id>
    <revision>
      <id>2621</id>
      <timestamp>2006-03-06T18:27:57Z</timestamp>
      <contributor>
        <username>HairyFotr</username>
        <id>26</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console.

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n){
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}
    
	public static void main(String[] args){
		for (int i=0;i&lt;10;i++)
			System.out.print(fib(i)+&quot;, &quot;);
	}
}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2630</id>
      <timestamp>2006-03-06T20:18:03Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>A more efficient implementation and note about Java integers only holding first 46</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console.

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n){
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}
    
	public static void main(String[] args){
		for (int i=0;i&lt;10;i++)
			System.out.print(fib(i)+&quot;, &quot;);
	}
}
&lt;/codeblock&gt;

Based directly on the definition, this algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n){
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}
    
	public static void main(String[] args){
		for (int i=0;i&lt;10;i++)
			System.out.print(fib(i)+&quot;, &quot;);
	}
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2634</id>
      <timestamp>2006-03-06T20:20:13Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Factor our test main</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console.

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

Based directly on the definition, this algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers. We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>2642</id>
      <timestamp>2006-03-06T20:25:16Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <comment>Tweak to fix cats</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

Based directly on the definition, this algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers. We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3726</id>
      <timestamp>2006-04-03T16:18:04Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Recursion */  add a few section headers</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers. 

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3734</id>
      <timestamp>2006-04-03T17:57:12Z</timestamp>
      <contributor>
        <username>Deco</username>
        <id>1</id>
      </contributor>
      <minor/>
      <comment>Tweak</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers. 

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4733</id>
      <timestamp>2006-05-14T20:05:39Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers. 

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10792</id>
      <timestamp>2007-07-28T03:10:13Z</timestamp>
      <contributor>
        <ip>218.199.228.253</ip>
      </contributor>
      <comment>/* Iteration */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
		if (n == 0) return 0;
		if (n == 1) return 1;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10923</id>
      <timestamp>2007-08-23T20:24:45Z</timestamp>
      <contributor>
        <ip>198.103.162.158</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2)
                   return n;
		return fib(n-1)+fib(n-2);
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10935</id>
      <timestamp>2007-08-31T04:14:51Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Recursion */ clarity</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Testing ==
We can test both of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10936</id>
      <timestamp>2007-08-31T04:54:50Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>Add memoized implementation with BigInts</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized ==

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;


== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10937</id>
      <timestamp>2007-08-31T05:03:36Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Memoized */ explanatory text</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14788</id>
      <timestamp>2008-09-29T11:20:44Z</timestamp>
      <contributor>
        <ip>129.215.63.153</ip>
      </contributor>
      <comment>/* Iteration */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14896</id>
      <timestamp>2008-10-09T06:25:12Z</timestamp>
      <contributor>
        <ip>61.186.95.141</ip>
      </contributor>
      <comment>orricvar</comment>
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{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14898</id>
      <timestamp>2008-10-09T06:47:24Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.186.95.141|61.186.95.141]] ([[User_talk:61.186.95.141|61.186.95.141]]); changed back to last version by [[User:129.215.63.153|129.215.63.153]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14990</id>
      <timestamp>2008-10-13T15:19:31Z</timestamp>
      <contributor>
        <ip>79.99.43.128</ip>
      </contributor>
      <comment>cavidomorc</comment>
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{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14992</id>
      <timestamp>2008-10-13T15:26:38Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15200</id>
      <timestamp>2008-10-21T09:54:17Z</timestamp>
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      </contributor>
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{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15209</id>
      <timestamp>2008-10-21T12:40:52Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/58.147.6.147|58.147.6.147]] ([[User_talk:58.147.6.147|58.147.6.147]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15381</id>
      <timestamp>2008-10-31T19:34:16Z</timestamp>
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{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15383</id>
      <timestamp>2008-10-31T22:49:03Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.150.176.219|200.150.176.219]] ([[User_talk:200.150.176.219|200.150.176.219]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15384</id>
      <timestamp>2008-11-01T02:00:03Z</timestamp>
      <contributor>
        <ip>83.227.158.70</ip>
      </contributor>
      <comment>acelric</comment>
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{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15385</id>
      <timestamp>2008-11-01T02:19:47Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/83.227.158.70|83.227.158.70]] ([[User_talk:83.227.158.70|83.227.158.70]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first to fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15481</id>
      <timestamp>2008-11-24T07:10:32Z</timestamp>
      <contributor>
        <ip>65.189.241.56</ip>
      </contributor>
      <comment>/* Memoized recursion */ to -&gt; two</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first two fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15667</id>
      <timestamp>2008-12-23T09:54:04Z</timestamp>
      <contributor>
        <ip>117.197.247.51</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;
//nice program

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first two fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15670</id>
      <timestamp>2008-12-23T20:01:13Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/117.197.247.51|117.197.247.51]] ([[User_talk:117.197.247.51|117.197.247.51]]); changed back to last version by [[User:65.189.241.56|65.189.241.56]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}} 

==Recursion==
This simple java program uses recursion to print the first 10 Fibonacci numbers to the console. 

&lt;codeblock language=java&gt;
&lt;&lt;Fibonacci.java&gt;&gt;=
public class Fibonacci {
	public static int fib(int n) {
                if (n &lt; 2) {
                   return n;
                }
                else {
		   return fib(n-1)+fib(n-2);
                }
	}

        &lt;&lt;test main&gt;&gt;    
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues:

&lt;codeblock language=java&gt;
&lt;&lt;FibonacciIterative.java&gt;&gt;=
public class FibonacciIterative {
	public static int fib(int n) {
                int prev1=0, prev2=1;
                for(int i=0; i&lt;n; i++) {
                    int savePrev1 = prev1;
                    prev1 = prev2;
                    prev2 = savePrev1 + prev2;
                }
                return prev1;
	}

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

Note that even this implementation is only suitable for small values of ''n'', since the Fibonacci function grows exponentially and 32-bit signed Java integers can only hold the first 46 Fibonacci numbers.

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. The iterative solution is faster, but still repeats a lot of calculations when computing successive fibonacci numbers. To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations.

We first establish a memoization &quot;cache&quot;, which stores previously computed fibonacci numbers. In this case we use an ArrayList, initialized with the first two fibonacci numbers, as the cache. Note that we have also moved from using &lt;code&gt;int&lt;/code&gt;s to using Java's &lt;code&gt;BigInteger&lt;/code&gt; class, which provides arbitrary-precision integers. As a result, the memoized implementation can also compute much larger fibonacci numbers than the previous solutions (although they too could have been implemented using &lt;code&gt;BigInteger&lt;/code&gt;s.

&lt;codeblock language=java&gt;
&lt;&lt;Memoization cache&gt;&gt;=
private static ArrayList&lt;BigInteger&gt; fibCache = new ArrayList&lt;BigInteger&gt;();
static {
      fibCache.add(BigInteger.ZERO);
      fibCache.add(BigInteger.ONE);
}
&lt;/codeblock&gt;

The actual implementation of the &lt;code&gt;fib()&lt;/code&gt; function using memoization looks quite similar to the basic recursive function. The difference is that a new fibonacci number is only computed if the cache does not already contain the necessary value. Newly computed fibonacci numbers are added to the cache, so that they become available during later calls to &lt;code&gt;fib()&lt;/code&gt;.
 
&lt;codeblock language=java&gt;
&lt;&lt;FibonacciMemoized.java&gt;&gt;=
import java.math.BigInteger;
import java.util.ArrayList;

public class FibonacciMemoized {
        
       &lt;&lt;Memoization cache&gt;&gt;

       public static BigInteger fib(int n) {
              if (n &gt;= fibCache.size()) {
                  fibCache.add(n, fib(n-1).add(fib(n-2)));
              }
              return fibCache.get(n);
       }

        &lt;&lt;test main&gt;&gt;
}
&lt;/codeblock&gt;

== Testing ==
We can test all of the above implementations up to this limit using a simple loop:

&lt;codeblock language=java&gt;
&lt;&lt;test main&gt;&gt;=
public static void main(String[] args) {
    for (int i=0; i&lt;=46; i++)
        System.out.print(fib(i)+&quot;, &quot;);
}
&lt;/codeblock&gt;

&lt;!-- TODO: Time both impls and compare --&gt;

[[Category:Fibonacci numbers|Java]]
[[Category:Programming language:Java]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (JavaScript)</title>
    <id>2222</id>
    <revision>
      <id>5547</id>
      <timestamp>2006-06-01T05:57:34Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>initial rev, based on C version</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?1:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
This is a faster, but also much more complicated way to calculate fibonacci numbers. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [1,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [1,1,2]
    fibs.shift();
 ''fibs'' now [1,2]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;=n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5773</id>
      <timestamp>2006-06-03T02:30:49Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>/* Iteration */ slighty better explanation, lifted from Java fibonacci article</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?1:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [1,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [1,1,2]
    fibs.shift();
 ''fibs'' now [1,2]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;=n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5774</id>
      <timestamp>2006-06-03T03:12:41Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Recursive */ bugfix</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [1,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [1,1,2]
    fibs.shift();
 ''fibs'' now [1,2]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;=n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5775</id>
      <timestamp>2006-06-03T03:16:25Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>/* Iteration */ bugfix</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11861</id>
      <timestamp>2007-12-29T21:30:39Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>boouc4t</comment>
      <text xml:space="preserve">trocaceltac4
{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11910</id>
      <timestamp>2007-12-31T03:09:25Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11992</id>
      <timestamp>2008-01-09T15:09:56Z</timestamp>
      <contributor>
        <ip>211.38.131.22</ip>
      </contributor>
      <comment>varolobaslac</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11997</id>
      <timestamp>2008-01-09T16:30:49Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/211.38.131.22|211.38.131.22]] ([[User_talk:211.38.131.22|211.38.131.22]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12147</id>
      <timestamp>2008-01-22T21:52:22Z</timestamp>
      <contributor>
        <ip>220.128.131.90</ip>
      </contributor>
      <comment>c4tligett</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12148</id>
      <timestamp>2008-01-23T02:33:36Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12399</id>
      <timestamp>2008-01-30T18:57:10Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>comontrcnari</comment>
      <text xml:space="preserve">varpasc
{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12420</id>
      <timestamp>2008-01-30T19:39:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12506</id>
      <timestamp>2008-02-17T19:19:40Z</timestamp>
      <contributor>
        <ip>202.84.17.42</ip>
      </contributor>
      <comment>trocacre</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12521</id>
      <timestamp>2008-02-18T22:55:44Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.84.17.42|202.84.17.42]] ([[User_talk:202.84.17.42|202.84.17.42]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12671</id>
      <timestamp>2008-03-02T23:25:41Z</timestamp>
      <contributor>
        <ip>222.159.133.158</ip>
      </contributor>
      <comment>delgetvira</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12676</id>
      <timestamp>2008-03-03T08:08:19Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12764</id>
      <timestamp>2008-03-10T04:03:22Z</timestamp>
      <contributor>
        <ip>218.16.224.243</ip>
      </contributor>
      <comment>dronoulir</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12765</id>
      <timestamp>2008-03-10T04:34:40Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/218.16.224.243|218.16.224.243]] ([[User_talk:218.16.224.243|218.16.224.243]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13435</id>
      <timestamp>2008-05-22T14:38:15Z</timestamp>
      <contributor>
        <ip>137.164.143.110</ip>
      </contributor>
      <comment>rotrri</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13436</id>
      <timestamp>2008-05-22T15:45:21Z</timestamp>
      <contributor>
        <ip>81.62.69.144</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14197</id>
      <timestamp>2008-08-05T14:44:15Z</timestamp>
      <contributor>
        <ip>121.11.69.194</ip>
      </contributor>
      <comment>rogetalsitge</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14200</id>
      <timestamp>2008-08-05T19:25:45Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/121.11.69.194|121.11.69.194]] ([[User_talk:121.11.69.194|121.11.69.194]]); changed back to last version by [[User:81.62.69.144|81.62.69.144]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14221</id>
      <timestamp>2008-08-09T06:57:37Z</timestamp>
      <contributor>
        <ip>117.74.97.174</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14226</id>
      <timestamp>2008-08-09T13:46:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14844</id>
      <timestamp>2008-10-07T04:56:53Z</timestamp>
      <contributor>
        <ip>207.61.213.196</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14853</id>
      <timestamp>2008-10-07T05:45:48Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15119</id>
      <timestamp>2008-10-19T05:27:51Z</timestamp>
      <contributor>
        <ip>59.144.46.25</ip>
      </contributor>
      <comment>ctrlicrozel</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15125</id>
      <timestamp>2008-10-19T05:39:58Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15172</id>
      <timestamp>2008-10-20T22:59:44Z</timestamp>
      <contributor>
        <ip>203.113.137.169</ip>
      </contributor>
      <comment>rolligete</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15178</id>
      <timestamp>2008-10-21T00:36:10Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/203.113.137.169|203.113.137.169]] ([[User_talk:203.113.137.169|203.113.137.169]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15195</id>
      <timestamp>2008-10-21T08:17:11Z</timestamp>
      <contributor>
        <ip>61.17.193.11</ip>
      </contributor>
      <comment>orvibasololi</comment>
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{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15204</id>
      <timestamp>2008-10-21T12:39:18Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.17.193.11|61.17.193.11]] ([[User_talk:61.17.193.11|61.17.193.11]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16831</id>
      <timestamp>2010-09-01T14:48:48Z</timestamp>
      <contributor>
        <username>El pablo</username>
        <id>2110</id>
      </contributor>
      <minor/>
      <comment>/* Iteration */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.shift();
     fibs.push(fibs[0] + fibs[1]);
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>16832</id>
      <timestamp>2010-09-02T05:59:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/El pablo|El pablo]] ([[User_talk:El pablo|El pablo]]); changed back to last version by [[User:Ce|Ce]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in JavaScript: 

&lt;codeblock language=javascript&gt;
&lt;&lt;fib.js&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fastfib&gt;&gt;
&lt;&lt;testdriver&gt;&gt;
&lt;/codeblock&gt;

== Recursive ==
This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=javascript&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n){
  return n&lt;2?n:fib(n-1)+fib(n-2);
}
&lt;/codeblock&gt;

== Iteration ==
Although it is based directly on the definition of a Fibonacci number, the recursive Fibonacci algorithm is extremely expensive, requiring time &lt;math&gt;O(2^n)&lt;/math&gt;. It also performs a huge amount of redundant work because it computes many Fibonnaci values from scratch many times. A simple linear-time iterative approach which calculates each value of fib successively can avoid these issues. The result from the 2 last calculations are stored in a dynamic array, to avoid all the recalculations in the recursive implementation.
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n){
   var i;
   var fibs = new Array();
&lt;/codeblock&gt;

We start by &lt;code&gt;push&lt;/code&gt;ing the first two values into the array, which is initially empty.

&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   fibs.push(0);
   fibs.push(1);
&lt;/codeblock&gt;

The heart of the function is a for-loop. In each iteration of the loop we first &lt;code&gt;push&lt;/code&gt; the sum of the current values of the array onto the end of the array, and then &lt;code&gt;shift&lt;/code&gt; the array to remove the first element of the array. Thus, the first iteration will proceed like this:

 ''fibs'' initially [0,1]
    fibs.push(fibs[0] + fibs[1]);
 ''fibs'' now [0,1,1]
    fibs.shift();
 ''fibs'' now [1,1]

The actual implementation is
&lt;codeblock language=javascript&gt;
&lt;&lt;fastfib&gt;&gt;=
   for(i=0; i&lt;n; i++){
     fibs.push(fibs[0] + fibs[1]);
     fibs.shift();
   }  
   return fibs[0];
}
&lt;/codeblock&gt;

== Test driver ==
&lt;codeblock language=javascript&gt;
&lt;&lt;testdriver&gt;&gt;=
for(i=0; i&lt;=20; i++) document.write(&quot;fib(&quot; + i + &quot;) = &quot; + fib(i) + &quot;&lt;br/&gt;&quot;);
for(i=0; i&lt;=20; i++) document.write(&quot;fastfib(&quot; + i + &quot;) = &quot; + fastfib(i) + &quot;&lt;br/&gt;&quot;);
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|JavaScript]]
[[Category:Programming language:JavaScript]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Lisp)</title>
    <id>1823</id>
    <revision>
      <id>3600</id>
      <timestamp>2006-03-24T23:19:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Initial upload</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [[http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci]] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Implementation ==

This is a recursive implmentation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

== Test driver ==

This function prints the fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib ~D)=~D~%&quot; start (fib start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib 1)=1&lt;br&gt;
(fib 2)=1&lt;br&gt;
(fib 3)=2&lt;br&gt;
(fib 4)=3&lt;br&gt;
(fib 5)=5&lt;br&gt;
...&lt;br&gt;
(fib 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3601</id>
      <timestamp>2006-03-24T23:42:21Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Link syntax</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Implementation ==

This is a recursive implmentation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

== Test driver ==

This function prints the fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib ~D)=~D~%&quot; start (fib start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib 1)=1&lt;br&gt;
(fib 2)=1&lt;br&gt;
(fib 3)=2&lt;br&gt;
(fib 4)=3&lt;br&gt;
(fib 5)=5&lt;br&gt;
...&lt;br&gt;
(fib 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3638</id>
      <timestamp>2006-03-27T16:11:55Z</timestamp>
      <contributor>
        <username>Ruediger Hanke</username>
        <id>16</id>
      </contributor>
      <minor/>
      <comment>Fix little typo</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Implementation ==

This is a recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

== Test driver ==

This function prints the fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib ~D)=~D~%&quot; start (fib start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib 1)=1&lt;br&gt;
(fib 2)=1&lt;br&gt;
(fib 3)=2&lt;br&gt;
(fib 4)=3&lt;br&gt;
(fib 5)=5&lt;br&gt;
...&lt;br&gt;
(fib 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3641</id>
      <timestamp>2006-03-27T16:38:04Z</timestamp>
      <contributor>
        <username>Ruediger Hanke</username>
        <id>16</id>
      </contributor>
      <comment>Add a faster tail-recursive function and compare efficiency</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Implementation ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock&gt;
* (trace fib)

(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows. Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

We can easily verify that this is much faster:

&lt;codeblock&gt;
* (time (fib 40))

Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
* (time (fib-trec 40))

Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib 1)=1&lt;br&gt;
(fib 2)=1&lt;br&gt;
(fib 3)=2&lt;br&gt;
(fib 4)=3&lt;br&gt;
(fib 5)=5&lt;br&gt;
...&lt;br&gt;
(fib 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3642</id>
      <timestamp>2006-03-27T17:52:34Z</timestamp>
      <contributor>
        <username>Ruediger Hanke</username>
        <id>16</id>
      </contributor>
      <minor/>
      <comment>Capitalize 'fibonacci'</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Implementation ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock&gt;
* (trace fib)

(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows. Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

We can easily verify that this is much faster:

&lt;codeblock&gt;
* (time (fib 40))

Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
* (time (fib-trec 40))

Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib 1)=1&lt;br&gt;
(fib 2)=1&lt;br&gt;
(fib 3)=2&lt;br&gt;
(fib 4)=3&lt;br&gt;
(fib 5)=5&lt;br&gt;
...&lt;br&gt;
(fib 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3643</id>
      <timestamp>2006-03-27T18:43:09Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>Added sections</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock&gt;
* (trace fib)

(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows. 

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3644</id>
      <timestamp>2006-03-27T18:47:53Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Simple Recursive */ +language=&quot;lisp&quot;</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3645</id>
      <timestamp>2006-03-27T18:49:14Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>/* Comparison */ +codeblock</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4734</id>
      <timestamp>2006-05-14T20:05:57Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11011</id>
      <timestamp>2007-10-03T01:00:59Z</timestamp>
      <contributor>
        <ip>74.231.24.2</ip>
      </contributor>
      <text xml:space="preserve">trlapaschida
{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11029</id>
      <timestamp>2007-10-04T04:08:22Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/74.231.24.2|74.231.24.2]] ([[User_talk:74.231.24.2|74.231.24.2]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11074</id>
      <timestamp>2007-10-08T15:35:17Z</timestamp>
      <contributor>
        <ip>85.17.186.161</ip>
      </contributor>
      <text xml:space="preserve">vichisitdoml
{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11091</id>
      <timestamp>2007-10-08T16:56:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11479</id>
      <timestamp>2007-11-06T18:59:07Z</timestamp>
      <contributor>
        <ip>195.242.99.77</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11480</id>
      <timestamp>2007-11-06T20:33:18Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/195.242.99.77|195.242.99.77]] ([[User_talk:195.242.99.77|195.242.99.77]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11842</id>
      <timestamp>2007-12-29T21:04:33Z</timestamp>
      <contributor>
        <ip>210.22.158.132</ip>
      </contributor>
      <comment>racrela</comment>
      <text xml:space="preserve">roleldomtro
{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11891</id>
      <timestamp>2007-12-31T03:04:42Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12016</id>
      <timestamp>2008-01-10T04:36:48Z</timestamp>
      <contributor>
        <ip>210.19.71.60</ip>
      </contributor>
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    </revision>
    <revision>
      <id>12020</id>
      <timestamp>2008-01-10T07:18:42Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12359</id>
      <timestamp>2008-01-29T12:26:38Z</timestamp>
      <contributor>
        <ip>12.181.204.36</ip>
      </contributor>
      <comment>cocaace</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12361</id>
      <timestamp>2008-01-29T14:30:31Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12386</id>
      <timestamp>2008-01-30T18:35:10Z</timestamp>
      <contributor>
        <ip>18.80.0.161</ip>
      </contributor>
      <comment>racgetdeldo</comment>
      <text xml:space="preserve">drontrocac
{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12407</id>
      <timestamp>2008-01-30T19:38:40Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/18.80.0.161|18.80.0.161]] ([[User_talk:18.80.0.161|18.80.0.161]]); changed back to last version by [[User:213.31.11.24|213.31.11.24]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12484</id>
      <timestamp>2008-02-08T02:05:49Z</timestamp>
      <contributor>
        <ip>162.42.207.34</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12571</id>
      <timestamp>2008-02-22T20:15:36Z</timestamp>
      <contributor>
        <ip>99.239.189.29</ip>
      </contributor>
      <comment>Deleted spam from the page</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12610</id>
      <timestamp>2008-02-25T17:47:51Z</timestamp>
      <contributor>
        <ip>61.92.180.7</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12613</id>
      <timestamp>2008-02-25T18:39:52Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12668</id>
      <timestamp>2008-03-02T17:51:35Z</timestamp>
      <contributor>
        <ip>86.96.226.14</ip>
      </contributor>
      <comment>c4ttro</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12670</id>
      <timestamp>2008-03-02T18:08:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12959</id>
      <timestamp>2008-04-02T02:27:08Z</timestamp>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12960</id>
      <timestamp>2008-04-02T03:48:28Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12976</id>
      <timestamp>2008-04-05T15:44:23Z</timestamp>
      <contributor>
        <ip>149.156.22.44</ip>
      </contributor>
      <comment>cabasdar</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12979</id>
      <timestamp>2008-04-05T18:35:33Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13300</id>
      <timestamp>2008-05-10T11:48:25Z</timestamp>
      <contributor>
        <ip>202.154.255.5</ip>
      </contributor>
      <comment>ervardomri</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13302</id>
      <timestamp>2008-05-10T16:45:02Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13330</id>
      <timestamp>2008-05-12T06:57:39Z</timestamp>
      <contributor>
        <ip>192.115.104.90</ip>
      </contributor>
      <comment>c4tlimonvi</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13331</id>
      <timestamp>2008-05-12T07:05:06Z</timestamp>
      <contributor>
        <ip>97.81.111.229</ip>
      </contributor>
      <comment>Removed junk at the top.</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13728</id>
      <timestamp>2008-06-21T03:08:12Z</timestamp>
      <contributor>
        <ip>219.117.198.42</ip>
      </contributor>
      <comment>crolracc4td</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13736</id>
      <timestamp>2008-06-21T11:00:36Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14035</id>
      <timestamp>2008-07-20T02:45:00Z</timestamp>
      <contributor>
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      </contributor>
      <comment>basc4te</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14039</id>
      <timestamp>2008-07-20T12:12:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14177</id>
      <timestamp>2008-08-04T09:24:22Z</timestamp>
      <contributor>
        <ip>205.178.184.113</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14184</id>
      <timestamp>2008-08-04T17:35:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/205.178.184.113|205.178.184.113]] ([[User_talk:205.178.184.113|205.178.184.113]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14348</id>
      <timestamp>2008-08-18T23:45:09Z</timestamp>
      <contributor>
        <ip>195.188.174.221</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14357</id>
      <timestamp>2008-08-19T05:06:19Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14468</id>
      <timestamp>2008-08-24T21:26:54Z</timestamp>
      <contributor>
        <ip>63.79.212.220</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14470</id>
      <timestamp>2008-08-24T22:13:26Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/63.79.212.220|63.79.212.220]] ([[User_talk:63.79.212.220|63.79.212.220]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14495</id>
      <timestamp>2008-08-27T23:19:21Z</timestamp>
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      <comment>colacoco</comment>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14497</id>
      <timestamp>2008-08-28T06:28:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15135</id>
      <timestamp>2008-10-19T19:26:33Z</timestamp>
      <contributor>
        <ip>202.63.101.226</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15136</id>
      <timestamp>2008-10-19T19:36:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15283</id>
      <timestamp>2008-10-25T04:12:27Z</timestamp>
      <contributor>
        <ip>200.64.191.50</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15288</id>
      <timestamp>2008-10-25T10:48:12Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.64.191.50|200.64.191.50]] ([[User_talk:200.64.191.50|200.64.191.50]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

The [http://en.wikipedia.org/wiki/Fibonacci_numbers Fibonacci] numbers in Common Lisp: 

&lt;codeblock language=lisp&gt;
&lt;&lt;fib.lisp&gt;&gt;=
&lt;&lt;fib&gt;&gt;
&lt;&lt;fib-trec&gt;&gt;
&lt;&lt;printfib&gt;&gt;
&lt;&lt;main&gt;&gt;
&lt;/codeblock&gt;

== Simple Recursive ==

This is a simple recursive implementation.

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib&gt;&gt;=
(defun fib (n)
  &quot;Simple recursive Fibonacci number function&quot;
  (if (&lt; n 2)
    n
    (+ (fib (- n 1)) (fib (- n 2)))))
&lt;/codeblock&gt;

This simple implementation takes exponential time to compute a Fibonacci number. When we trace the execution, we can see what's happening:

&lt;codeblock language=&quot;lisp&quot;&gt;
(trace fib)
&lt;/codeblock&gt;

&lt;codeblock&gt;
(FIB)
* (fib 4)
  0: (FIB 4)
    1: (FIB 3)
      2: (FIB 2)
        3: (FIB 1)
        3: FIB returned 1
        3: (FIB 0)
        3: FIB returned 0
      2: FIB returned 1
      2: (FIB 1)
      2: FIB returned 1
    1: FIB returned 2
    1: (FIB 2)
      2: (FIB 1)
      2: FIB returned 1
      2: (FIB 0)
      2: FIB returned 0
    1: FIB returned 1
  0: FIB returned 3
3
&lt;/codeblock&gt;

&lt;code&gt;(FIB 1)&lt;/code&gt; and &lt;code&gt;(FIB 0)&lt;/code&gt; are calculated multiple times. You should have a look at the traces of &lt;code&gt;(FIB 5)&lt;/code&gt; and &lt;code&gt;(FIB 6)&lt;/code&gt; to see how fast it grows.

== Tail-recursive ==

Here is a faster version that uses a local helper function which gets the last two numbers passed and is also tail-recursive:

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;fib-trec&gt;&gt;=
(defun fib-trec (n)
  &quot;Tail-recursive Fibonacci number function&quot;
  (labels ((calc-fib (n a b)
                     (if (= n 0)
                       a
                       (calc-fib (- n 1) b (+ a b)))))
    (calc-fib n 0 1)))
&lt;/codeblock&gt;

== Comparison ==

We can easily verify that this is much faster:

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  17.793 seconds of real time
  17.562605 seconds of user run time
  0.072149 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

&lt;codeblock language=&quot;lisp&quot;&gt;
(time (fib-trec 40))
&lt;/codeblock&gt;

&lt;codeblock&gt;
Evaluation took:
  0.0 seconds of real time
  7.e-6 seconds of user run time
  4.e-6 seconds of system run time
  0 page faults and
  48 bytes consed.
102334155
&lt;/codeblock&gt;

== Test driver ==

This function prints the Fibonacci numbers in the range from ''start'' to ''end'' (inclusive).

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;printfib&gt;&gt;=
(defun printfib (start end)
  (format t &quot;(fib-trec ~D)=~D~%&quot; start (fib-trec start))
  (if (&lt; start end)
    (printfib (+ start 1) end)))
&lt;/codeblock&gt;

When calling ''printfib'', the output should be:&lt;br&gt;
(fib-trec 1)=1&lt;br&gt;
(fib-trec 2)=1&lt;br&gt;
(fib-trec 3)=2&lt;br&gt;
(fib-trec 4)=3&lt;br&gt;
(fib-trec 5)=5&lt;br&gt;
...&lt;br&gt;
(fib-trec 30)=832040

&lt;codeblock language=&quot;lisp&quot;&gt;
&lt;&lt;main&gt;&gt;=
(printfib 1 30)
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lisp]]
[[Category:Programming language:Lisp]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Logo)</title>
    <id>3484</id>
    <revision>
      <id>13674</id>
      <timestamp>2008-06-15T05:46:14Z</timestamp>
      <contributor>
        <ip>63.105.26.46</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
&lt;codeblock language=logo&gt;
to fib :n
  if :n &lt; 2 [output :n]
  output sum fib :n-1 fib :n-2
end
&lt;/codeblock&gt;

==Tail Recursive==
Like Scheme, Logo also optimizes tail recursion.
&lt;codeblock language=logo&gt;
to fib.loop :n :a :b
  if :n = 0 [output :a]
  output fib.loop :n-1 :b :a+:b
end
to fib :n
  output fib.loop :n 0 1
end
&lt;/codeblock&gt;

[[Category:Programming languages|Logo]]
[[Category:Fibonacci numbers|Logo]]</text>
    </revision>
    <revision>
      <id>13678</id>
      <timestamp>2008-06-17T21:22:40Z</timestamp>
      <contributor>
        <ip>71.34.83.43</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
&lt;codeblock language=logo&gt;
to fib :n
  if :n &lt; 2 [output :n]
  output sum fib :n-1 fib :n-2
end
&lt;/codeblock&gt;

==Tail Recursive==
Like Scheme, Logo also optimizes tail recursion.
&lt;codeblock language=logo&gt;
to fib.loop :n :a :b
  if :n = 0 [output :a]
  output fib.loop :n-1 :b :a+:b
end
to fib :n
  output fib.loop :n 0 1
end
&lt;/codeblock&gt;

[[Category:Programming language:Logo]]
[[Category:Fibonacci numbers|Logo]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Lua)</title>
    <id>2196</id>
    <revision>
      <id>5290</id>
      <timestamp>2006-05-28T21:22:44Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>resursive and iterative implementations</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table.

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1}

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>5293</id>
      <timestamp>2006-05-28T21:38:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>section header</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table.

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1}

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6666</id>
      <timestamp>2006-07-11T12:40:39Z</timestamp>
      <contributor>
        <username>Willy on Wheels</username>
        <id>76</id>
      </contributor>
      <minor/>
      <comment>[[Fibonacci numbers (Lua)]] moved to [[Fibonacci numbers (Lua) on Wheels]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table.

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1}

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>6844</id>
      <timestamp>2006-07-11T14:13:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>[[Fibonacci numbers (Lua) on Wheels]] moved to [[Fibonacci numbers (Lua)]]: revert</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table.

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1}

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10235</id>
      <timestamp>2007-05-17T19:56:46Z</timestamp>
      <contributor>
        <ip>139.82.100.35</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster then the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10537</id>
      <timestamp>2007-06-20T10:25:03Z</timestamp>
      <contributor>
        <ip>82.69.44.204</ip>
      </contributor>
      <comment>typo fix</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11013</id>
      <timestamp>2007-10-03T01:03:23Z</timestamp>
      <contributor>
        <ip>61.153.43.246</ip>
      </contributor>
      <text xml:space="preserve">eltacelrac
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11031</id>
      <timestamp>2007-10-04T04:09:16Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.153.43.246|61.153.43.246]] ([[User_talk:61.153.43.246|61.153.43.246]]); changed back to last version by [[User:82.69.44.204|82.69.44.204]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11076</id>
      <timestamp>2007-10-08T15:36:15Z</timestamp>
      <contributor>
        <ip>85.17.186.161</ip>
      </contributor>
      <text xml:space="preserve">acvarbocp
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11093</id>
      <timestamp>2007-10-08T16:56:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11140</id>
      <timestamp>2007-10-12T17:38:50Z</timestamp>
      <contributor>
        <ip>87.101.244.8</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11143</id>
      <timestamp>2007-10-12T17:44:39Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11294</id>
      <timestamp>2007-10-26T10:11:09Z</timestamp>
      <contributor>
        <ip>47.230.0.43</ip>
      </contributor>
      <text xml:space="preserve">monlal
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11307</id>
      <timestamp>2007-10-26T14:42:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11468</id>
      <timestamp>2007-11-05T13:16:44Z</timestamp>
      <contributor>
        <ip>198.7.225.7</ip>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11470</id>
      <timestamp>2007-11-06T04:16:59Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/198.7.225.7|198.7.225.7]] ([[User_talk:198.7.225.7|198.7.225.7]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11559</id>
      <timestamp>2007-11-12T23:10:20Z</timestamp>
      <contributor>
        <ip>202.91.9.6</ip>
      </contributor>
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    </revision>
    <revision>
      <id>11561</id>
      <timestamp>2007-11-13T00:46:20Z</timestamp>
      <contributor>
        <ip>70.73.142.85</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11782</id>
      <timestamp>2007-12-07T23:53:13Z</timestamp>
      <contributor>
        <ip>221.208.174.223</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11785</id>
      <timestamp>2007-12-08T00:44:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11844</id>
      <timestamp>2007-12-29T21:05:34Z</timestamp>
      <contributor>
        <ip>210.22.158.132</ip>
      </contributor>
      <comment>viccletot</comment>
      <text xml:space="preserve">rolelttro
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11893</id>
      <timestamp>2007-12-31T03:04:51Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12388</id>
      <timestamp>2008-01-30T18:37:00Z</timestamp>
      <contributor>
        <ip>200.67.141.214</ip>
      </contributor>
      <comment>nodeltacna</comment>
      <text xml:space="preserve">bocelte
{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12409</id>
      <timestamp>2008-01-30T19:39:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.67.141.214|200.67.141.214]] ([[User_talk:200.67.141.214|200.67.141.214]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12540</id>
      <timestamp>2008-02-21T03:46:12Z</timestamp>
      <contributor>
        <ip>200.68.73.193</ip>
      </contributor>
      <comment>reltro</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12542</id>
      <timestamp>2008-02-21T06:14:25Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.68.73.193|200.68.73.193]] ([[User_talk:200.68.73.193|200.68.73.193]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12808</id>
      <timestamp>2008-03-13T16:17:34Z</timestamp>
      <contributor>
        <ip>222.127.228.24</ip>
      </contributor>
      <comment>chitroczel</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12809</id>
      <timestamp>2008-03-13T16:26:51Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/222.127.228.24|222.127.228.24]] ([[User_talk:222.127.228.24|222.127.228.24]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12842</id>
      <timestamp>2008-03-18T02:10:06Z</timestamp>
      <contributor>
        <ip>200.130.24.47</ip>
      </contributor>
      <comment>eltcochi</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12853</id>
      <timestamp>2008-03-18T06:08:49Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/200.130.24.47|200.130.24.47]] ([[User_talk:200.130.24.47|200.130.24.47]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={1,1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=1,30 do print(fib(n)) end
for n=1,30 do print(fastfib(n)) end
for n=1,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12891</id>
      <timestamp>2008-03-23T05:25:20Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>include fib(0) in memoized versions</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12977</id>
      <timestamp>2008-04-05T18:13:29Z</timestamp>
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      </contributor>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12980</id>
      <timestamp>2008-04-05T18:35:50Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13732</id>
      <timestamp>2008-06-21T11:00:00Z</timestamp>
      <contributor>
        <ip>194.103.241.229</ip>
      </contributor>
      <comment>getnov</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13738</id>
      <timestamp>2008-06-21T11:02:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14036</id>
      <timestamp>2008-07-20T06:43:18Z</timestamp>
      <contributor>
        <ip>150.146.129.51</ip>
      </contributor>
      <comment>dronchivarcn</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14040</id>
      <timestamp>2008-07-20T12:12:28Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14352</id>
      <timestamp>2008-08-19T02:22:49Z</timestamp>
      <contributor>
        <ip>200.182.9.44</ip>
      </contributor>
      <comment>trolotroclib</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14361</id>
      <timestamp>2008-08-19T05:06:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14712</id>
      <timestamp>2008-09-24T03:57:32Z</timestamp>
      <contributor>
        <ip>59.90.167.10</ip>
      </contributor>
      <comment>noc4tdomg</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14713</id>
      <timestamp>2008-09-24T05:24:45Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15141</id>
      <timestamp>2008-10-19T23:11:10Z</timestamp>
      <contributor>
        <ip>122.116.246.167</ip>
      </contributor>
      <comment>elrolcnat</comment>
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{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15146</id>
      <timestamp>2008-10-19T23:20:35Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/122.116.246.167|122.116.246.167]] ([[User_talk:122.116.246.167|122.116.246.167]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

In this article we show two ways of calculating [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Lua_programming_language Lua].

&lt;codeblock language=lua&gt;
&lt;&lt;fib.lua&gt;&gt;=

&lt;&lt;fib&gt;&gt;

&lt;&lt;fastfib&gt;&gt;

&lt;&lt;metafib&gt;&gt;

&lt;&lt;test&gt;&gt;

&lt;/codeblock&gt;

== Recursive ==

This is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.

&lt;codeblock language=lua&gt;
&lt;&lt;fib&gt;&gt;=
function fib(n) return n&lt;2 and n or fib(n-1)+fib(n-2) end
&lt;/codeblock&gt;

== Iterative with table ==

This is a faster, but also somewhat more complicated way to calculate Fibonacci numbers. To avoid recalculation and recursion, all results are stored in a table. This is a common technique called [http://en.wikipedia.org/wiki/Memoization memoization].

&lt;codeblock language=lua&gt;
&lt;&lt;fastfib&gt;&gt;=
function fastfib(n)
	fibs={[0]=0, 1, 1} -- global variable, outside the function

	for i=3,n do
		fibs[i]=fibs[i-1]+fibs[i-2]
	end

	return fibs[n]
end
&lt;/codeblock&gt;

== Metatables ==

The outer table can be avoided by using [http://www.lua.org/pil/13.html metatables] to fuse the external table and the function in a single object.

&lt;codeblock language=lua&gt;
&lt;&lt;metafib&gt;&gt;=
metafib = { [0]=0, 1, 1 }
local mt = {
	__call = function(t, ...)
		local args = {...}
		local n = args[1]
		
		if not t[n] then
			for i = 3, n do
				t[i] = t[i-2] + t[i-1]
			end
		end

		return t[n]
	end
}

setmetatable(metafib, mt) -- now, metafib can be called as if it were a normal function
&lt;/codeblock&gt;

== Test ==

If we run this test code, we can see that the iterative method is significantly faster than the recursive.

&lt;codeblock language=lua&gt;
&lt;&lt;test&gt;&gt;=
for n=0,30 do print(fib(n)) end
for n=0,30 do print(fastfib(n)) end
for n=0,30 do print(metafib(n)) end
&lt;/codeblock&gt;


[[Category:Fibonacci numbers|Lua]]
[[Category:Programming language:Lua]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Mercury)</title>
    <id>1873</id>
    <revision>
      <id>3930</id>
      <timestamp>2006-04-06T23:21:12Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_recursive.mercury&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.
:- import_module int.



fibonacci(N) = F :- ( N = 0 -&gt; F = 0
                    ; N = 1 -&gt; F = 1 
                    ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                    ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.mercury&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
&lt;pre&gt;
mmc --make-int fibonacci
mmc fibotest.m fibonacci
fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==
&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tail_recursive.mercury&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F :- F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F :- ( N = 0 -&gt; F = Result
                                ; F = fibo_tr(N - 1, Result + Next, Next) 
                                ).
&lt;/codeblock&gt;</text>
    </revision>
    <revision>
      <id>3931</id>
      <timestamp>2006-04-06T23:28:07Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.
:- import_module int.



fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m
&lt;pre&gt;
mmc --make-int fibonacci
mmc fibotest.m fibonacci
fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F :- ( N = 0 -&gt; F = Result
                                ; F = fibo_tr(N - 1, Result + Next, Next) 
                                ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3932</id>
      <timestamp>2006-04-06T23:31:34Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ... */

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m
&lt;pre&gt;
mmc --make-int fibonacci
mmc fibotest.m fibonacci
fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3933</id>
      <timestamp>2006-04-06T23:56:06Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury borrows a lot from Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you want to define.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
       :- pred fibonacci( int, int)
*/

/* mode first_param as input '=' result as output is deterministic (has only one solution) */

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
                               ; cond_goal -&gt; then_goal
                               ; else_goal
                              )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
mmc --make-int fibonacci.m
mmc fibotest.m fibonacci
fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3938</id>
      <timestamp>2006-04-07T00:39:56Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury borrows a lot from Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the kind of solutions.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
       :- pred fibonacci( int, int)
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) */

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
                               ; cond_goal -&gt; then_goal
                               ; else_goal
                              )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
mmc --make-int fibonacci.m
mmc fibotest.m fibonacci
fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3939</id>
      <timestamp>2006-04-07T00:44:47Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury borrows a lot from Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the kind of solutions.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
       :- pred fibonacci( int, int)
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
                               ; cond_goal -&gt; then_goal
                               ; else_goal
                              )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3955</id>
      <timestamp>2006-04-07T08:37:22Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the kind of solutions.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3956</id>
      <timestamp>2006-04-07T08:41:59Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of solutions.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3957</id>
      <timestamp>2006-04-07T08:47:41Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of solutions. Then facts and rules.

This module will implement fibonacci /2 as a function, not a predicate

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3961</id>
      <timestamp>2006-04-07T09:13:51Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of solutions. Then facts and rules.

This module will implement fibonacci /2 with the ''function'' pattern equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3965</id>
      <timestamp>2006-04-07T09:17:57Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of solutions. Then facts and rules.

This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m as a module
# compile fibotest.m specifying the modules used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3968</id>
      <timestamp>2006-04-07T10:32:25Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of solutions. Then facts and rules.

This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (--make-int)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3969</id>
      <timestamp>2006-04-07T10:34:31Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of the solutions. Then facts and rules.

This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (--make-int)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive internal function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>3970</id>
      <timestamp>2006-04-07T10:52:57Z</timestamp>
      <contributor>
        <ip>80.28.207.114</ip>
      </contributor>
      <comment>/* Tail Recursive */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the input/ouput modes of the relation that you will define and the cardinality of the solutions. Then facts and rules.

This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io__state, io__state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io__write_string(&quot;fibonacci(7) = &quot;),
	io__write_int(fibonacci(7)),
	io__nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (--make-int)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4013</id>
      <timestamp>2006-04-08T18:49:13Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (--make-int)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc --make-int fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4040</id>
      <timestamp>2006-04-10T00:53:30Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>change switch --make-int  for shorter alias -i</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0
                        ; N = 1 -&gt; F = 1 
                        ; F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   ( N = 0 -&gt; F = Result
                                    ; F = fibo_tr(N - 1, Result + Next, Next) 
                                    ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4052</id>
      <timestamp>2006-04-10T11:08:57Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>cosmetic semicolon placement</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 ;
                          N = 1 -&gt; F = 1 ;

                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=mercury&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=mercury&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result ;

        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4517</id>
      <timestamp>2006-05-09T16:43:17Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>disjunction separators to the left side</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, equivalent to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4520</id>
      <timestamp>2006-05-09T17:17:20Z</timestamp>
      <contributor>
        <username>Griba2010</username>
        <id>52</id>
      </contributor>
      <minor/>
      <comment>/* Recursion */  text correction</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>4735</id>
      <timestamp>2006-05-14T20:06:17Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <minor/>
      <comment>subject-area cat sorting key</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>7693</id>
      <timestamp>2006-09-26T15:11:08Z</timestamp>
      <contributor>
        <ip>83.50.166.47</ip>
      </contributor>
      <comment>/* Tail Recursive */</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11137</id>
      <timestamp>2007-10-12T07:31:14Z</timestamp>
      <contributor>
        <ip>199.245.188.252</ip>
      </contributor>
      <text xml:space="preserve">codelrol
{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11139</id>
      <timestamp>2007-10-12T14:53:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11857</id>
      <timestamp>2007-12-29T21:23:44Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>caerchiacelp</comment>
      <text xml:space="preserve">mondomtro
{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11906</id>
      <timestamp>2007-12-31T03:08:15Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12037</id>
      <timestamp>2008-01-11T10:05:37Z</timestamp>
      <contributor>
        <ip>211.5.165.122</ip>
      </contributor>
      <comment>vielel</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12038</id>
      <timestamp>2008-01-11T10:10:42Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12144</id>
      <timestamp>2008-01-22T18:36:02Z</timestamp>
      <contributor>
        <ip>211.157.121.190</ip>
      </contributor>
      <comment>zelacelc</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12145</id>
      <timestamp>2008-01-22T18:48:25Z</timestamp>
      <contributor>
        <ip>72.3.131.54</ip>
      </contributor>
      <comment>ermoncna</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12146</id>
      <timestamp>2008-01-22T19:51:33Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12395</id>
      <timestamp>2008-01-30T18:52:26Z</timestamp>
      <contributor>
        <ip>202.86.197.4</ip>
      </contributor>
      <comment>cnanorol</comment>
      <text xml:space="preserve">varsitcab
{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12416</id>
      <timestamp>2008-01-30T19:39:35Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/202.86.197.4|202.86.197.4]] ([[User_talk:202.86.197.4|202.86.197.4]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12453</id>
      <timestamp>2008-02-01T02:18:20Z</timestamp>
      <contributor>
        <ip>64.56.106.137</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12458</id>
      <timestamp>2008-02-01T07:02:43Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12549</id>
      <timestamp>2008-02-21T11:28:18Z</timestamp>
      <contributor>
        <ip>219.136.230.60</ip>
      </contributor>
      <comment>taacelrolr</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12550</id>
      <timestamp>2008-02-21T12:14:44Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12936</id>
      <timestamp>2008-03-30T08:10:24Z</timestamp>
      <contributor>
        <ip>202.28.27.4</ip>
      </contributor>
      <comment>taletotr</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12939</id>
      <timestamp>2008-03-30T12:00:20Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13252</id>
      <timestamp>2008-05-01T12:01:58Z</timestamp>
      <contributor>
        <ip>147.102.5.3</ip>
      </contributor>
      <comment>boalmonoloel</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13255</id>
      <timestamp>2008-05-01T14:03:02Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>rv spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13372</id>
      <timestamp>2008-05-17T22:40:55Z</timestamp>
      <contributor>
        <ip>216.35.68.197</ip>
      </contributor>
      <comment>monliolozel</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13375</id>
      <timestamp>2008-05-18T01:43:18Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>13739</id>
      <timestamp>2008-06-21T14:37:39Z</timestamp>
      <contributor>
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    </revision>
    <revision>
      <id>13740</id>
      <timestamp>2008-06-21T17:21:26Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14155</id>
      <timestamp>2008-07-31T23:14:21Z</timestamp>
      <contributor>
        <ip>130.160.63.110</ip>
      </contributor>
      <comment>talipasouri</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14158</id>
      <timestamp>2008-08-01T05:54:06Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/130.160.63.110|130.160.63.110]] ([[User_talk:130.160.63.110|130.160.63.110]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14904</id>
      <timestamp>2008-10-09T10:30:01Z</timestamp>
      <contributor>
        <ip>61.186.95.141</ip>
      </contributor>
      <comment>getortaoulae</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>14911</id>
      <timestamp>2008-10-09T12:02:23Z</timestamp>
      <contributor>
        <username>Ce</username>
        <id>132</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/61.186.95.141|61.186.95.141]] ([[User_talk:61.186.95.141|61.186.95.141]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15355</id>
      <timestamp>2008-10-29T18:56:22Z</timestamp>
      <contributor>
        <ip>84.38.65.64</ip>
      </contributor>
      <comment>deldomca</comment>
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{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15357</id>
      <timestamp>2008-10-29T21:02:06Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

==Recursion==
The recursive definition can be translated directly into Mercury as follows:  

Mercury is descendant of Prolog.
 
Here you specify relations. Then you specify the modes of in/out combinations of the relation parameters that you will implement and the determinism of the solutions. Then facts and rules.

The determinism possibilities are the following:
* have exactly one solution, then that mode is deterministic (det);
* either have no solutions or have one solution, then that mode is semideterministic (semidet);
* have at least one solution but may have more, then that mode is multisolution (multi);
* have zero or more solutions, then that mode is nondeterministic (nondet);
* fail without producing a solution, then that mode has a determinism of failure. 
* If no possible calls to a particular mode of a predicate or function can return to the caller, then that mode has a determinism of erroneous.


This module will implement fibonacci /2 with the ''function'' pattern, similar to the ''predicate'' pattern but with a more familiar layout.

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci.m&gt;&gt;=
:- module fibonacci.

:- interface.

:- func fibonacci(int) = int.

/* an alternative way, using predicates would be
*       :- pred fibonacci( int, int).
*/

/* mode first_param as input '=' result as output is deterministic (has one solution) 
*/

:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.

/* fibonacci(N) = F  implies ( cond_goal -&gt; then_goal
*                             ; cond_goal -&gt; then_goal
*                             ; else_goal
*                             )
*/

fibonacci(N) = F   :-   ( N = 0 -&gt; F = 0 
                        ;
                          N = 1 -&gt; F = 1 
                        ;
                          /* else */
                          F = fibonacci(N - 1) + fibonacci(N - 2) 
                        ).
&lt;/codeblock&gt;

Test module:

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibotest.m&gt;&gt;=

:- module fibotest.

:- interface.

:- import_module io.

:- pred main(io.state, io.state).
:- mode main(di, uo) is det.

:- implementation.

:- import_module fibonacci.

main --&gt;
	io.write_string(&quot;fibonacci(7) = &quot;),
	io.write_int(fibonacci(7)),
	io.nl.
&lt;/codeblock&gt;

Compilation and run
# compile fibonacci.m exporting interfaces (-i)
# compile fibotest.m specifying the interfaces used (without extension)

&lt;pre&gt;
&gt;mmc -i fibonacci.m
&gt;mmc fibotest.m fibonacci
&gt;
&gt;fibotest

&gt;fibonacci(7) = 13
&gt;
&lt;/pre&gt;

==Tail Recursive==

&lt;codeblock language=&quot;mercury&quot;&gt;
&lt;&lt;fibonacci_tr.m&gt;&gt;=
:- module fibonacci_tr.

:- interface.

:- func fibonacci(int) = int.
:- mode fibonacci(in) = out is det.

:- implementation.

:- import_module int.
 
fibonacci(N) = F  :-   F = fibo_tr( N, 1, 0). 

/* tail recursive private function */

:- func fibo_tr(int, int, int) = int.
:- mode fibo_tr(in, in, in) = out is det.

fibo_tr(N, Next, Result) = F   :-   

      ( N = 0 -&gt; F = Result 

      ;
        /* else */
        F = fibo_tr(N - 1, Result + Next, Next) 
      ).
&lt;/codeblock&gt;
[[Category:Fibonacci numbers|Mercury]]
[[Category:Programming language:Mercury]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (OCaml)</title>
    <id>2932</id>
    <revision>
      <id>8673</id>
      <timestamp>2007-01-24T21:41:57Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <comment>Initial article entry</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
  let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
  | 0 -&gt; a
  | 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
  | k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
  | _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

&lt;codeblock langage=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 

open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n&lt;/codeblock&gt;
  

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock langage=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8674</id>
      <timestamp>2007-01-24T21:44:50Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <minor/>
      <comment>Fixed code formatting issues</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function
&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock langage=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock langage=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8675</id>
      <timestamp>2007-01-24T21:46:20Z</timestamp>
      <contributor>
        <username>WDN</username>
        <id>111</id>
      </contributor>
      <minor/>
      <comment>More code formatting tweaks</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock langage=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock langage=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock langage=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>8677</id>
      <timestamp>2007-01-25T19:50:26Z</timestamp>
      <contributor>
        <username>Chris Rathman</username>
        <id>133</id>
      </contributor>
      <minor/>
      <comment>fix spelling of &quot;language&quot; to get syntax highlighting</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;ackermann&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>10434</id>
      <timestamp>2007-06-03T01:01:44Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>/* A Recursive Solution */ s/ackermann/fibonacci/</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11018</id>
      <timestamp>2007-10-03T01:05:54Z</timestamp>
      <contributor>
        <ip>88.198.25.14</ip>
      </contributor>
      <text xml:space="preserve">ornoliz
{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11036</id>
      <timestamp>2007-10-04T04:10:58Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/88.198.25.14|88.198.25.14]] ([[User_talk:88.198.25.14|88.198.25.14]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11193</id>
      <timestamp>2007-10-13T04:15:18Z</timestamp>
      <contributor>
        <ip>212.72.56.31</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11208</id>
      <timestamp>2007-10-13T07:56:30Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11336</id>
      <timestamp>2007-10-27T16:26:58Z</timestamp>
      <contributor>
        <ip>190.8.194.30</ip>
      </contributor>
      <text xml:space="preserve">tadelsi
{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly di</text>
    </revision>
    <revision>
      <id>11338</id>
      <timestamp>2007-10-27T16:29:31Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/190.8.194.30|190.8.194.30]] ([[User_talk:190.8.194.30|190.8.194.30]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11849</id>
      <timestamp>2007-12-29T21:15:47Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>covarcar</comment>
      <text xml:space="preserve">tarole
{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11898</id>
      <timestamp>2007-12-31T03:05:59Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12018</id>
      <timestamp>2008-01-10T05:45:19Z</timestamp>
      <contributor>
        <ip>218.84.25.250</ip>
      </contributor>
      <comment>eltrolchira</comment>
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{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12022</id>
      <timestamp>2008-01-10T07:18:49Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12110</id>
      <timestamp>2008-01-14T10:24:40Z</timestamp>
      <contributor>
        <ip>70.86.151.66</ip>
      </contributor>
      <comment>bocouer</comment>
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{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12111</id>
      <timestamp>2008-01-14T10:30:09Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12284</id>
      <timestamp>2008-01-23T13:06:28Z</timestamp>
      <contributor>
        <ip>193.85.202.161</ip>
      </contributor>
      <comment>troccaalda</comment>
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{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12285</id>
      <timestamp>2008-01-23T14:53:13Z</timestamp>
      <contributor>
        <ip>213.31.11.24</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12493</id>
      <timestamp>2008-02-16T14:54:30Z</timestamp>
      <contributor>
        <ip>217.9.231.214</ip>
      </contributor>
      <comment>chiacelvar</comment>
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{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12494</id>
      <timestamp>2008-02-16T15:40:27Z</timestamp>
      <contributor>
        <ip>70.162.220.11</ip>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>15728</id>
      <timestamp>2009-01-03T13:38:18Z</timestamp>
      <contributor>
        <ip>212.62.97.23</ip>
      </contributor>
      <comment>field_other</comment>
      <text xml:space="preserve">http://www.message_varrodomo.com/</text>
    </revision>
    <revision>
      <id>15739</id>
      <timestamp>2009-01-03T19:26:05Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/212.62.97.23|212.62.97.23]] ([[User_talk:212.62.97.23|212.62.97.23]]); changed back to last version by [[User:70.162.220.11|70.162.220.11]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>17076</id>
      <timestamp>2011-02-22T21:18:09Z</timestamp>
      <contributor>
        <username>Gcardoso</username>
        <id>2217</id>
      </contributor>
      <comment>A tail recursive solution</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

This page explains how to implement '''Fibonacci numbers''' in OCaml. 
For this example, we will be using OCaml's [http://caml.inria.fr/pub/docs/manual-ocaml/manual015.html#@manual.kwd41 &quot;function&quot; syntax] for defining functions.  We choose this style as it most closely resembles the problem definition.

==A Recursive Solution==
A simple recursive solution can be constructed in OCaml in a way that directly mirrors the mathematical definition of the function.  We begin the code for this solution by defining a recursive value named &lt;code&gt;fibonacci&lt;/code&gt; and indicate that this value will be a function
&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec fibonacci = function&lt;/codeblock&gt;

We then use pattern matching on the function's parameter to handle the three cases given in the definition of the Fibonacci numbers.  The first two cases we handle are the base cases of the recursion, when n = 0 or n = 1.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
| 0 -&gt; 0
| 1 -&gt; 1&lt;/codeblock&gt;

In the third case, when n &gt; 1, a pair of recursive calls are made.  The first call determines the F(n-1), and the second determines F(n-2), adding the two values to compute the F(n), the nth Fibonacci number.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| n when n &gt; 1 -&gt; fibonacci (n-1) + fibonacci (n-2)&lt;/codeblock&gt;

Finally, we add a final case to our pattern matching to catch all other cases.  This is done for two reasons.  First, Fibonacci numbers are only defined for non-negative integers.  While that may be fine in math, when it comes to programming, one should be aware that invalid inputs may be used.  These cases should be caught and handled.  Here we raise an exception with an informative message that can be handled by the caller of &lt;code&gt;fibonacci&lt;/code&gt;.  Secondly, when using the &lt;code&gt;when&lt;/code&gt; style guards in pattern matching, OCaml may be unable to determine if all possible cases are covered, and it issues a warning.  Using the universal match pattern, _, we can catch any cases not covered by the above patterns (in this case anything involving negative integers).

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=  
| _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
&lt;/codeblock&gt;

== A Tail Recursive Solution ==
&lt;codeblock language=ocaml&gt;
let fib n = 
  let rec aux n b a = 
  if n &lt;= 0 then a
  else aux (n-1) (a+b) b in
aux n 1 0
&lt;/codeblock&gt;
Will return &lt;code&gt;0&lt;/code&gt; for &lt;code&gt;n &lt;= 0&lt;/code&gt;

==An Iterative Solution==
Unfortunately, the recursive solution shown above is a rather inefficient one, doubling the number of recursive calls for each successive value of n, thus requiring 2**n total function calls.  A much more efficient iterative solution can be constructed, requiring just n recursive calls, at the expense of a bit of clarity.

For this solution, we will start with a recursive function definition that has a slightly different interface than the recursive solution above:

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
let rec i_fib a b = function&lt;/codeblock&gt;
  
Here, the parameters a and b represent the ith and i+1st Fibonacci numbers, and the third parameter represents how far we are from our goal.  That is, if our goal is to compute F(n), and we have passed in F(i) as the parameter a, then the third parameter will be k = n-i.  

If k = 0 or 1, then we can simply return a or b respectively, as they represent F(i) and F(i+1).
  
&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| 0 -&gt; a
| 1 -&gt; b&lt;/codeblock&gt;
  
If k is greater than 1, however, we simply move one step further in the iteration by computing Fibonacci number i+2 = a + b, and making a recursive call with parameters F(i+1), F(i+2), and (n-(i+1))=k-1.  And finally we add our case to catch any invalid inputs.

&lt;codeblock language=ocaml&gt;
&lt;&lt;i_fib&gt;&gt;=  
| k when k &gt; 1 -&gt; i_fib b (a+b) (k-1)
| _  -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)&lt;/codeblock&gt;


Now, it should be easy to see that this definition will correctly compute the nth Fibonacci number when the initial arguments are 0 (F(0)), 1 (F(1)), and n.  Unfortunately, this function requires the caller to pass in more arguments to compute the nth Fibonacci number than with the recursive solution.  Additionally, if incorrect values are passed in for a and b, the returned value will not be equal to the nth Fibonacci number.  In order to aleviate both of these problems, we will use i_fib as a function local to a wrapper function that presents the same interface to the caller as the recursive solution does..

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let iterative_fib n =
  &lt;&lt;i_fib&gt;&gt;
  in
  i_fib 0 1 n

&lt;/codeblock&gt;
  
==Stream Based Solutions==

One can also use the streams of OCaml to build the Fibonacci numbers in a lazy fashion.  This is host easily done with the [http://en.wikipedia.org/wiki/Camlp4 camlp4] stream building syntax.  To enable the use of this syntax in the OCaml toplevel environment, first enter the following directives:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;camlp4o.cma&quot;;; 
#load &quot;pa_extend.cmo&quot;;;
&lt;/codeblock&gt;


Now the Fibonacci sequence can be defined as a function that takes in the ith and i+1st Fibonacci numbers and returns an infinite stream of Fibonacci numbers starting from i.

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec f a b = [&lt; 'a; f b (a+b) &gt;]
&lt;/codeblock&gt;

One can see how this works by introducing the &lt;code&gt;next&lt;/code&gt; parser, that strips the head off of the specified stream and returns it:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let next = parser [&lt; 'x &gt;] -&gt; x
&lt;/codeblock&gt;

Some examples of the arbitrary precision variants are:

&lt;codeblock language=ocaml&gt;
# let fibs = f 0 1;;
val fibs : int Stream.t = &lt;abstr&gt;
# next fibs;;
- : int = 0
# next fibs;;
- : int = 1
# next fibs;;
- : int = 1
# next fibs;;
- : int = 2
# next fibs;;
- : int = 3
# next fibs;;
- : int = 5
# next fibs;;
- : int = 8
&lt;/codeblock&gt;

==Arbitrary Precision==
One minor problem with all of these solutions is that they are defined using the native int type in OCaml which has an upper limit of (2**30) - 1 on 32 bit systems, and (2**62) - 1 on 64 bit systems.  Because of this, the results will be incorrect for larger values of n (e.g. n &gt; 44 on 32 bit systems).  This can be fixed by using OCaml's arbitrary precision integer [http://caml.inria.fr/pub/docs/manual-ocaml/manual036.html Big_int module].  To use this module in the toplevel, enter the following directive:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
#load &quot;nums.cma&quot;;; 
open Big_int;;
&lt;/codeblock&gt;

Now we can rewrite the examples using the Big_int module:

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let bfib n =
  let rec bfib_i a b = function
  | 0 -&gt; a
  | 1 -&gt; b
  | n when n &gt; 1 -&gt;  bfib_i b (add_big_int a b) (n-1)
  | _ -&gt; raise (Invalid_argument &quot;Fibonacci numbers are only defined over the non-negative integers&quot;)
  in
  bfib_i zero_big_int unit_big_int n
&lt;/codeblock&gt;
  

&lt;codeblock language=ocaml&gt;
&lt;&lt;fibonacci.ml&gt;&gt;=
let rec big_f a b = [&lt; 'a; big_f b (add_big_int a b) &gt;]
let big_fibs = big_f zero_big_int unit_big_int
let big_next = parser [&lt; 'x &gt;] -&gt; string_of_big_int x&lt;/codeblock&gt;

&lt;codeblock language=ocaml&gt;
# iterative_fib 44;;
- : int = 701408733
# string_of_big_int (bfib 44);;
- : string = &quot;701408733&quot;
# iterative_fib 45;;
- : int = -1012580478
# string_of_big_int (bfib 45);;
- : string = &quot;1134903170&quot;

# big_next big_fibs;;
- : string = &quot;0&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;1&quot;
# big_next big_fibs;;
- : string = &quot;2&quot;
# big_next big_fibs;;
- : string = &quot;3&quot;
# big_next big_fibs;;
- : string = &quot;5&quot;
# big_next big_fibs;;
- : string = &quot;8&quot;
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|OCaml]]
[[Category:Programming language:OCaml]]
[[Category:Environment:Portable]]</text>
    </revision>
  </page>
  <page>
    <title>Fibonacci numbers (Oz)</title>
    <id>2258</id>
    <revision>
      <id>5776</id>
      <timestamp>2006-06-03T04:10:11Z</timestamp>
      <contributor>
        <username>Allan McInnes</username>
        <id>2</id>
      </contributor>
      <comment>creation</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11019</id>
      <timestamp>2007-10-03T01:06:10Z</timestamp>
      <contributor>
        <ip>88.198.25.14</ip>
      </contributor>
      <text xml:space="preserve">c4tviou
{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11037</id>
      <timestamp>2007-10-04T04:11:19Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/88.198.25.14|88.198.25.14]] ([[User_talk:88.198.25.14|88.198.25.14]]); changed back to last version by [[User:Allan McInnes|Allan McInnes]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11167</id>
      <timestamp>2007-10-12T21:02:18Z</timestamp>
      <contributor>
        <ip>87.101.244.6</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11171</id>
      <timestamp>2007-10-12T21:52:27Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11249</id>
      <timestamp>2007-10-25T09:05:58Z</timestamp>
      <contributor>
        <ip>202.70.201.34</ip>
      </contributor>
      <text xml:space="preserve">bovitac4tba
{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11263</id>
      <timestamp>2007-10-25T20:02:41Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11469</id>
      <timestamp>2007-11-05T16:45:25Z</timestamp>
      <contributor>
        <ip>219.87.178.116</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11471</id>
      <timestamp>2007-11-06T04:20:26Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/219.87.178.116|219.87.178.116]] ([[User_talk:219.87.178.116|219.87.178.116]]); changed back to last version by [[User:Ahy1|Ahy1]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11573</id>
      <timestamp>2007-11-14T23:43:47Z</timestamp>
      <contributor>
        <ip>213.192.59.78</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11574</id>
      <timestamp>2007-11-15T00:04:04Z</timestamp>
      <contributor>
        <username>Derek Ross</username>
        <id>9</id>
      </contributor>
      <minor/>
      <comment>Reverted edits by [[Special:Contributions/213.192.59.78|213.192.59.78]] ([[User_talk:213.192.59.78|213.192.59.78]]); changed back to last version by [[User:Derek Ross|Derek Ross]]</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11850</id>
      <timestamp>2007-12-29T21:17:09Z</timestamp>
      <contributor>
        <ip>63.238.216.253</ip>
      </contributor>
      <comment>altrrolgettr</comment>
      <text xml:space="preserve">acletor
{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>11899</id>
      <timestamp>2007-12-31T03:06:03Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert vandalism</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12323</id>
      <timestamp>2008-01-27T15:42:41Z</timestamp>
      <contributor>
        <ip>212.142.143.116</ip>
      </contributor>
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{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12325</id>
      <timestamp>2008-01-27T15:54:29Z</timestamp>
      <contributor>
        <username>Ahy1</username>
        <id>20</id>
      </contributor>
      <comment>revert spam</comment>
      <text xml:space="preserve">{{Category:Fibonacci numbers}}

== Implementation ==
We describe several different implementations for calculating the [http://en.wikipedia.org/wiki/Fibonacci_numbers fibonacci] numbers in [http://en.wikipedia.org/wiki/Oz_programming_language Oz]:

&lt;codeblock language=oz&gt;
&lt;&lt;Fib.oz&gt;&gt;=
functor
import
   System
   Application
define
   &lt;&lt;recursive fib&gt;&gt;
   &lt;&lt;memoized fib&gt;&gt;
   &lt;&lt;iterative fib&gt;&gt;
   &lt;&lt;testdriver&gt;&gt;
end
&lt;/codeblock&gt;

== Recursive ==
Here is a very simple recursive implementation. This will become slow on big numbers, because the numbers are recalculated for each recursion.
&lt;codeblock language=oz&gt;
&lt;&lt;recursive fib&gt;&gt;=
fun {RecursiveFib N}
   if N &lt; 2 then N else {RecursiveFib N - 1} + {RecursiveFib N - 2} end
end
&lt;/codeblock&gt;

== Memoized recursion ==
Although the recursive implementation given above is elegant and close to the mathematical definition, it is not very practical. Calculating the ''n''th fibonacci number requires calculating two smaller fibonacci numbers, which in turn require two additional recursive calls each, and so on until all branches reach 1. As a consequence, the time required to calculate the fibonacci numbers is exponential in ''n'' (it is about &amp;Phi;&lt;sup&gt;''n''&lt;/sup&gt;, where &amp;Phi; is the golden ratio). To remedy this, we can employ [http://en.wikipedia.org/wiki/Memoization memoization] to cache previous computations:

&lt;codeblock language=oz&gt;
&lt;&lt;memoized fib&gt;&gt;=
Memo = {NewDictionary}
fun {MemoizedFib N}
   if {Dictionary.member Memo N}
   then {Dictionary.get Memo N}
   else
      FibN
   in
      if N &lt; 2 then FibN = N else FibN = {MemoizedFib N - 1} + {MemoizedFib N - 2} end
      {Dictionary.put Memo N FibN}
      FibN
   end
end
&lt;/codeblock&gt;

This memoized recursive implementation makes use of Oz's mutable &lt;code&gt;Dictionary&lt;/code&gt; datatype to store and retrieve previously computed values.

== Iteration ==
Another alternative for fast computation of fibonacci numbers is a simple linear-time iterative approach which calculates each fibonacci number successively. Although Oz supports mutable variables and &lt;code&gt;for&lt;/code&gt;-loops, we have chosen here to implement a compact iterative routine that performs a tail-recursive, accumulative calculation:
&lt;codeblock language=oz&gt;
&lt;&lt;iterative fib&gt;&gt;=
fun {IterativeFib N}
   fun {Fib N F1 F2}
     if N &lt; 1 then F1 else {Fib (N - 1) F2 (F1 + F2)} end
   end
in
   {Fib N 0 1}
end
&lt;/codeblock&gt;

== Test driver ==
The test driver procedure &lt;code&gt;runFib&lt;/code&gt; computes and prints the fibonacci numbers from ''n'' = 0 up to ''n'' = 30.  
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
proc {RunFib F}
   for X in 0..30 do
      {System.showInfo &quot;{&quot; # {System.printName F} # &quot; &quot; # X # &quot;} = &quot; # {F X}}
   end
end
&lt;/codeblock&gt;

We apply &lt;code&gt;RunFib&lt;/code&gt; to each of the implementations described above, and then exit.
&lt;codeblock language=oz&gt;
&lt;&lt;testdriver&gt;&gt;=
{RunFib RecursiveFib}
{RunFib MemoizedFib}
{RunFib IterativeFib}
{Application.exit 0}
&lt;/codeblock&gt;

[[Category:Fibonacci numbers|Oz]]
[[Category:Programming language:Oz]]
[[Category:Environment:Portable]]</text>
    </revision>
    <revision>
      <id>12452</id>
      <timestamp>2008-02-01T02:09:35Z</timestamp>
      <contributor>
        <ip>64.56.106.137</ip>
      </contributor>
      <comment>bocalizelbo</comment>
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